From 537f235d211bae4130c1a1a5339152e0b8d47562 Mon Sep 17 00:00:00 2001
From: MACarlsen <44873424+MACarlsen@users.noreply.github.com>
Date: Tue, 12 May 2026 21:27:24 +0200
Subject: [PATCH 01/17] Add files via upload

---
 ...gaussian_splatting_diffraction_patterns.png | Bin 0 -> 109669 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 docs/_static/gaussian_splatting_diffraction_patterns.png

diff --git a/docs/_static/gaussian_splatting_diffraction_patterns.png b/docs/_static/gaussian_splatting_diffraction_patterns.png
new file mode 100644
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HcmV?d00001


From c146b781a87b831118c52237cfbb2a870aba1506 Mon Sep 17 00:00:00 2001
From: MACarlsen <44873424+MACarlsen@users.noreply.github.com>
Date: Tue, 12 May 2026 21:29:36 +0200
Subject: [PATCH 02/17] Update README.rst

---
 README.rst | 300 +----------------------------------------------------
 1 file changed, 2 insertions(+), 298 deletions(-)

diff --git a/README.rst b/README.rst
index 30031e1..6e51d8f 100644
--- a/README.rst
+++ b/README.rst
@@ -1,299 +1,3 @@
-.. image:: https://github.com/FABLE-3DXRD/xrd_simulator/blob/main/docs/source/images/logo.png?raw=true
+.. image:: https://github.com/MACarlsen/xrd_simulator_gs/blob/main/docs/_static/gaussian_splatting_diffraction_patterns.png
 
-.. image:: https://img.shields.io/pypi/pyversions/xrd-simulator.svg?
-	:target: https://pypi.org/project/xrd-simulator/
-
-.. image:: https://github.com/FABLE-3DXRD/xrd_simulator/actions/workflows/python-package-run-tests-linux-py313.yml/badge.svg?
-	:target: https://github.com/FABLE-3DXRD/xrd_simulator/actions/workflows/python-package-run-tests-linux-py313.yml/badge.svg
-
-.. image:: https://github.com/FABLE-3DXRD/xrd_simulator/actions/workflows/pages/pages-build-deployment/badge.svg?
-	:target: https://github.com/FABLE-3DXRD/xrd_simulator/actions/workflows/pages/pages-build-deployment/
-
-.. image:: https://badge.fury.io/py/xrd-simulator.svg?
-	:target: https://pypi.org/project/xrd-simulator/
-
-.. image:: https://anaconda.org/conda-forge/vsc-install/badges/platforms.svg?
-	:target: https://anaconda.org/conda-forge/xrd_simulator/
-
-.. image:: https://anaconda.org/conda-forge/xrd_simulator/badges/latest_release_relative_date.svg?
-	:target: https://anaconda.org/conda-forge/xrd_simulator/
-
-===================================================================================================
-Simulate X-ray Diffraction from Polycrystals in 3D.
-===================================================================================================
-.. image:: https://img.shields.io/badge/stability-alpha-f4d03f.svg?
-	:target: https://github.com/FABLE-3DXRD/xrd_simulator/
-
-
-The **X**-**R** ay **D** iffraction **SIMULATOR** package defines polycrystals as a mesh of tetrahedral single crystals
-and simulates diffraction as collected by a 2D discretized detector array while the sample is rocked
-around an arbitrary rotation axis. The full journal paper associated to the release of this code can be found here:
-
-*xrd_simulator: 3D X-ray diffraction simulation software supporting 3D polycrystalline microstructure morphology descriptions
-Henningsson, A. & Hall, S. A. (2023). J. Appl. Cryst. 56, 282-292.*
-`https://doi.org/10.1107/S1600576722011001`_
-
-``xrd_simulator`` was originally developed with the hope to answer questions about measurement optimization in
-scanning x-ray diffraction experiments. However, ``xrd_simulator`` can simulate a wide range of experimental
-diffraction setups. The essential idea is that the sample and beam topology can be arbitrarily specified,
-and their interaction simulated as the sample is rocked. This means that standard "non-powder" experiments
-such as `scanning-3dxrd`_ and full-field `3dxrd`_ (or HEDM if you like) can be simulated as well as more advanced
-measurement sequences such as helical scans for instance. It is also possible to simulate `powder like`_
-scenarios using orientation density functions as input.
-
-===================================================================================================
-Introduction
-===================================================================================================
-Before reading all the boring documentation (`which is hosted here`_) let's dive into some end to end
-examples to get us started on a good flavour.
-
-The ``xrd_simulator`` is built around four python objects which reflect a diffraction experiment:
-
-   * A **beam** of x-rays (using the ``xrd_simulator.beam`` module)
-   * A 2D area **detector** (using the ``xrd_simulator.detector`` module)
-   * A 3D **polycrystal** sample (using the ``xrd_simulator.polycrystal`` module)
-   * A rigid body sample **motion** (using the ``xrd_simulator.motion`` module)
-
-Once these objects are defined it is possible to let the **detector** collect scattering of the **polycrystal**
-as the sample undergoes the prescribed rigid body **motion** while being illuminated by the xray **beam**.
-
-Let's go ahead and build ourselves some x-rays:
-
-   .. code:: python
-
-      import numpy as np
-      from xrd_simulator.beam import Beam
-
-      # The beam of xrays is represented as a convex polyhedron
-      # We specify the vertices in a numpy array.
-      beam_vertices = np.array(
-         [
-            [-1e6, -500.0, -500.0],
-            [-1e6, 500.0, -500.0],
-            [-1e6, 500.0, 500.0],
-            [-1e6, -500.0, 500.0],
-            [1e6, -500.0, -500.0],
-            [1e6, 500.0, -500.0],
-            [1e6, 500.0, 500.0],
-            [1e6, -500.0, 500.0],
-         ]
-      )
-
-      beam = Beam(
-         beam_vertices,
-         xray_propagation_direction=np.array([1.0, 0.0, 0.0]),
-         wavelength=0.28523,
-         polarization_vector=np.array([0.0, 1.0, 0.0]),
-      )
-
-We will also need to define a detector:
-
-   .. code:: python
-
-      from xrd_simulator.detector import Detector
-
-      # The detector plane is defined by it's corner coordinates det_corner_0,det_corner_1,det_corner_2
-      detector = Detector(
-         det_corner_0=np.array([142938.3, -38400.0, -38400.0]),
-         det_corner_1=np.array([142938.3, 38400.0, -38400.0]),
-         det_corner_2=np.array([142938.3, -38400.0, 38400.0]),
-         pixel_size=(55.0, 55.0),
-         gaussian_sigma=1.0,
-         max_gaussian_kernel_radius=5,
-      )
-
-Next we go ahead and produce a sample, to do this we need to first define a mesh that
-describes the topology of the sample, in this example we make the sample shaped as a ball:
-
-   .. code:: python
-
-      from xrd_simulator.mesh import TetraMesh
-
-      # xrd_simulator supports several ways to generate a mesh, here we
-      # generate meshed solid sphere using a level set.
-      mesh = TetraMesh.generate_mesh_from_levelset(
-         level_set=lambda x: np.linalg.norm(x) - 768.0,
-         bounding_radius=769.0,
-         max_cell_circumradius=550.0,
-      )
-
-Every element in the sample is composed of some material, or "phase", we define the present phases
-in a list of ``xrd_simulator.phase.Phase`` objects, in this example only a single phase is present:
-
-   .. code:: python
-
-      from xrd_simulator.phase import Phase
-
-      quartz = Phase(
-         unit_cell=[4.926, 4.926, 5.4189, 90.0, 90.0, 120.0],
-         sgname="P3221",  # (Quartz)
-         path_to_cif_file=None,  # phases can be defined from crystalographic information files
-      )
-
-The polycrystal sample can now be created. In this example the crystal elements have random orientations
-and the strain is uniformly zero in the sample:
-
-   .. code:: python
-
-      from scipy.spatial.transform import Rotation as R
-      from xrd_simulator.polycrystal import Polycrystal
-
-      orientation = R.random(mesh.number_of_elements).as_matrix()
-      # element_phase_map assigns each mesh element to a phase (0 = first phase)
-      element_phase_map = np.zeros(mesh.number_of_elements, dtype=int)
-      polycrystal = Polycrystal(
-         mesh,
-         orientation,
-         strain=np.zeros((3, 3)),
-         phases=quartz,
-         element_phase_map=element_phase_map,
-      )
-
-We may save the polycrystal to disc by using the builtin ``save()`` command as
-
-   .. code:: python
-
-      polycrystal.save('my_polycrystal', save_mesh_as_xdmf=True)
-
-We can visualize the sample by loading the .xdmf file into your favorite 3D rendering program.
-In `paraview`_ the sampled colored by one of its Euler angles looks like this:
-
-.. image:: https://github.com/FABLE-3DXRD/xrd_simulator/blob/main/docs/source/images/example_polycrystal_readme.png?raw=true
-   :align: center
-
-We can now define some motion of the sample over which to integrate the diffraction signal:
-
-   .. code:: python
-
-      from xrd_simulator.motion import RigidBodyMotion
-
-      motion = RigidBodyMotion(
-         rotation_axis=np.array([0, 1 / np.sqrt(2), -1 / np.sqrt(2)]),
-         rotation_angle=np.radians(0.1),
-         translation=np.array([123, -153.3, 3.42]),
-      )
-
-Now that we have an experimental setup we may collect diffraction by letting the beam and detector
-interact with the sample:
-
-   .. code:: python
-
-      peaks_dict = polycrystal.diffract(beam, motion, detector=detector)
-      diffraction_pattern, peaks_dict = detector.render(
-         peaks_dict, frames_to_render=0, method="micro"
-      )
-
-The resulting rendered detector frame will look something like the below. Note that the positions of the diffraction spots may vary as the crystal orientations were randomly generated!:
-
-   .. code:: python
-
-      import matplotlib.pyplot as plt
-
-      fig, ax = plt.subplots(1, 1, figsize=(12, 12))
-      # render returns (frames, height, width), take first frame
-      pattern = (
-         diffraction_pattern[0].cpu().numpy()
-         if hasattr(diffraction_pattern, "cpu")
-         else diffraction_pattern[0]
-      )
-      ax.imshow(pattern, cmap="gray", vmax=5000)
-      plt.show()
-
-.. image:: https://github.com/FABLE-3DXRD/xrd_simulator/blob/main/docs/source/images/diffraction_pattern.png?raw=true
-   :align: center
-   :width: 95%
-
-To compute several frames simply change the motion and collect the diffraction again. The sample may be moved before
-each computation using the same or another motion.
-
-   .. code:: python
-
-      polycrystal.transform(motion, time=1.0)
-      peaks_dict = polycrystal.diffract(beam, motion, detector=detector)
-
-Many more options for experimental setups and intensity rendering exist, have fun experimenting!
-The above example code can be found as a `single .py file here.`_
-
-======================================
-Installation
-======================================
-
-Anaconda installation (Linux and Macos)
-=============================================
-``xrd_simulator`` is distributed on the `conda-forge channel`_ and the preferred way to install
-the xrd_simulator package is via `Anaconda`_::
-
-   conda install -c conda-forge xrd_simulator
-   conda create -n xrd_simulator
-   conda activate xrd_simulator
-
-This is meant to work across OS-systems and requires an `Anaconda`_ installation.
-
-(The conda-forge feedstock of ``xrd_simulator`` `can be found here.`_)
-
-Anaconda installation (Windows)
-======================================
-``xrd_simulator`` can be installed on Windows via Anaconda. The package now uses `meshpy`_ which provides
-better cross-platform support than the previous pygalmesh dependency.
-
-Pip Installation
-======================================
-Pip installation is possible. The package uses `meshpy`_ which generally installs cleanly via pip::
-
-   pip install xrd-simulator
-
-Source installation
-===============================
-Naturally one may also install from the sources::
-
-   git clone https://github.com/FABLE-3DXRD/xrd_simulator.git
-   cd xrd_simulator
-   python setup.py install
-
-This will use `meshpy`_ which generally has better cross-platform support than pygalmesh.
-
-Credits
-===============================
-``xrd_simulator`` makes good use of xfab and meshpy for tetrahedral mesh generation.
-The source code of related repos can be found here:
-
-* `https://github.com/FABLE-3DXRD/xfab`_
-* `meshpy`_
-
-Citation
-===============================
-If you feel that ``xrd_simulator`` was helpful in your research we would love for you to cite us.
-
-*xrd_simulator: 3D X-ray diffraction simulation software supporting 3D polycrystalline microstructure morphology descriptions
-Henningsson, A. & Hall, S. A. (2023). J. Appl. Cryst. 56, 282-292.*
-`https://doi.org/10.1107/S1600576722011001`_
-
-.. _https://doi.org/10.1107/S1600576722011001: https://doi.org/10.1107/S1600576722011001
-
-.. _https://github.com/FABLE-3DXRD/xfab: https://github.com/FABLE-3DXRD/xfab
-
-.. _https://github.com/marmakoide/miniball: https://github.com/marmakoide/miniball
-
-.. _Anaconda: https://www.anaconda.com/products/individual
-
-.. _meshpy: https://github.com/inducer/meshpy
-
-.. _https://github.com/inducer/meshpy: https://github.com/inducer/meshpy
-
-.. _scanning-3dxrd: https://doi.org/10.1107/S1600576720001016
-
-.. _3dxrd: https://en.wikipedia.org/wiki/3DXRD
-
-.. _powder like: https://en.wikipedia.org/wiki/Powder_diffraction
-
-.. _which is hosted here: https://FABLE-3DXRD.github.io/xrd_simulator/
-
-.. _which is hosted here: https://FABLE-3DXRD.github.io/xrd_simulator/
-
-.. _single .py file here.: https://github.com/FABLE-3DXRD/xrd_simulator/blob/main/docs/source/examples/readme_tutorial.py
-
-.. _paraview: https://www.paraview.org/
-
-.. _can be found here.: https://github.com/conda-forge/xrd_simulator-feedstock
-
-.. _conda-forge channel: https://anaconda.org/conda-forge/xrd_simulator
+The future is now!

From 5a7cd07d298bfa6a683e21e2d59877e47c91af6e Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Thu, 14 May 2026 13:01:38 +0200
Subject: [PATCH 03/17] getting comfortable

---
 xrd_simulator/detector.py               |  7 +++++++
 xrd_simulator/gaussian_crystal_model.py | 27 +++++++++++++++++++++++++
 xrd_simulator/phase.py                  |  3 ++-
 3 files changed, 36 insertions(+), 1 deletion(-)
 create mode 100644 xrd_simulator/gaussian_crystal_model.py

diff --git a/xrd_simulator/detector.py b/xrd_simulator/detector.py
index b520994..79c8e76 100644
--- a/xrd_simulator/detector.py
+++ b/xrd_simulator/detector.py
@@ -177,6 +177,13 @@ def __init__(
         self.polarization_factor = use_polarization
         self.structure_factor = use_structure_factor
 
+        # Mads' favourite parametrization
+        self.shape = self.pixel_coordinates.shape[:2]
+        self.ori = self.pixel_coordinates[0,0]
+        v = torch.tensordot(self.pixel_coordinates - self.pixel_coordinates[0,0], self.ydhat, ((2,),(0,)))
+        u = torch.tensordot(self.pixel_coordinates - self.pixel_coordinates[0,0], self.zdhat, ((2,),(0,)))
+        self.W = np.stack([self.zdhat, self.ydhat])
+
     def save(self, path: str) -> None:
         """Save detector to disk.
 
diff --git a/xrd_simulator/gaussian_crystal_model.py b/xrd_simulator/gaussian_crystal_model.py
new file mode 100644
index 0000000..860fd75
--- /dev/null
+++ b/xrd_simulator/gaussian_crystal_model.py
@@ -0,0 +1,27 @@
+from scipy.spatial.transform import Rotation as R
+import numpy as np
+import numpy.typing as npt
+import torch
+from torch import Tensor
+from xrd_simulator.phase import Phase
+
+
+class GaussianGrainish:
+    """It's not a grain, it's a grain-ish.
+    """
+
+    def __init__(self,
+        phase: Phase,
+        position: npt.NDArray | Tensor = np.array([0, 0, 0]), 
+        shape_tensor: npt.NDArray | Tensor = np.eye(3),
+        orientation: npt.NDArray | Tensor = np.eye(3), # 3by3 Rotation matrix.
+        misorientation_tensor: npt.NDArray | Tensor = 0.0175**2 * np.eye(3), # Default one degree isotropic
+        strain_tensor: npt.NDArray | Tensor = np.zeros((3, 3,)),
+    ):
+        
+        self.phase = phase
+        self.position = position
+        self.shape_tensor = shape_tensor
+        self.orientation = orientation
+        self.misorientation_tensor = misorientation_tensor
+        self.strain_tensor = strain_tensor
diff --git a/xrd_simulator/phase.py b/xrd_simulator/phase.py
index 8821f60..1cbb8ce 100644
--- a/xrd_simulator/phase.py
+++ b/xrd_simulator/phase.py
@@ -20,7 +20,7 @@
 .. _The .cif file used in the above example can be found here.: https://github.com/FABLE-3DXRD/xrd_simulator/blob/main/docs/source/examples/quartz.cif?raw=true
 """
 import numpy as np
-from xfab import tools, structure
+from xfab import tools, structure, sg
 from xrd_simulator import utils
 
 class Phase(object):
@@ -68,6 +68,7 @@ class Phase(object):
     def __init__(self, unit_cell, sgname, path_to_cif_file=None):
         self.unit_cell = unit_cell
         self.sgname = sgname
+        self.rot = sg.sg(sgname=sgname).rot
         self.miller_indices = None
         self.structure_factors = None
         self.path_to_cif_file = path_to_cif_file

From 27135c6dc102955f2af099fbf41150a955d6d709 Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Thu, 14 May 2026 16:23:34 +0200
Subject: [PATCH 04/17] used xfab wrong

---
 xrd_simulator/phase.py | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/xrd_simulator/phase.py b/xrd_simulator/phase.py
index 1cbb8ce..01f7f10 100644
--- a/xrd_simulator/phase.py
+++ b/xrd_simulator/phase.py
@@ -20,7 +20,7 @@
 .. _The .cif file used in the above example can be found here.: https://github.com/FABLE-3DXRD/xrd_simulator/blob/main/docs/source/examples/quartz.cif?raw=true
 """
 import numpy as np
-from xfab import tools, structure, sg
+from xfab import tools, structure, sg, symmetry
 from xrd_simulator import utils
 
 class Phase(object):
@@ -68,7 +68,11 @@ class Phase(object):
     def __init__(self, unit_cell, sgname, path_to_cif_file=None):
         self.unit_cell = unit_cell
         self.sgname = sgname
-        self.rot = sg.sg(sgname=sgname).rot
+
+        # Warning, this is the pointgroup of the lattice, not of the system. So you cannot deal with all spacegroups this way
+        # there seems to be no way to get the proper point group in xfab.
+        self.rot = symmetry.rotations(sg.sg(sgname=sgname).crystal_system)
+
         self.miller_indices = None
         self.structure_factors = None
         self.path_to_cif_file = path_to_cif_file

From e75db8a5a6e7c141da3b65ef84349ec6dd721c70 Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Thu, 14 May 2026 17:16:15 +0200
Subject: [PATCH 05/17] polefigures completed

---
 xrd_simulator/gaussian_crystal_model.py | 156 ++++++++++++++++++++++++
 xrd_simulator/phase.py                  |  11 +-
 2 files changed, 163 insertions(+), 4 deletions(-)

diff --git a/xrd_simulator/gaussian_crystal_model.py b/xrd_simulator/gaussian_crystal_model.py
index 860fd75..820f1e0 100644
--- a/xrd_simulator/gaussian_crystal_model.py
+++ b/xrd_simulator/gaussian_crystal_model.py
@@ -3,7 +3,11 @@
 import numpy.typing as npt
 import torch
 from torch import Tensor
+
 from xrd_simulator.phase import Phase
+from xrd_simulator.utils import ensure_torch
+
+from xfab.tools import form_a_mat
 
 
 class GaussianGrainish:
@@ -25,3 +29,155 @@ def __init__(self,
         self.orientation = orientation
         self.misorientation_tensor = misorientation_tensor
         self.strain_tensor = strain_tensor
+
+
+
+
+levi_cita_symbol = np.zeros((3,3,3))
+levi_cita_symbol[0, 1, 2] = 1
+levi_cita_symbol[1, 2, 0] = 1
+levi_cita_symbol[2, 0, 1] = 1
+levi_cita_symbol[0, 2, 1] = -1
+levi_cita_symbol[1, 0, 2] = -1
+levi_cita_symbol[2, 1, 0] = -1
+
+levi_cita_symbol = torch.tensor(levi_cita_symbol)
+
+
+class GaussianPolycrystal:
+
+    def __init__(self,
+        grain_list: List[GaussianGrainish],
+    ):
+        
+        phases_list = list(set([grain.phase for grain in grain_list]))
+        n_phases = len(phases_list)
+        assert n_phases == 1
+
+        self.n_grains = len(grain_list)
+        self.phase = phases_list[0]
+
+        self.positions = torch.stack([ensure_torch(grain.position) for grain in grain_list])
+        self.shape_concentration_tensors = torch.stack([ensure_torch(np.linalg.inv(grain.shape_tensor)) for grain in grain_list])
+
+        self.orientaions = torch.stack([ensure_torch(grain.orientation) for grain in grain_list])
+        self.misori_concentration_tensors = torch.stack([ensure_torch(np.linalg.inv(grain.misorientation_tensor)) for grain in grain_list])
+        
+        self.strains = torch.stack([ensure_torch(grain.strain_tensor) for grain in grain_list])
+
+
+    def splat_onto_polefigure(
+            self,
+            hkl: tuple[int],
+        ):
+
+
+        A = form_a_mat(self.phase.unit_cell)
+        B = 2 * np.pi * np.linalg.inv(A).T
+        h = torch.tensor(B @ hkl)
+        h = h / torch.linalg.norm(h)
+
+        # TODO reduce the number of symmetries evaluated for low-multiplicity peaks
+
+        n_symmetries = len(self.phase.rot)
+        
+        volumes = torch.sqrt(torch.linalg.det(self.shape_concentration_tensors))
+        p_vectors = torch.einsum('gij,sjk,k->gsi', self.orientaions, ensure_torch(self.phase.rot), h)        
+        
+        # This is the trick:
+        pTp = torch.einsum('gsi,gij,gsj->gs', p_vectors, self.misori_concentration_tensors, p_vectors)
+        inner_part = self.misori_concentration_tensors[:, None, :, :] - torch.einsum(
+            'gij,gsj,gsk,gkl->gsil',
+            self.misori_concentration_tensors,
+            p_vectors,
+            p_vectors,
+            self.misori_concentration_tensors,
+        ) / pTp[:, :, None, None]
+        projected_misorientation = torch.einsum(
+            'gsj,ijk,gsil,lmn,gsm->gskn',
+            p_vectors,
+            levi_cita_symbol,
+            inner_part,
+            levi_cita_symbol,
+            p_vectors,
+        )
+        
+        scale = 1 / n_symmetries / torch.sum(volumes) * volumes[:, None] * 2 * torch.sqrt(torch.linalg.det(self.misori_concentration_tensors))[:, None] / np.sqrt( pTp )
+        
+        return p_vectors, scale, projected_misorientation                
+
+    def render_polefigure(
+        self,
+        hkl: tuple[int],
+        resolution_in_degrees: float = 1.0,
+        both_hemispheres: bool = False,
+        max_misorientation: float = 0.1,
+    ):
+        
+        # Make coordinate arrays
+        if both_hemispheres:
+            polar, azim = np.meshgrid(np.linspace(0, np.pi, int(180//resolution_in_degrees)+1),
+                                      np.linspace(0, 2*np.pi, int(360//resolution_in_degrees)+1))
+        else:
+            polar, azim = np.meshgrid(np.linspace(0, np.pi/2, int(90//resolution_in_degrees)+1),
+                                      np.linspace(0, 2*np.pi, int(360//resolution_in_degrees)+1))
+            
+        y_map = torch.tensor(np.stack([
+            np.sin(polar) * np.cos(azim),
+            np.sin(polar) * np.sin(azim),
+            np.cos(polar)
+            ], axis=-1))
+        
+        p, scale, T_proj = self.splat_onto_polefigure(hkl)
+        patch_size = 16
+        
+        f = self.rasterize_on_unitvector_map(
+            y_map,
+            p,
+            scale,
+            T_proj,
+            max_angle=3*max_misorientation + (resolution_in_degrees*np.pi/180) * patch_size/2,
+        )
+
+        return f, polar, azim
+
+    def rasterize_on_unitvector_map(
+        self,
+        y : Tensor,
+        p : Tensor,
+        scale : Tensor,
+        T_proj : Tensor,
+        max_angle: float,
+        patch_size: int = 16,
+    ):
+        
+        shape = y.shape[:2]
+        min_dp = np.cos(max_angle)
+        n_patches_dim1 = (shape[0]-1)//patch_size+1
+        n_patches_dim2 = (shape[1]-1)//patch_size+1
+
+        # Rasterization
+        f = torch.zeros(shape)
+
+        for patch_index_1 in range(n_patches_dim1):
+            for patch_index_2 in range(n_patches_dim2):
+
+                # Figure out what splat lie in this pole figure patch
+                y_patch = y[patch_size*patch_index_1:patch_size*(patch_index_1+1),
+                            patch_size*patch_index_2:patch_size*(patch_index_2+1)]
+                patch_mean = torch.mean(y_patch, axis=(0, 1))
+                patch_mean_y = patch_mean / torch.linalg.norm(patch_mean)
+                include_index = torch.abs(torch.einsum('gsj,j->gs', p, patch_mean_y)) > min_dp
+                                # If none, continue
+                if not torch.any(include_index):
+                    continue
+
+                # Evaluate gaussians
+                arg = -torch.einsum('pai,xij,paj->xpa', y_patch, T_proj[include_index], y_patch)
+                vals = torch.exp(arg) * scale[include_index, np.newaxis, np.newaxis]
+                
+                f[patch_size*patch_index_1:patch_size*(patch_index_1+1),
+                  patch_size*patch_index_2:patch_size*(patch_index_2+1)]\
+                    += torch.sum(vals, axis=0)
+        
+        return f
diff --git a/xrd_simulator/phase.py b/xrd_simulator/phase.py
index 01f7f10..f6ddefc 100644
--- a/xrd_simulator/phase.py
+++ b/xrd_simulator/phase.py
@@ -20,7 +20,8 @@
 .. _The .cif file used in the above example can be found here.: https://github.com/FABLE-3DXRD/xrd_simulator/blob/main/docs/source/examples/quartz.cif?raw=true
 """
 import numpy as np
-from xfab import tools, structure, sg, symmetry
+from xfab import tools, structure, sg
+from xfab.tools import form_a_mat
 from xrd_simulator import utils
 
 class Phase(object):
@@ -69,9 +70,11 @@ def __init__(self, unit_cell, sgname, path_to_cif_file=None):
         self.unit_cell = unit_cell
         self.sgname = sgname
 
-        # Warning, this is the pointgroup of the lattice, not of the system. So you cannot deal with all spacegroups this way
-        # there seems to be no way to get the proper point group in xfab.
-        self.rot = symmetry.rotations(sg.sg(sgname=sgname).crystal_system)
+        # These are rotations in the reference coordinate system where the lattice matrix is upper triangular
+        A = form_a_mat(unit_cell)
+        A_inv = np.linalg.inv(A)
+        sg_obj = sg.sg(sgname=sgname)
+        self.rot = rots = np.stack([A @ rot_lattce_space @ A_inv for rot_lattce_space in sg_obj.rot])
 
         self.miller_indices = None
         self.structure_factors = None

From 2495d873fe14f5911b7d799e298f0903107a5f7b Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Thu, 14 May 2026 22:43:02 +0200
Subject: [PATCH 06/17] almost done with detector splatting

---
 xrd_simulator/gaussian_crystal_model.py | 216 +++++++++++++++++++++---
 1 file changed, 188 insertions(+), 28 deletions(-)

diff --git a/xrd_simulator/gaussian_crystal_model.py b/xrd_simulator/gaussian_crystal_model.py
index 820f1e0..9a4b4fc 100644
--- a/xrd_simulator/gaussian_crystal_model.py
+++ b/xrd_simulator/gaussian_crystal_model.py
@@ -6,6 +6,7 @@
 
 from xrd_simulator.phase import Phase
 from xrd_simulator.utils import ensure_torch
+from xrd_simulator.detector import Detector
 
 from xfab.tools import form_a_mat
 
@@ -31,8 +32,6 @@ def __init__(self,
         self.strain_tensor = strain_tensor
 
 
-
-
 levi_cita_symbol = np.zeros((3,3,3))
 levi_cita_symbol[0, 1, 2] = 1
 levi_cita_symbol[1, 2, 0] = 1
@@ -47,7 +46,7 @@ def __init__(self,
 class GaussianPolycrystal:
 
     def __init__(self,
-        grain_list: List[GaussianGrainish],
+        grain_list: list[GaussianGrainish],
     ):
         
         phases_list = list(set([grain.phase for grain in grain_list]))
@@ -65,46 +64,167 @@ def __init__(self,
         
         self.strains = torch.stack([ensure_torch(grain.strain_tensor) for grain in grain_list])
 
+    def render_detector_frame(
+        self,
+        detector: Detector,
+        xray_propagation_direction: npt.NDArray | Tensor,
+        wavelength: float,
+        sample_orientation: npt.NDArray | Tensor = np.eye(3),
+        sample_rotation_during_exposure: npt.NDArray | Tensor = np.zeros(3),
+        max_misorientation: float = 0.1,
+    ):
 
-    def splat_onto_polefigure(
+
+        #TODO Rotate detector or sample?
+        xray_propagation_direction = ensure_torch(xray_propagation_direction)
+        detector_norm = ensure_torch(np.cross(detector.W[0,:], detector.W[1,:]))
+        detector_origin = ensure_torch(detector.ori)
+        W = ensure_torch(detector.W)
+        # d = torch.dot(detector_norm, detector_origin) / torch.dot(detector_norm, xray_propagation_direction)
+        pixellengths = torch.tensor([detector.pixel_size_y, detector.pixel_size_z])
+        
+        # TODO generate hkl_list and structurefactors
+        hkl_list = [(1, 1, 0), (2, 0, 0), (0, 0, 1)]
+        structurefactors = [1, 1, 1]
+
+        uv_corrds_list = []
+        splat_concentration_tensors_list = []
+        scalefactors_list = []
+
+        for hkl, S in zip(hkl_list, structurefactors):
+            
+            #Figure out what reflections are in the bragg-condition
+            A = form_a_mat(self.phase.unit_cell)
+            B = 2 * np.pi * np.linalg.inv(A).T
+            h = torch.tensor(B @ hkl)
+            h_norm = torch.linalg.norm(h)
+            theta_angle_unstrained = np.asin( h_norm * wavelength / 4 / np.pi )
+
+            # TODO reduce the number of symmetries evaluated for low-multiplicity peaks
+            n_symmetries = len(self.phase.rot)
+
+            p_vectors = torch.einsum('ghi,gij,sjk,k->gsh', torch.eye(3)[None,:,:] - self.strains, self.orientaions, ensure_torch(self.phase.rot), h)
+            p_vectors_norm = torch.linalg.norm(p_vectors, axis=-1)
+            
+            dp = torch.einsum('i,gsi->gs', xray_propagation_direction, p_vectors) / p_vectors_norm            
+            does_diffract = torch.abs( dp + torch.sin(theta_angle_unstrained) ) <  torch.abs(3 * max_misorientation * torch.cos(theta_angle_unstrained))
+
+            oris = torch.tile(self.orientaions[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
+            misori_tensors = torch.tile(self.misori_concentration_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
+            p_vecs = p_vectors[does_diffract]
+
+            #Subsample polefigure-splats on ring
+            mean_scattering_directions, partiality, azim_direction, azim_width = self.get_diffraction_arcsegment(
+                oris, p_vecs, misori_tensors, xray_propagation_direction, wavelength
+            )
+
+            #TODO Splat grain realspace shapes
+            realspace_splat_concentration = 1/20**2*torch.tile(torch.eye(2)[None, :, :], (len(partiality), 1, 1))
+
+            #TODO Do smearing due to angular divergence.
+            
+            # Direct beam is pos + mean_scatt_dir * x, detector is det_ori dot det_norm = 0 
+            pos = torch.tile(self.positions[:, None, :], (1, n_symmetries, 1,))[does_diffract]
+            ray_lengths = torch.einsum('xi,i->x', detector_origin[None, :] - pos, detector_norm) / torch.einsum('xi,i->x', mean_scattering_directions, detector_norm)
+            point_of_detector_intersection = pos + ray_lengths[:,None] * mean_scattering_directions
+            uv_coords = torch.einsum('xi, vi, v->xv',point_of_detector_intersection - detector_origin[None, :], W, 1/pixellengths)
+
+            uv_corrds_list.append(uv_coords)
+            scalefactors_list.append(partiality)
+            splat_concentration_tensors_list.append(realspace_splat_concentration)
+
+        f = self.rasterize_on_detector(
+            torch.concat(uv_corrds_list),
+            torch.concat(scalefactors_list),
+            torch.concat(splat_concentration_tensors_list),
+            detector.shape,
+        )
+
+        return f
+            
+    def rasterize_on_detector(
             self,
-            hkl: tuple[int],
+            uv_corrds: Tensor,
+            scale_factors: Tensor,
+            concentration_tensors: Tensor,
+            shape: Tuple,
+            patch_size: int = 16,
+            splat_max_size: float = 100.0
         ):
 
 
-        A = form_a_mat(self.phase.unit_cell)
-        B = 2 * np.pi * np.linalg.inv(A).T
-        h = torch.tensor(B @ hkl)
-        h = h / torch.linalg.norm(h)
+        u, v = torch.meshgrid(torch.arange(shape[0]), torch.arange(shape[1]))
+        f = torch.zeros(shape)
 
-        # TODO reduce the number of symmetries evaluated for low-multiplicity peaks
+        patch_size = 16
+        n_patches_dim1 = (shape[0]-1)//patch_size+1
+        n_patches_dim2 = (shape[1]-1)//patch_size+1
 
-        n_symmetries = len(self.phase.rot)
-        
-        volumes = torch.sqrt(torch.linalg.det(self.shape_concentration_tensors))
-        p_vectors = torch.einsum('gij,sjk,k->gsi', self.orientaions, ensure_torch(self.phase.rot), h)        
-        
-        # This is the trick:
-        pTp = torch.einsum('gsi,gij,gsj->gs', p_vectors, self.misori_concentration_tensors, p_vectors)
-        inner_part = self.misori_concentration_tensors[:, None, :, :] - torch.einsum(
-            'gij,gsj,gsk,gkl->gsil',
-            self.misori_concentration_tensors,
+        for patch_index_1 in range(n_patches_dim1):
+            for patch_index_2 in range(n_patches_dim2):
+
+                patch_slice = (slice(patch_size*patch_index_1, patch_size*(patch_index_1+1)),
+                               slice(patch_size*patch_index_2, patch_size*(patch_index_2+1)),)
+
+                patch_mean_u = patch_size*(patch_index_1+0.5)
+                patch_mean_v = patch_size*(patch_index_2+0.5)
+                
+                include_index = (uv_corrds[:, 0]-patch_mean_u)**2 + (uv_corrds[:, 1]-patch_mean_v)**2 < splat_max_size**2
+                if not torch.any(include_index):
+                    continue
+
+
+                local_coords = torch.stack([u[patch_slice][None, :, :] - uv_corrds[include_index, 0, None, None],
+                                         v[patch_slice][None, :, :] - uv_corrds[include_index, 1, None, None],
+                                         ], axis=1)
+
+                f[patch_slice] +=  torch.sum(scale_factors[include_index, None, None]\
+                    * torch.exp(- torch.einsum('xiuv,xij,xjuv->xuv' ,local_coords, concentration_tensors[include_index, :, :], local_coords)), axis=0)
+
+        return f
+
+    def get_diffraction_arcsegment(self, oris, p_vectors, misori_tensors, xray_propagation_direction, wavelength):
+
+        # Splat onto poelfigure
+        p_norm = torch.linalg.norm(p_vectors, axis=-1)
+        D = torch.einsum('xi,xij,xj->x', p_vectors, misori_tensors, p_vectors)/ p_norm**2
+
+        inner_part = misori_tensors - torch.einsum(
+            'xij,xj,xk,xkl->xil',
+            misori_tensors,
             p_vectors,
             p_vectors,
-            self.misori_concentration_tensors,
-        ) / pTp[:, :, None, None]
-        projected_misorientation = torch.einsum(
-            'gsj,ijk,gsil,lmn,gsm->gskn',
+            misori_tensors,
+        ) / D[:, None, None] / p_norm[:, None, None]**2
+        T_proj = torch.einsum(
+            'xj,ijk,xil,lmn,xm->xkn',
             p_vectors,
             levi_cita_symbol,
             inner_part,
             levi_cita_symbol,
             p_vectors,
-        )
+        ) / p_norm[:, None, None]**2
+
+        # Compute point of "exact bragg condition" in the plane Span(k_0, p)
+        theta_angle = np.asin( p_norm * wavelength / 4 / np.pi )
+        dir_scatteringplane_norm = (p_vectors - xray_propagation_direction[None, :] * np.einsum('xi,i->x', p_vectors, xray_propagation_direction)[:, None] )
+        dir_scatteringplane_norm = dir_scatteringplane_norm / torch.linalg.norm(dir_scatteringplane_norm, axis=-1)[:, None]
+        q_0_unit = torch.cos(theta_angle)[:, None] * dir_scatteringplane_norm - torch.sin(theta_angle)[:, None] * xray_propagation_direction[None, :]
+        dir_scatteringplane_orth = torch.einsum('ijk,j,xk->xi', levi_cita_symbol, xray_propagation_direction, dir_scatteringplane_norm)
+
+        # Compute partiality, mean direction, and azimthal spread
+        A = torch.einsum('xi,xij,xj->x', q_0_unit, T_proj, q_0_unit,)
+        B = torch.einsum('xi,xij,xj->x', q_0_unit, T_proj, dir_scatteringplane_orth,)
+        C = torch.einsum('xi,xij,xj->x', dir_scatteringplane_orth, T_proj, dir_scatteringplane_orth,)
         
-        scale = 1 / n_symmetries / torch.sum(volumes) * volumes[:, None] * 2 * torch.sqrt(torch.linalg.det(self.misori_concentration_tensors))[:, None] / np.sqrt( pTp )
+        partiality = torch.exp(-A - B**2 / C) * 2 * torch.sqrt( torch.linalg.det(misori_tensors) / D )
         
-        return p_vectors, scale, projected_misorientation                
+        azim_divergence = np.sqrt(1 / C)
+        azim_offset = B / C
+        mean_scattering_directions = torch.cos(2*theta_angle)[:, None] * xray_propagation_direction[None, :]\
+            + torch.sin(2*theta_angle)[:, None]*(torch.cos(azim_offset)[:, None]*dir_scatteringplane_norm + torch.sin(azim_offset)[:, None]*dir_scatteringplane_orth)
+
+        return mean_scattering_directions, partiality, dir_scatteringplane_orth, azim_divergence 
 
     def render_polefigure(
         self,
@@ -136,11 +256,51 @@ def render_polefigure(
             p,
             scale,
             T_proj,
-            max_angle=3*max_misorientation + (resolution_in_degrees*np.pi/180) * patch_size/2,
+            max_angle= 3*max_misorientation + (resolution_in_degrees*np.pi/180)*patch_size/2,
         )
 
         return f, polar, azim
 
+    def splat_onto_polefigure(
+            self,
+            hkl: tuple[int],
+        ):
+
+
+        A = form_a_mat(self.phase.unit_cell)
+        B = 2 * np.pi * np.linalg.inv(A).T
+        h = torch.tensor(B @ hkl)
+        h = h / torch.linalg.norm(h)
+
+        # TODO reduce the number of symmetries evaluated for low-multiplicity peaks
+
+        n_symmetries = len(self.phase.rot)
+        
+        volumes = torch.sqrt(torch.linalg.det(self.shape_concentration_tensors))
+        p_vectors = torch.einsum('gij,sjk,k->gsi', self.orientaions, ensure_torch(self.phase.rot), h)        
+        
+        # This is the trick:
+        pTp = torch.einsum('gsi,gij,gsj->gs', p_vectors, self.misori_concentration_tensors, p_vectors)
+        inner_part = self.misori_concentration_tensors[:, None, :, :] - torch.einsum(
+            'gij,gsj,gsk,gkl->gsil',
+            self.misori_concentration_tensors,
+            p_vectors,
+            p_vectors,
+            self.misori_concentration_tensors,
+        ) / pTp[:, :, None, None]
+        projected_misorientation = torch.einsum(
+            'gsj,ijk,gsil,lmn,gsm->gskn',
+            p_vectors,
+            levi_cita_symbol,
+            inner_part,
+            levi_cita_symbol,
+            p_vectors,
+        )
+        
+        scale = 1 / n_symmetries / torch.sum(volumes) * volumes[:, None] * 2 * torch.sqrt(torch.linalg.det(self.misori_concentration_tensors))[:, None] / np.sqrt( pTp )
+        
+        return p_vectors, scale, projected_misorientation                
+
     def rasterize_on_unitvector_map(
         self,
         y : Tensor,

From 78b9ad90fc4298f43cc907307f7013daeebb1aee Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Fri, 15 May 2026 00:01:49 +0200
Subject: [PATCH 07/17] first working version of detector-space splatting

---
 xrd_simulator/gaussian_crystal_model.py | 24 ++++++++++++++----------
 1 file changed, 14 insertions(+), 10 deletions(-)

diff --git a/xrd_simulator/gaussian_crystal_model.py b/xrd_simulator/gaussian_crystal_model.py
index 9a4b4fc..344877e 100644
--- a/xrd_simulator/gaussian_crystal_model.py
+++ b/xrd_simulator/gaussian_crystal_model.py
@@ -83,7 +83,7 @@ def render_detector_frame(
         # d = torch.dot(detector_norm, detector_origin) / torch.dot(detector_norm, xray_propagation_direction)
         pixellengths = torch.tensor([detector.pixel_size_y, detector.pixel_size_z])
         
-        # TODO generate hkl_list and structurefactors
+        # TODO generate hkl_list and structurefactors with xfab?
         hkl_list = [(1, 1, 0), (2, 0, 0), (0, 0, 1)]
         structurefactors = [1, 1, 1]
 
@@ -119,19 +119,23 @@ def render_detector_frame(
             )
 
             #TODO Splat grain realspace shapes
-            realspace_splat_concentration = 1/20**2*torch.tile(torch.eye(2)[None, :, :], (len(partiality), 1, 1))
+            samplespace_splat_concentration = 1/3**2*torch.tile(torch.eye(2)[None, :, :], (len(partiality), 1, 1))
 
-            #TODO Do smearing due to angular divergence.
-            
             # Direct beam is pos + mean_scatt_dir * x, detector is det_ori dot det_norm = 0 
             pos = torch.tile(self.positions[:, None, :], (1, n_symmetries, 1,))[does_diffract]
             ray_lengths = torch.einsum('xi,i->x', detector_origin[None, :] - pos, detector_norm) / torch.einsum('xi,i->x', mean_scattering_directions, detector_norm)
             point_of_detector_intersection = pos + ray_lengths[:,None] * mean_scattering_directions
             uv_coords = torch.einsum('xi, vi, v->xv',point_of_detector_intersection - detector_origin[None, :], W, 1/pixellengths)
 
+            #Do smearing due to angular divergence.
+            azimuthal_direction_uv = torch.einsum('xi,ui->xu', azim_direction, W) / pixellengths[None, :] * ray_lengths[:, None] * azim_width[:, None] / (1 - torch.einsum('xi,ui->xu', mean_scattering_directions, W)**2)
+            azimuthal_smearing_tensor = torch.einsum('xu,xv->xuv',azimuthal_direction_uv, azimuthal_direction_uv)
+            detspace_splat_concentration = torch.linalg.inv( torch.linalg.inv(samplespace_splat_concentration) + azimuthal_smearing_tensor)
+
             uv_corrds_list.append(uv_coords)
-            scalefactors_list.append(partiality)
-            splat_concentration_tensors_list.append(realspace_splat_concentration)
+            scalefactors_list.append(S * partiality)
+            splat_concentration_tensors_list.append(detspace_splat_concentration)
+                         
 
         f = self.rasterize_on_detector(
             torch.concat(uv_corrds_list),
@@ -147,7 +151,7 @@ def rasterize_on_detector(
             uv_corrds: Tensor,
             scale_factors: Tensor,
             concentration_tensors: Tensor,
-            shape: Tuple,
+            shape: tuple,
             patch_size: int = 16,
             splat_max_size: float = 100.0
         ):
@@ -175,8 +179,8 @@ def rasterize_on_detector(
 
 
                 local_coords = torch.stack([u[patch_slice][None, :, :] - uv_corrds[include_index, 0, None, None],
-                                         v[patch_slice][None, :, :] - uv_corrds[include_index, 1, None, None],
-                                         ], axis=1)
+                                            v[patch_slice][None, :, :] - uv_corrds[include_index, 1, None, None],
+                                            ], axis=1)
 
                 f[patch_slice] +=  torch.sum(scale_factors[include_index, None, None]\
                     * torch.exp(- torch.einsum('xiuv,xij,xjuv->xuv' ,local_coords, concentration_tensors[include_index, :, :], local_coords)), axis=0)
@@ -219,7 +223,7 @@ def get_diffraction_arcsegment(self, oris, p_vectors, misori_tensors, xray_propa
         
         partiality = torch.exp(-A - B**2 / C) * 2 * torch.sqrt( torch.linalg.det(misori_tensors) / D )
         
-        azim_divergence = np.sqrt(1 / C)
+        azim_divergence = np.sqrt(1 / C) * torch.sin(theta_angle) # TODO Check trigonometric function here
         azim_offset = B / C
         mean_scattering_directions = torch.cos(2*theta_angle)[:, None] * xray_propagation_direction[None, :]\
             + torch.sin(2*theta_angle)[:, None]*(torch.cos(azim_offset)[:, None]*dir_scatteringplane_norm + torch.sin(azim_offset)[:, None]*dir_scatteringplane_orth)

From f72309813fe04baa575855728da8619bf12456fd Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Fri, 15 May 2026 17:44:30 +0200
Subject: [PATCH 08/17] tested normalization and sense-of-rotation

---
 xrd_simulator/gaussian_crystal_model.py | 113 +++++++++++++++++-------
 1 file changed, 83 insertions(+), 30 deletions(-)

diff --git a/xrd_simulator/gaussian_crystal_model.py b/xrd_simulator/gaussian_crystal_model.py
index 344877e..7273836 100644
--- a/xrd_simulator/gaussian_crystal_model.py
+++ b/xrd_simulator/gaussian_crystal_model.py
@@ -8,7 +8,8 @@
 from xrd_simulator.utils import ensure_torch
 from xrd_simulator.detector import Detector
 
-from xfab.tools import form_a_mat
+from xfab.tools import form_a_mat, genhkl_base
+from xfab import sg
 
 
 class GaussianGrainish:
@@ -74,52 +75,77 @@ def render_detector_frame(
         max_misorientation: float = 0.1,
     ):
 
+        sample_orientation = ensure_torch(sample_orientation)
+        sample_rotation_during_exposure = ensure_torch(sample_rotation_during_exposure)
 
-        #TODO Rotate detector or sample?
-        xray_propagation_direction = ensure_torch(xray_propagation_direction)
-        detector_norm = ensure_torch(np.cross(detector.W[0,:], detector.W[1,:]))
-        detector_origin = ensure_torch(detector.ori)
-        W = ensure_torch(detector.W)
-        # d = torch.dot(detector_norm, detector_origin) / torch.dot(detector_norm, xray_propagation_direction)
+        #Rotate detector and incident beam by inverse of sample-rotation.
+        xray_propagation_direction = torch.einsum('ij,i->j', sample_orientation, ensure_torch(xray_propagation_direction) )
+        detector_norm = torch.einsum('ij,i->j', sample_orientation, ensure_torch(np.cross(detector.W[0,:], detector.W[1,:])))
+        detector_origin = torch.einsum('ij,i->j', sample_orientation, ensure_torch(detector.ori))
+        W = torch.einsum('ij,ui->uj', sample_orientation, ensure_torch(detector.W))
         pixellengths = torch.tensor([detector.pixel_size_y, detector.pixel_size_z])
         
-        # TODO generate hkl_list and structurefactors with xfab?
-        hkl_list = [(1, 1, 0), (2, 0, 0), (0, 0, 1)]
-        structurefactors = [1, 1, 1]
+        # Simulate sample-rotation by adding a rotation to the grain misorientation
+        rotation_vector = torch.einsum('ij,i->j', sample_orientation, sample_rotation_during_exposure)
+        smeared_misorientation_tensors = torch.linalg.inv(torch.linalg.inv(self.misori_concentration_tensors) + torch.outer(rotation_vector, rotation_vector))
+
+        #Figure out what reflections are in the bragg-condition
+        A = form_a_mat(self.phase.unit_cell)
+        B = 2 * np.pi * np.linalg.inv(A).T # TODO Check if the 2 pi is conventional here 
+
+        # Generate structure-factors and 
+        max_angle = detector._get_wrapping_cone(xray_propagation_direction, np.mean([0, 0, 0]))
+        self.phase._setup_diffracting_planes(wavelength=wavelength, min_bragg_angle=0.0, max_bragg_angle=max_angle)  #TODO Using private method
+        sg_obj = sg.sg(sgname=self.phase.sgname)
+
+        hkl_list = genhkl_base(
+            self.phase.unit_cell,
+            sg_obj.syscond,
+            0.0, np.sin(max_angle) / wavelength,
+            sg_obj.crystal_system,
+            sg_obj.Laue,
+        )
+        self.phase._set_structure_factors(hkl_list)  #TODO Using private method
+        structurefactors = ensure_torch(np.sum(self.phase.structure_factors**2, axis=1))
 
         uv_corrds_list = []
         splat_concentration_tensors_list = []
         scalefactors_list = []
 
+        # Loop over reflection orders
         for hkl, S in zip(hkl_list, structurefactors):
-            
-            #Figure out what reflections are in the bragg-condition
-            A = form_a_mat(self.phase.unit_cell)
-            B = 2 * np.pi * np.linalg.inv(A).T
-            h = torch.tensor(B @ hkl)
-            h_norm = torch.linalg.norm(h)
-            theta_angle_unstrained = np.asin( h_norm * wavelength / 4 / np.pi )
 
             # TODO reduce the number of symmetries evaluated for low-multiplicity peaks
             n_symmetries = len(self.phase.rot)
 
+
+            # Quick test to discard reflections far from Bragg-condition
+            h = torch.tensor(B @ hkl)
+            h_norm = torch.linalg.norm(h)
+            theta_angle_unstrained = np.asin( h_norm * wavelength / 4 / np.pi )
             p_vectors = torch.einsum('ghi,gij,sjk,k->gsh', torch.eye(3)[None,:,:] - self.strains, self.orientaions, ensure_torch(self.phase.rot), h)
             p_vectors_norm = torch.linalg.norm(p_vectors, axis=-1)
-            
             dp = torch.einsum('i,gsi->gs', xray_propagation_direction, p_vectors) / p_vectors_norm            
             does_diffract = torch.abs( dp + torch.sin(theta_angle_unstrained) ) <  torch.abs(3 * max_misorientation * torch.cos(theta_angle_unstrained))
 
-            oris = torch.tile(self.orientaions[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
-            misori_tensors = torch.tile(self.misori_concentration_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
-            p_vecs = p_vectors[does_diffract]
+            # Select the relevant reflections and flatten grain- and symetry-indexes.
+            orientations = torch.tile(self.orientaions[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
+            misori_concentration_tensors = torch.tile(smeared_misorientation_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
+            p_vectors = p_vectors[does_diffract]
 
-            #Subsample polefigure-splats on ring
+            # Do pole-figure part of the calculation
             mean_scattering_directions, partiality, azim_direction, azim_width = self.get_diffraction_arcsegment(
-                oris, p_vecs, misori_tensors, xray_propagation_direction, wavelength
+                orientations, p_vectors, misori_concentration_tensors, xray_propagation_direction, wavelength
             )
 
-            #TODO Splat grain realspace shapes
-            samplespace_splat_concentration = 1/3**2*torch.tile(torch.eye(2)[None, :, :], (len(partiality), 1, 1))
+            # Splat grain realspace shapes (Consider using the non-strained non-azimuthally shifted directions to simplify gradients later)
+            shape_concentration_tensors = torch.tile(self.shape_concentration_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
+            detectorspace_grainshape_projections, projected_thicknes_scale_factor = self.splat_grainshapes(
+                mean_scattering_directions,
+                shape_concentration_tensors,
+                W,
+                pixellengths,
+            )
 
             # Direct beam is pos + mean_scatt_dir * x, detector is det_ori dot det_norm = 0 
             pos = torch.tile(self.positions[:, None, :], (1, n_symmetries, 1,))[does_diffract]
@@ -130,10 +156,12 @@ def render_detector_frame(
             #Do smearing due to angular divergence.
             azimuthal_direction_uv = torch.einsum('xi,ui->xu', azim_direction, W) / pixellengths[None, :] * ray_lengths[:, None] * azim_width[:, None] / (1 - torch.einsum('xi,ui->xu', mean_scattering_directions, W)**2)
             azimuthal_smearing_tensor = torch.einsum('xu,xv->xuv',azimuthal_direction_uv, azimuthal_direction_uv)
-            detspace_splat_concentration = torch.linalg.inv( torch.linalg.inv(samplespace_splat_concentration) + azimuthal_smearing_tensor)
+            detspace_splat_concentration = torch.linalg.inv( torch.linalg.inv(detectorspace_grainshape_projections) + azimuthal_smearing_tensor)
+            intensity_spread_out_factor = torch.sqrt( torch.linalg.det(detspace_splat_concentration) / torch.linalg.det(detectorspace_grainshape_projections) )  #TODO This was (organically) vibe-coded. Check on paper if there is a simplification.
+            
 
             uv_corrds_list.append(uv_coords)
-            scalefactors_list.append(S * partiality)
+            scalefactors_list.append(S * projected_thicknes_scale_factor * partiality * intensity_spread_out_factor)
             splat_concentration_tensors_list.append(detspace_splat_concentration)
                          
 
@@ -145,6 +173,32 @@ def render_detector_frame(
         )
 
         return f
+    
+    def splat_grainshapes(
+            self,
+            mean_scattering_directions: Tensor,
+            shape_concentration_tensors: Tensor,
+            W: Tensor,
+            pixellengths: Tensor,
+    ):
+        
+        # grain_volume = torch.sqrt(1/torch.linalg.det(shape_concentration_tensors))
+        dSd = torch.einsum('xi,xij,xj->x', mean_scattering_directions, shape_concentration_tensors, mean_scattering_directions)
+
+        inner_term = shape_concentration_tensors - torch.einsum(
+            'xij,xj,xk,xkl->xil',
+            shape_concentration_tensors,
+            mean_scattering_directions,
+            mean_scattering_directions,
+            shape_concentration_tensors,
+        ) / dSd[:, None, None]
+        
+        W_scaled = W * pixellengths[:, None]
+        projected_shape_pixelunits = torch.einsum(
+            'ui,xij,vj->xuv', W_scaled, inner_term, W_scaled, 
+        )
+
+        return projected_shape_pixelunits, 1/torch.sqrt(dSd)
             
     def rasterize_on_detector(
             self,
@@ -153,7 +207,7 @@ def rasterize_on_detector(
             concentration_tensors: Tensor,
             shape: tuple,
             patch_size: int = 16,
-            splat_max_size: float = 100.0
+            splat_max_size: float = 300.0
         ):
 
 
@@ -221,12 +275,11 @@ def get_diffraction_arcsegment(self, oris, p_vectors, misori_tensors, xray_propa
         B = torch.einsum('xi,xij,xj->x', q_0_unit, T_proj, dir_scatteringplane_orth,)
         C = torch.einsum('xi,xij,xj->x', dir_scatteringplane_orth, T_proj, dir_scatteringplane_orth,)
         
-        partiality = torch.exp(-A - B**2 / C) * 2 * torch.sqrt( torch.linalg.det(misori_tensors) / D )
-        
         azim_divergence = np.sqrt(1 / C) * torch.sin(theta_angle) # TODO Check trigonometric function here
         azim_offset = B / C
         mean_scattering_directions = torch.cos(2*theta_angle)[:, None] * xray_propagation_direction[None, :]\
             + torch.sin(2*theta_angle)[:, None]*(torch.cos(azim_offset)[:, None]*dir_scatteringplane_norm + torch.sin(azim_offset)[:, None]*dir_scatteringplane_orth)
+        partiality = torch.exp(-A + B**2 / C) * 2 * torch.sqrt( torch.linalg.det(misori_tensors) / D ) / torch.sqrt(C)
 
         return mean_scattering_directions, partiality, dir_scatteringplane_orth, azim_divergence 
 

From 7750f860d677fac0c46f9c3cd0e7e44ec46d3973 Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Fri, 15 May 2026 20:46:27 +0200
Subject: [PATCH 09/17] exception for no cif file

---
 xrd_simulator/gaussian_crystal_model.py | 19 +++++++++++++------
 1 file changed, 13 insertions(+), 6 deletions(-)

diff --git a/xrd_simulator/gaussian_crystal_model.py b/xrd_simulator/gaussian_crystal_model.py
index 7273836..8250202 100644
--- a/xrd_simulator/gaussian_crystal_model.py
+++ b/xrd_simulator/gaussian_crystal_model.py
@@ -73,6 +73,7 @@ def render_detector_frame(
         sample_orientation: npt.NDArray | Tensor = np.eye(3),
         sample_rotation_during_exposure: npt.NDArray | Tensor = np.zeros(3),
         max_misorientation: float = 0.1,
+        max_grain_shape:float = 1000,
     ):
 
         sample_orientation = ensure_torch(sample_orientation)
@@ -84,7 +85,8 @@ def render_detector_frame(
         detector_origin = torch.einsum('ij,i->j', sample_orientation, ensure_torch(detector.ori))
         W = torch.einsum('ij,ui->uj', sample_orientation, ensure_torch(detector.W))
         pixellengths = torch.tensor([detector.pixel_size_y, detector.pixel_size_z])
-        
+        d = torch.dot(detector_origin, detector_norm) / torch.dot(xray_propagation_direction, detector_norm)
+
         # Simulate sample-rotation by adding a rotation to the grain misorientation
         rotation_vector = torch.einsum('ij,i->j', sample_orientation, sample_rotation_during_exposure)
         smeared_misorientation_tensors = torch.linalg.inv(torch.linalg.inv(self.misori_concentration_tensors) + torch.outer(rotation_vector, rotation_vector))
@@ -105,8 +107,12 @@ def render_detector_frame(
             sg_obj.crystal_system,
             sg_obj.Laue,
         )
-        self.phase._set_structure_factors(hkl_list)  #TODO Using private method
-        structurefactors = ensure_torch(np.sum(self.phase.structure_factors**2, axis=1))
+
+        if self.phase.path_to_cif_file is None:
+            structurefactors = torch.ones(hkl_list.shape[0])
+        else:
+            self.phase._set_structure_factors(hkl_list)  #TODO Using private method
+            structurefactors = ensure_torch(np.sum(self.phase.structure_factors**2, axis=1))
 
         uv_corrds_list = []
         splat_concentration_tensors_list = []
@@ -159,17 +165,17 @@ def render_detector_frame(
             detspace_splat_concentration = torch.linalg.inv( torch.linalg.inv(detectorspace_grainshape_projections) + azimuthal_smearing_tensor)
             intensity_spread_out_factor = torch.sqrt( torch.linalg.det(detspace_splat_concentration) / torch.linalg.det(detectorspace_grainshape_projections) )  #TODO This was (organically) vibe-coded. Check on paper if there is a simplification.
             
-
+            # Append to list
             uv_corrds_list.append(uv_coords)
             scalefactors_list.append(S * projected_thicknes_scale_factor * partiality * intensity_spread_out_factor)
             splat_concentration_tensors_list.append(detspace_splat_concentration)
-                         
 
         f = self.rasterize_on_detector(
             torch.concat(uv_corrds_list),
             torch.concat(scalefactors_list),
             torch.concat(splat_concentration_tensors_list),
             detector.shape,
+            splat_max_size= (d * max_misorientation + max_grain_shape ) / torch.min(pixellengths)
         )
 
         return f
@@ -207,7 +213,8 @@ def rasterize_on_detector(
             concentration_tensors: Tensor,
             shape: tuple,
             patch_size: int = 16,
-            splat_max_size: float = 300.0
+            splat_max_size: float = 50.0 # Todo, come pu with good rule here. 
+                                         # d times max misorientation + max grainsize
         ):
 
 

From 33fc3cbcfadda9d8885c21ed5aa4f8a7c7fd3384 Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Sat, 16 May 2026 18:00:05 +0200
Subject: [PATCH 10/17] doctrings and moving functions

---
 xrd_simulator/detector.py               |  74 ++++++++-
 xrd_simulator/gaussian_crystal_model.py | 210 ++++++++++--------------
 xrd_simulator/laue.py                   |  85 ++++++++++
 3 files changed, 241 insertions(+), 128 deletions(-)

diff --git a/xrd_simulator/detector.py b/xrd_simulator/detector.py
index 79c8e76..e41376a 100644
--- a/xrd_simulator/detector.py
+++ b/xrd_simulator/detector.py
@@ -18,6 +18,7 @@
 import numpy as np
 import numpy.typing as npt
 import torch
+from torch import Tensor
 import torch.nn.functional as F
 from scipy.special import j1
 
@@ -176,13 +177,8 @@ def __init__(
         self.lorentz_factor = use_lorentz
         self.polarization_factor = use_polarization
         self.structure_factor = use_structure_factor
-
-        # Mads' favourite parametrization
         self.shape = self.pixel_coordinates.shape[:2]
-        self.ori = self.pixel_coordinates[0,0]
-        v = torch.tensordot(self.pixel_coordinates - self.pixel_coordinates[0,0], self.ydhat, ((2,),(0,)))
-        u = torch.tensordot(self.pixel_coordinates - self.pixel_coordinates[0,0], self.zdhat, ((2,),(0,)))
-        self.W = np.stack([self.zdhat, self.ydhat])
+
 
     def save(self, path: str) -> None:
         """Save detector to disk.
@@ -404,6 +400,72 @@ def contains(self, zd: torch.Tensor, yd: torch.Tensor) -> torch.Tensor:
         """
         return (zd >= 0) & (zd <= self.zmax) & (yd >= 0) & (yd <= self.ymax)
 
+
+    def render_gaussian_splats(
+            self,
+            uv_corrds: Tensor,
+            scale_factors: Tensor,
+            concentration_tensors: Tensor,
+            patch_size: int = 16,
+            splat_max_size: float = 50.0 # Todo, come pu with good rule here. 
+                                         # d times max misorientation + max grainsize
+        ):
+        """ Basic 2D Gaussian rasterizer. Each gaussian has the expression:
+
+        .. math:: f = s \exp(-[u-u_0, v-v_0] S [u-u_0, v-v_0]^T).
+
+        Parameters
+        ----------
+        uv_corrds : Tensor
+            Centroid pixel coordinates, shape ``(N, 2)``
+        scale_factors : Tensor
+            Intensity scale factors, shape ``(N,)``
+        concentration_tensors : Tensor
+            Shape concentration tensors, shape ``(N, 2, 2)``
+        shape : tuple
+            Detector shape as a 2-length tuple
+        patch_size : int
+            For evaluation the detector is split into patches of shize `patch_size` by `patch_size`.
+        splat_max_size : float
+            Maximum size of a gaussian splat.
+
+        Returns
+        -------
+        detector_image : Tensor
+            Detector image, shape ``shape``.
+        """
+
+        shape = self.shape
+        u, v = torch.meshgrid(torch.arange(shape[0]), torch.arange(shape[1]))
+        f = torch.zeros(shape)
+
+        patch_size = 16
+        n_patches_dim1 = (shape[0]-1)//patch_size+1
+        n_patches_dim2 = (shape[1]-1)//patch_size+1
+
+        for patch_index_1 in range(n_patches_dim1):
+            for patch_index_2 in range(n_patches_dim2):
+
+                patch_slice = (slice(patch_size*patch_index_1, patch_size*(patch_index_1+1)),
+                               slice(patch_size*patch_index_2, patch_size*(patch_index_2+1)),)
+
+                patch_mean_u = patch_size*(patch_index_1+0.5)
+                patch_mean_v = patch_size*(patch_index_2+0.5)
+                
+                include_index = (uv_corrds[:, 0]-patch_mean_u)**2 + (uv_corrds[:, 1]-patch_mean_v)**2 < splat_max_size**2
+                if not torch.any(include_index):
+                    continue
+
+
+                local_coords = torch.stack([u[patch_slice][None, :, :] - uv_corrds[include_index, 0, None, None],
+                                            v[patch_slice][None, :, :] - uv_corrds[include_index, 1, None, None],
+                                            ], axis=1)
+
+                f[patch_slice] +=  torch.sum(scale_factors[include_index, None, None]\
+                    * torch.exp(- torch.einsum('xiuv,xij,xjuv->xuv' ,local_coords, concentration_tensors[include_index, :, :], local_coords)), axis=0)
+
+        return f
+
     # ------------------------------------------------------------------
     # 3. Geometry & coordinate helpers
     # ------------------------------------------------------------------
diff --git a/xrd_simulator/gaussian_crystal_model.py b/xrd_simulator/gaussian_crystal_model.py
index 8250202..4c2f4bb 100644
--- a/xrd_simulator/gaussian_crystal_model.py
+++ b/xrd_simulator/gaussian_crystal_model.py
@@ -7,6 +7,7 @@
 from xrd_simulator.phase import Phase
 from xrd_simulator.utils import ensure_torch
 from xrd_simulator.detector import Detector
+from xrd_simulator.laue import _get_diffraction_arcsegment
 
 from xfab.tools import form_a_mat, genhkl_base
 from xfab import sg
@@ -14,6 +15,25 @@
 
 class GaussianGrainish:
     """It's not a grain, it's a grain-ish.
+    
+    A grain-ish has a 3D-gaussian density distribution and a narrow (<=0.1 rad) 3D
+    orientation distribution function.
+
+    Attributes
+    ----------
+    phase : Phase
+        Object representing the crystal structure of the grain.
+    position : torch.Tensor | np.array
+        Position of the grain centroid, shape ``(3,)``
+    shape_tensor : torch.Tensor | np.array
+        Covariance tensor of the real-space grain shape. ``(3, 3,)``.
+    orientation : torch.Tensor | np.array
+        Orientation of the centroid of the ODF as a rotation matrix, shape ``(3, 3,)``
+    misorientation_tensor : torch.Tensor | np.array
+        Covariance tensor of the grain orientation in the left-hand tangent space. 
+        aka. laboratory coordinates, shape ``(3, 3,)``
+    strain_tensor : torch.Tensor | np.array
+        Strain tensor in laboratory coordinates, shape ``(3, 3,)``
     """
 
     def __init__(self,
@@ -33,17 +53,6 @@ def __init__(self,
         self.strain_tensor = strain_tensor
 
 
-levi_cita_symbol = np.zeros((3,3,3))
-levi_cita_symbol[0, 1, 2] = 1
-levi_cita_symbol[1, 2, 0] = 1
-levi_cita_symbol[2, 0, 1] = 1
-levi_cita_symbol[0, 2, 1] = -1
-levi_cita_symbol[1, 0, 2] = -1
-levi_cita_symbol[2, 1, 0] = -1
-
-levi_cita_symbol = torch.tensor(levi_cita_symbol)
-
-
 class GaussianPolycrystal:
 
     def __init__(self,
@@ -79,11 +88,14 @@ def render_detector_frame(
         sample_orientation = ensure_torch(sample_orientation)
         sample_rotation_during_exposure = ensure_torch(sample_rotation_during_exposure)
 
+        
         #Rotate detector and incident beam by inverse of sample-rotation.
         xray_propagation_direction = torch.einsum('ij,i->j', sample_orientation, ensure_torch(xray_propagation_direction) )
-        detector_norm = torch.einsum('ij,i->j', sample_orientation, ensure_torch(np.cross(detector.W[0,:], detector.W[1,:])))
-        detector_origin = torch.einsum('ij,i->j', sample_orientation, ensure_torch(detector.ori))
-        W = torch.einsum('ij,ui->uj', sample_orientation, ensure_torch(detector.W))
+        detector_origin = detector.pixel_coordinates[0,0]
+        W = np.stack([detector.zdhat, detector.ydhat])
+        detector_norm = torch.einsum('ij,i->j', sample_orientation, ensure_torch(np.cross(W[0,:], W[1,:])))
+        detector_origin = torch.einsum('ij,i->j', sample_orientation, ensure_torch(detector_origin))
+        W = torch.einsum('ij,ui->uj', sample_orientation, ensure_torch(W))
         pixellengths = torch.tensor([detector.pixel_size_y, detector.pixel_size_z])
         d = torch.dot(detector_origin, detector_norm) / torch.dot(xray_propagation_direction, detector_norm)
 
@@ -91,15 +103,14 @@ def render_detector_frame(
         rotation_vector = torch.einsum('ij,i->j', sample_orientation, sample_rotation_during_exposure)
         smeared_misorientation_tensors = torch.linalg.inv(torch.linalg.inv(self.misori_concentration_tensors) + torch.outer(rotation_vector, rotation_vector))
 
-        #Figure out what reflections are in the bragg-condition
+        #Construct some crystal and geometry information.
         A = form_a_mat(self.phase.unit_cell)
         B = 2 * np.pi * np.linalg.inv(A).T # TODO Check if the 2 pi is conventional here 
-
-        # Generate structure-factors and 
+        
         max_angle = detector._get_wrapping_cone(xray_propagation_direction, np.mean([0, 0, 0]))
         self.phase._setup_diffracting_planes(wavelength=wavelength, min_bragg_angle=0.0, max_bragg_angle=max_angle)  #TODO Using private method
+        
         sg_obj = sg.sg(sgname=self.phase.sgname)
-
         hkl_list = genhkl_base(
             self.phase.unit_cell,
             sg_obj.syscond,
@@ -107,13 +118,13 @@ def render_detector_frame(
             sg_obj.crystal_system,
             sg_obj.Laue,
         )
-
         if self.phase.path_to_cif_file is None:
             structurefactors = torch.ones(hkl_list.shape[0])
         else:
             self.phase._set_structure_factors(hkl_list)  #TODO Using private method
             structurefactors = ensure_torch(np.sum(self.phase.structure_factors**2, axis=1))
 
+        # Initialize lists of 2D gaussian splat parameters
         uv_corrds_list = []
         splat_concentration_tensors_list = []
         scalefactors_list = []
@@ -122,64 +133,70 @@ def render_detector_frame(
         for hkl, S in zip(hkl_list, structurefactors):
 
             # TODO reduce the number of symmetries evaluated for low-multiplicity peaks
+            symmetries = ensure_torch(self.phase.rot)
             n_symmetries = len(self.phase.rot)
-
-
-            # Quick test to discard reflections far from Bragg-condition
+            
+            # Cheap test to discard reflections far from Bragg-condition
             h = torch.tensor(B @ hkl)
             h_norm = torch.linalg.norm(h)
             theta_angle_unstrained = np.asin( h_norm * wavelength / 4 / np.pi )
-            p_vectors = torch.einsum('ghi,gij,sjk,k->gsh', torch.eye(3)[None,:,:] - self.strains, self.orientaions, ensure_torch(self.phase.rot), h)
+            p_vectors = torch.einsum('ghi,gij,sjk,k->gsh', torch.eye(3)[None,:,:] - self.strains, self.orientaions, symmetries, h)
             p_vectors_norm = torch.linalg.norm(p_vectors, axis=-1)
             dp = torch.einsum('i,gsi->gs', xray_propagation_direction, p_vectors) / p_vectors_norm            
             does_diffract = torch.abs( dp + torch.sin(theta_angle_unstrained) ) <  torch.abs(3 * max_misorientation * torch.cos(theta_angle_unstrained))
 
-            # Select the relevant reflections and flatten grain- and symetry-indexes.
-            orientations = torch.tile(self.orientaions[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
+            # Select the relevant reflections and flatten the grain- and symetry-indexes.
             misori_concentration_tensors = torch.tile(smeared_misorientation_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
             p_vectors = p_vectors[does_diffract]
+            shape_concentration_tensors = torch.tile(self.shape_concentration_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
 
             # Do pole-figure part of the calculation
-            mean_scattering_directions, partiality, azim_direction, azim_width = self.get_diffraction_arcsegment(
-                orientations, p_vectors, misori_concentration_tensors, xray_propagation_direction, wavelength
+            mean_scattering_directions, partialities, azim_directions, azim_widths = _get_diffraction_arcsegment(
+                p_vectors,
+                misori_concentration_tensors,
+                xray_propagation_direction,
+                wavelength,
             )
 
             # Splat grain realspace shapes (Consider using the non-strained non-azimuthally shifted directions to simplify gradients later)
-            shape_concentration_tensors = torch.tile(self.shape_concentration_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
-            detectorspace_grainshape_projections, projected_thicknes_scale_factor = self.splat_grainshapes(
+            detectorspace_grainshape_projections, projected_thicknes_scale_factors = self.splat_grainshapes(
                 mean_scattering_directions,
                 shape_concentration_tensors,
                 W,
                 pixellengths,
             )
 
-            # Direct beam is pos + mean_scatt_dir * x, detector is det_ori dot det_norm = 0 
+            # This part involves propagation from sample to detector. unclear where it belongs
+            # --------------------------------------------------------------------------------
+            # Ray-trace onto detector plane
             pos = torch.tile(self.positions[:, None, :], (1, n_symmetries, 1,))[does_diffract]
             ray_lengths = torch.einsum('xi,i->x', detector_origin[None, :] - pos, detector_norm) / torch.einsum('xi,i->x', mean_scattering_directions, detector_norm)
             point_of_detector_intersection = pos + ray_lengths[:,None] * mean_scattering_directions
-            uv_coords = torch.einsum('xi, vi, v->xv',point_of_detector_intersection - detector_origin[None, :], W, 1/pixellengths)
+            uv_coords = torch.einsum('xi, vi, v->xv',point_of_detector_intersection - detector_origin[None, :], W, 1/pixellengths) #TODO Tests with un-equal pixel sizes
 
-            #Do smearing due to angular divergence.
-            azimuthal_direction_uv = torch.einsum('xi,ui->xu', azim_direction, W) / pixellengths[None, :] * ray_lengths[:, None] * azim_width[:, None] / (1 - torch.einsum('xi,ui->xu', mean_scattering_directions, W)**2)
+            # Do smearing due to angular divergence
+            azimuthal_direction_uv = torch.einsum('xi,ui->xu', azim_directions, W) / pixellengths[None, :] * ray_lengths[:, None] * azim_widths[:, None]\
+                / (1 - torch.einsum('xi,ui->xu', mean_scattering_directions, W)**2)
             azimuthal_smearing_tensor = torch.einsum('xu,xv->xuv',azimuthal_direction_uv, azimuthal_direction_uv)
             detspace_splat_concentration = torch.linalg.inv( torch.linalg.inv(detectorspace_grainshape_projections) + azimuthal_smearing_tensor)
             intensity_spread_out_factor = torch.sqrt( torch.linalg.det(detspace_splat_concentration) / torch.linalg.det(detectorspace_grainshape_projections) )  #TODO This was (organically) vibe-coded. Check on paper if there is a simplification.
-            
+            # --------------------------------------------------------------------------------
+
             # Append to list
             uv_corrds_list.append(uv_coords)
-            scalefactors_list.append(S * projected_thicknes_scale_factor * partiality * intensity_spread_out_factor)
+            scalefactors_list.append(S * projected_thicknes_scale_factors * partialities * intensity_spread_out_factor)
             splat_concentration_tensors_list.append(detspace_splat_concentration)
 
-        f = self.rasterize_on_detector(
+        f = detector.render_gaussian_splats(
             torch.concat(uv_corrds_list),
             torch.concat(scalefactors_list),
             torch.concat(splat_concentration_tensors_list),
-            detector.shape,
             splat_max_size= (d * max_misorientation + max_grain_shape ) / torch.min(pixellengths)
         )
 
         return f
     
+
     def splat_grainshapes(
             self,
             mean_scattering_directions: Tensor,
@@ -187,7 +204,28 @@ def splat_grainshapes(
             W: Tensor,
             pixellengths: Tensor,
     ):
-        
+        """ Project the laoratory space shape-concentration-tensors of a range of grains along a the scattering directions
+        into 2D detector pixels space.
+
+        Parameters
+        ----------
+        mean_scattering_directions : Tensor
+            Scattering direction unit vectors, shape ``(N, 3)``
+        shape_concentration_tensors : Tensor
+            Shape concentration tensors in laboratory coordinates, shape ``(N, 3, 3)``
+        W : Tensor
+            Pixel-direction unit vectors stacked, shape ``(2, 3)``
+        pixellengths : Tensor
+            Pixel lengths, shape ``(2, 3)``
+            
+        Returns
+        -------
+        projected_shape_pixelunits : Tensor
+            Concentarion tensor of the projected grainshape in detector pixel units, shape ``(N, 2, 2)``  
+        projected_thicknes_scale_factors : Tensor
+            Intensity scaling factor due the projected thickness of the grain, shape ``(N,)``
+        """
+
         # grain_volume = torch.sqrt(1/torch.linalg.det(shape_concentration_tensors))
         dSd = torch.einsum('xi,xij,xj->x', mean_scattering_directions, shape_concentration_tensors, mean_scattering_directions)
 
@@ -205,91 +243,10 @@ def splat_grainshapes(
         )
 
         return projected_shape_pixelunits, 1/torch.sqrt(dSd)
-            
-    def rasterize_on_detector(
-            self,
-            uv_corrds: Tensor,
-            scale_factors: Tensor,
-            concentration_tensors: Tensor,
-            shape: tuple,
-            patch_size: int = 16,
-            splat_max_size: float = 50.0 # Todo, come pu with good rule here. 
-                                         # d times max misorientation + max grainsize
-        ):
-
-
-        u, v = torch.meshgrid(torch.arange(shape[0]), torch.arange(shape[1]))
-        f = torch.zeros(shape)
-
-        patch_size = 16
-        n_patches_dim1 = (shape[0]-1)//patch_size+1
-        n_patches_dim2 = (shape[1]-1)//patch_size+1
-
-        for patch_index_1 in range(n_patches_dim1):
-            for patch_index_2 in range(n_patches_dim2):
-
-                patch_slice = (slice(patch_size*patch_index_1, patch_size*(patch_index_1+1)),
-                               slice(patch_size*patch_index_2, patch_size*(patch_index_2+1)),)
-
-                patch_mean_u = patch_size*(patch_index_1+0.5)
-                patch_mean_v = patch_size*(patch_index_2+0.5)
-                
-                include_index = (uv_corrds[:, 0]-patch_mean_u)**2 + (uv_corrds[:, 1]-patch_mean_v)**2 < splat_max_size**2
-                if not torch.any(include_index):
-                    continue
-
-
-                local_coords = torch.stack([u[patch_slice][None, :, :] - uv_corrds[include_index, 0, None, None],
-                                            v[patch_slice][None, :, :] - uv_corrds[include_index, 1, None, None],
-                                            ], axis=1)
-
-                f[patch_slice] +=  torch.sum(scale_factors[include_index, None, None]\
-                    * torch.exp(- torch.einsum('xiuv,xij,xjuv->xuv' ,local_coords, concentration_tensors[include_index, :, :], local_coords)), axis=0)
-
-        return f
-
-    def get_diffraction_arcsegment(self, oris, p_vectors, misori_tensors, xray_propagation_direction, wavelength):
-
-        # Splat onto poelfigure
-        p_norm = torch.linalg.norm(p_vectors, axis=-1)
-        D = torch.einsum('xi,xij,xj->x', p_vectors, misori_tensors, p_vectors)/ p_norm**2
-
-        inner_part = misori_tensors - torch.einsum(
-            'xij,xj,xk,xkl->xil',
-            misori_tensors,
-            p_vectors,
-            p_vectors,
-            misori_tensors,
-        ) / D[:, None, None] / p_norm[:, None, None]**2
-        T_proj = torch.einsum(
-            'xj,ijk,xil,lmn,xm->xkn',
-            p_vectors,
-            levi_cita_symbol,
-            inner_part,
-            levi_cita_symbol,
-            p_vectors,
-        ) / p_norm[:, None, None]**2
-
-        # Compute point of "exact bragg condition" in the plane Span(k_0, p)
-        theta_angle = np.asin( p_norm * wavelength / 4 / np.pi )
-        dir_scatteringplane_norm = (p_vectors - xray_propagation_direction[None, :] * np.einsum('xi,i->x', p_vectors, xray_propagation_direction)[:, None] )
-        dir_scatteringplane_norm = dir_scatteringplane_norm / torch.linalg.norm(dir_scatteringplane_norm, axis=-1)[:, None]
-        q_0_unit = torch.cos(theta_angle)[:, None] * dir_scatteringplane_norm - torch.sin(theta_angle)[:, None] * xray_propagation_direction[None, :]
-        dir_scatteringplane_orth = torch.einsum('ijk,j,xk->xi', levi_cita_symbol, xray_propagation_direction, dir_scatteringplane_norm)
-
-        # Compute partiality, mean direction, and azimthal spread
-        A = torch.einsum('xi,xij,xj->x', q_0_unit, T_proj, q_0_unit,)
-        B = torch.einsum('xi,xij,xj->x', q_0_unit, T_proj, dir_scatteringplane_orth,)
-        C = torch.einsum('xi,xij,xj->x', dir_scatteringplane_orth, T_proj, dir_scatteringplane_orth,)
-        
-        azim_divergence = np.sqrt(1 / C) * torch.sin(theta_angle) # TODO Check trigonometric function here
-        azim_offset = B / C
-        mean_scattering_directions = torch.cos(2*theta_angle)[:, None] * xray_propagation_direction[None, :]\
-            + torch.sin(2*theta_angle)[:, None]*(torch.cos(azim_offset)[:, None]*dir_scatteringplane_norm + torch.sin(azim_offset)[:, None]*dir_scatteringplane_orth)
-        partiality = torch.exp(-A + B**2 / C) * 2 * torch.sqrt( torch.linalg.det(misori_tensors) / D ) / torch.sqrt(C)
-
-        return mean_scattering_directions, partiality, dir_scatteringplane_orth, azim_divergence 
 
+    # ------------------------------------------------------------------------------------------
+    # The methods below here are for computing polefigures, not needed for diffraction patterns.
+    # ------------------------------------------------------------------------------------------
     def render_polefigure(
         self,
         hkl: tuple[int],
@@ -336,6 +293,15 @@ def splat_onto_polefigure(
         h = torch.tensor(B @ hkl)
         h = h / torch.linalg.norm(h)
 
+        levi_cita_symbol = np.zeros((3,3,3))
+        levi_cita_symbol[0, 1, 2] = 1
+        levi_cita_symbol[1, 2, 0] = 1
+        levi_cita_symbol[2, 0, 1] = 1
+        levi_cita_symbol[0, 2, 1] = -1
+        levi_cita_symbol[1, 0, 2] = -1
+        levi_cita_symbol[2, 1, 0] = -1
+        levi_cita_symbol = torch.tensor(levi_cita_symbol)
+
         # TODO reduce the number of symmetries evaluated for low-multiplicity peaks
 
         n_symmetries = len(self.phase.rot)
diff --git a/xrd_simulator/laue.py b/xrd_simulator/laue.py
index 9881447..8ab7d20 100644
--- a/xrd_simulator/laue.py
+++ b/xrd_simulator/laue.py
@@ -7,6 +7,7 @@
 
 import numpy as np
 import torch
+from torch import Tensor
 
 torch.set_default_dtype(torch.float64)
 from xrd_simulator.utils import ensure_torch
@@ -155,6 +156,90 @@ def _find_solutions_to_tangens_half_angle_equation(
     return grains, planes, times, G
 
 
+_levi_cita_symbol = np.zeros((3,3,3))
+_levi_cita_symbol[0, 1, 2] = 1
+_levi_cita_symbol[1, 2, 0] = 1
+_levi_cita_symbol[2, 0, 1] = 1
+_levi_cita_symbol[0, 2, 1] = -1
+_levi_cita_symbol[1, 0, 2] = -1
+_levi_cita_symbol[2, 1, 0] = -1
+_levi_cita_symbol = torch.tensor(_levi_cita_symbol)
+
+
+def _get_diffraction_arcsegment(
+        p_vectors: Tensor,
+        T: Tensor,
+        xray_propagation_direction: Tensor,
+        wavelength: Tensor,
+    ):
+    """ Given a range of orientation-concentration-tensors and reflection-information, compute the propeties
+    of the scattered beam.
+
+    Parameters
+    ----------
+    p_vectors : Tensor
+        Lattice vectors in lattice reference frame (not hkl-tuples), shape ``(N, 3)``
+        Uses the convention with
+        .. math:: |h| = 4 \pi\sin\theta / \lambda
+    T : Tensor
+        Lab-space orientation concentration tensors, shape ``(N, 3, 3)``
+    xray_propagation_direction : Tensor
+        Incident x-ray propagation direction unit vector, shape ``(3,)``
+    wavelength : float
+        
+
+    Returns
+    -------
+    mean_scattering_directions : Tensor
+        Propagation direction unit vectors of the center of the scattered beams, shape ``(N, 3,)``
+    partialities : Tenor
+        Intensity of the scattered beams per unit-volume sample, shape ``(N,)``
+    dir_scatteringplane_orth : Tensor
+        Dispersion direction unit vectors of the scattered beams, shape ``(N, 3,)``
+    azimuthal_divergence : Tensor
+        Divergence of the scattered beams in radians, shape ``(N,)``        
+    """
+
+    # Splat onto poelfigure
+    p_norm = torch.linalg.norm(p_vectors, axis=-1)
+    D = torch.einsum('xi,xij,xj->x', p_vectors, T, p_vectors)/ p_norm**2
+
+    inner_part = T - torch.einsum(
+        'xij,xj,xk,xkl->xil',
+        T,
+        p_vectors,
+        p_vectors,
+        T,
+    ) / D[:, None, None] / p_norm[:, None, None]**2
+    T_proj = torch.einsum(
+        'xj,ijk,xil,lmn,xm->xkn',
+        p_vectors,
+        _levi_cita_symbol,
+        inner_part,
+        _levi_cita_symbol,
+        p_vectors,
+    ) / p_norm[:, None, None]**2
+
+    # Compute point of "exact bragg condition" in the plane Span(k_0, p)
+    theta_angle = np.asin( p_norm * wavelength / 4 / np.pi )
+    dir_scatteringplane_norm = (p_vectors - xray_propagation_direction[None, :] * np.einsum('xi,i->x', p_vectors, xray_propagation_direction)[:, None] )
+    dir_scatteringplane_norm = dir_scatteringplane_norm / torch.linalg.norm(dir_scatteringplane_norm, axis=-1)[:, None]
+    q_0_unit = torch.cos(theta_angle)[:, None] * dir_scatteringplane_norm - torch.sin(theta_angle)[:, None] * xray_propagation_direction[None, :]
+    dir_scatteringplane_orth = torch.einsum('ijk,j,xk->xi', _levi_cita_symbol, xray_propagation_direction, dir_scatteringplane_norm)
+
+    # Compute partiality, mean direction, and azimthal spread
+    A = torch.einsum('xi,xij,xj->x', q_0_unit, T_proj, q_0_unit,)
+    B = torch.einsum('xi,xij,xj->x', q_0_unit, T_proj, dir_scatteringplane_orth,)
+    C = torch.einsum('xi,xij,xj->x', dir_scatteringplane_orth, T_proj, dir_scatteringplane_orth,)
+    
+    azimuthal_divergence = np.sqrt(1 / C) * torch.sin( 2 * theta_angle )
+    azim_offset = B / C
+    mean_scattering_directions = torch.cos(2*theta_angle)[:, None] * xray_propagation_direction[None, :]\
+        + torch.sin(2*theta_angle)[:, None]*(torch.cos(azim_offset)[:, None]*dir_scatteringplane_norm + torch.sin(azim_offset)[:, None]*dir_scatteringplane_orth)
+    partialities = torch.exp(-A + B**2 / C) * 2 * torch.sqrt( torch.linalg.det(T) / D ) / torch.sqrt(C)
+
+    return mean_scattering_directions, partialities, dir_scatteringplane_orth, azimuthal_divergence
+
 # ==============================================================================
 # DEPRECATED METHODS - TO BE REMOVED IN FUTURE VERSION
 # ==============================================================================

From c692df0099f40f17a4f35316806d57fcc7b592e2 Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Sat, 16 May 2026 18:01:30 +0200
Subject: [PATCH 11/17] hotfix

---
 xrd_simulator/detector.py | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/xrd_simulator/detector.py b/xrd_simulator/detector.py
index e41376a..66388ca 100644
--- a/xrd_simulator/detector.py
+++ b/xrd_simulator/detector.py
@@ -422,8 +422,6 @@ def render_gaussian_splats(
             Intensity scale factors, shape ``(N,)``
         concentration_tensors : Tensor
             Shape concentration tensors, shape ``(N, 2, 2)``
-        shape : tuple
-            Detector shape as a 2-length tuple
         patch_size : int
             For evaluation the detector is split into patches of shize `patch_size` by `patch_size`.
         splat_max_size : float
@@ -432,7 +430,7 @@ def render_gaussian_splats(
         Returns
         -------
         detector_image : Tensor
-            Detector image, shape ``shape``.
+            Detector image, shape ``self.shape``.
         """
 
         shape = self.shape

From c0aabd0491cbbd7ae2043b4ebad68901803cedee Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Sat, 16 May 2026 22:17:26 +0200
Subject: [PATCH 12/17] xfab uses warren's upper triangular B matrices...

---
 xrd_simulator/gaussian_crystal_model.py | 121 ++++++++++++------------
 1 file changed, 62 insertions(+), 59 deletions(-)

diff --git a/xrd_simulator/gaussian_crystal_model.py b/xrd_simulator/gaussian_crystal_model.py
index 4c2f4bb..ec0b0c3 100644
--- a/xrd_simulator/gaussian_crystal_model.py
+++ b/xrd_simulator/gaussian_crystal_model.py
@@ -9,7 +9,7 @@
 from xrd_simulator.detector import Detector
 from xrd_simulator.laue import _get_diffraction_arcsegment
 
-from xfab.tools import form_a_mat, genhkl_base
+from xfab.tools import form_b_mat, genhkl_base
 from xfab import sg
 
 
@@ -104,8 +104,9 @@ def render_detector_frame(
         smeared_misorientation_tensors = torch.linalg.inv(torch.linalg.inv(self.misori_concentration_tensors) + torch.outer(rotation_vector, rotation_vector))
 
         #Construct some crystal and geometry information.
-        A = form_a_mat(self.phase.unit_cell)
-        B = 2 * np.pi * np.linalg.inv(A).T # TODO Check if the 2 pi is conventional here 
+        # A = form_a_mat(self.phase.unit_cell)
+        # B = 2 * np.pi * np.linalg.inv(A).T # TODO Check if the 2 pi is conventional here 
+        B = form_b_mat(self.phase.unit_cell)
         
         max_angle = detector._get_wrapping_cone(xray_propagation_direction, np.mean([0, 0, 0]))
         self.phase._setup_diffracting_planes(wavelength=wavelength, min_bragg_angle=0.0, max_bragg_angle=max_angle)  #TODO Using private method
@@ -131,61 +132,62 @@ def render_detector_frame(
 
         # Loop over reflection orders
         for hkl, S in zip(hkl_list, structurefactors):
+            for friedel_sign in [1, -1]:
 
-            # TODO reduce the number of symmetries evaluated for low-multiplicity peaks
-            symmetries = ensure_torch(self.phase.rot)
-            n_symmetries = len(self.phase.rot)
-            
-            # Cheap test to discard reflections far from Bragg-condition
-            h = torch.tensor(B @ hkl)
-            h_norm = torch.linalg.norm(h)
-            theta_angle_unstrained = np.asin( h_norm * wavelength / 4 / np.pi )
-            p_vectors = torch.einsum('ghi,gij,sjk,k->gsh', torch.eye(3)[None,:,:] - self.strains, self.orientaions, symmetries, h)
-            p_vectors_norm = torch.linalg.norm(p_vectors, axis=-1)
-            dp = torch.einsum('i,gsi->gs', xray_propagation_direction, p_vectors) / p_vectors_norm            
-            does_diffract = torch.abs( dp + torch.sin(theta_angle_unstrained) ) <  torch.abs(3 * max_misorientation * torch.cos(theta_angle_unstrained))
-
-            # Select the relevant reflections and flatten the grain- and symetry-indexes.
-            misori_concentration_tensors = torch.tile(smeared_misorientation_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
-            p_vectors = p_vectors[does_diffract]
-            shape_concentration_tensors = torch.tile(self.shape_concentration_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
-
-            # Do pole-figure part of the calculation
-            mean_scattering_directions, partialities, azim_directions, azim_widths = _get_diffraction_arcsegment(
-                p_vectors,
-                misori_concentration_tensors,
-                xray_propagation_direction,
-                wavelength,
-            )
-
-            # Splat grain realspace shapes (Consider using the non-strained non-azimuthally shifted directions to simplify gradients later)
-            detectorspace_grainshape_projections, projected_thicknes_scale_factors = self.splat_grainshapes(
-                mean_scattering_directions,
-                shape_concentration_tensors,
-                W,
-                pixellengths,
-            )
-
-            # This part involves propagation from sample to detector. unclear where it belongs
-            # --------------------------------------------------------------------------------
-            # Ray-trace onto detector plane
-            pos = torch.tile(self.positions[:, None, :], (1, n_symmetries, 1,))[does_diffract]
-            ray_lengths = torch.einsum('xi,i->x', detector_origin[None, :] - pos, detector_norm) / torch.einsum('xi,i->x', mean_scattering_directions, detector_norm)
-            point_of_detector_intersection = pos + ray_lengths[:,None] * mean_scattering_directions
-            uv_coords = torch.einsum('xi, vi, v->xv',point_of_detector_intersection - detector_origin[None, :], W, 1/pixellengths) #TODO Tests with un-equal pixel sizes
-
-            # Do smearing due to angular divergence
-            azimuthal_direction_uv = torch.einsum('xi,ui->xu', azim_directions, W) / pixellengths[None, :] * ray_lengths[:, None] * azim_widths[:, None]\
-                / (1 - torch.einsum('xi,ui->xu', mean_scattering_directions, W)**2)
-            azimuthal_smearing_tensor = torch.einsum('xu,xv->xuv',azimuthal_direction_uv, azimuthal_direction_uv)
-            detspace_splat_concentration = torch.linalg.inv( torch.linalg.inv(detectorspace_grainshape_projections) + azimuthal_smearing_tensor)
-            intensity_spread_out_factor = torch.sqrt( torch.linalg.det(detspace_splat_concentration) / torch.linalg.det(detectorspace_grainshape_projections) )  #TODO This was (organically) vibe-coded. Check on paper if there is a simplification.
-            # --------------------------------------------------------------------------------
-
-            # Append to list
-            uv_corrds_list.append(uv_coords)
-            scalefactors_list.append(S * projected_thicknes_scale_factors * partialities * intensity_spread_out_factor)
-            splat_concentration_tensors_list.append(detspace_splat_concentration)
+                # TODO reduce the number of symmetries evaluated for low-multiplicity peaks
+                symmetries = ensure_torch(self.phase.rot)
+                n_symmetries = len(self.phase.rot)
+                
+                # Cheap test to discard reflections far from Bragg-condition
+                h = friedel_sign * torch.tensor(B @ hkl)
+                h_norm = torch.linalg.norm(h)
+                theta_angle_unstrained = np.asin( h_norm * wavelength / 4 / np.pi )
+                p_vectors = torch.einsum('ghi,gij,sjk,k->gsh', torch.eye(3)[None,:,:] - self.strains, self.orientaions, symmetries, h)
+                p_vectors_norm = torch.linalg.norm(p_vectors, axis=-1)
+                dp = torch.einsum('i,gsi->gs', xray_propagation_direction, p_vectors) / p_vectors_norm            
+                does_diffract = torch.abs( dp + torch.sin(theta_angle_unstrained) ) <  torch.abs(3 * max_misorientation * torch.cos(theta_angle_unstrained))
+
+                # Select the relevant reflections and flatten the grain- and symetry-indexes.
+                misori_concentration_tensors = torch.tile(smeared_misorientation_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
+                p_vectors = p_vectors[does_diffract]
+                shape_concentration_tensors = torch.tile(self.shape_concentration_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
+
+                # Do pole-figure part of the calculation
+                mean_scattering_directions, partialities, azim_directions, azim_widths = _get_diffraction_arcsegment(
+                    p_vectors,
+                    misori_concentration_tensors,
+                    xray_propagation_direction,
+                    wavelength,
+                )
+
+                # Splat grain realspace shapes (Consider using the non-strained non-azimuthally shifted directions to simplify gradients later)
+                detectorspace_grainshape_projections, projected_thicknes_scale_factors = self.splat_grainshapes(
+                    mean_scattering_directions,
+                    shape_concentration_tensors,
+                    W,
+                    pixellengths,
+                )
+
+                # This part involves propagation from sample to detector. unclear where it belongs
+                # --------------------------------------------------------------------------------
+                # Ray-trace onto detector plane
+                pos = torch.tile(self.positions[:, None, :], (1, n_symmetries, 1,))[does_diffract]
+                ray_lengths = torch.einsum('xi,i->x', detector_origin[None, :] - pos, detector_norm) / torch.einsum('xi,i->x', mean_scattering_directions, detector_norm)
+                point_of_detector_intersection = pos + ray_lengths[:,None] * mean_scattering_directions
+                uv_coords = torch.einsum('xi, vi, v->xv',point_of_detector_intersection - detector_origin[None, :], W, 1/pixellengths) #TODO Tests with un-equal pixel sizes
+
+                # Do smearing due to angular divergence
+                azimuthal_direction_uv = torch.einsum('xi,ui->xu', azim_directions, W) / pixellengths[None, :] * ray_lengths[:, None] * azim_widths[:, None]\
+                    / (1 - torch.einsum('xi,ui->xu', mean_scattering_directions, W)**2)
+                azimuthal_smearing_tensor = torch.einsum('xu,xv->xuv',azimuthal_direction_uv, azimuthal_direction_uv)
+                detspace_splat_concentration = torch.linalg.inv( torch.linalg.inv(detectorspace_grainshape_projections) + azimuthal_smearing_tensor)
+                intensity_spread_out_factor = torch.sqrt( torch.linalg.det(detspace_splat_concentration) / torch.linalg.det(detectorspace_grainshape_projections) )  #TODO This was (organically) vibe-coded. Check on paper if there is a simplification.
+                # --------------------------------------------------------------------------------
+
+                # Append to list
+                uv_corrds_list.append(uv_coords)
+                scalefactors_list.append(S * projected_thicknes_scale_factors * partialities * intensity_spread_out_factor)
+                splat_concentration_tensors_list.append(detspace_splat_concentration)
 
         f = detector.render_gaussian_splats(
             torch.concat(uv_corrds_list),
@@ -288,8 +290,9 @@ def splat_onto_polefigure(
         ):
 
 
-        A = form_a_mat(self.phase.unit_cell)
-        B = 2 * np.pi * np.linalg.inv(A).T
+        # A = form_a_mat(self.phase.unit_cell)
+        # B = 2 * np.pi * np.linalg.inv(A).T
+        B = form_b_mat(self.phase.unit_cell)
         h = torch.tensor(B @ hkl)
         h = h / torch.linalg.norm(h)
 

From 7fec52c1fbb6772c8fc620d7c4bc3a1bd4d6f29f Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Tue, 26 May 2026 16:16:20 +0200
Subject: [PATCH 13/17] Gaussian beam and intersection with gaussian grains

---
 xrd_simulator/beam.py | 76 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 76 insertions(+)

diff --git a/xrd_simulator/beam.py b/xrd_simulator/beam.py
index 8724621..17b4b60 100644
--- a/xrd_simulator/beam.py
+++ b/xrd_simulator/beam.py
@@ -448,3 +448,79 @@ def _get_proximity_intervals(
                 all_intersections.append(merged_intersection)
 
         return all_intersections
+
+
+class GaussianBeam:
+
+    def __init__(
+        self,
+        beam_centroid_position,
+        xray_propagation_direction,
+        wavelength,
+        long_axis_width=None,
+        long_axis_direction=None,
+        short_axis_width=None,
+        short_axis_direction=None,
+    ):
+        
+        # Convert to torch tensors first, then normalize using torch operations
+        self.xray_dir = ensure_torch(xray_propagation_direction)
+        self.xray_dir = self.xray_dir / torch.linalg.norm(self.xray_dir)
+        self.beam_center = ensure_torch(beam_centroid_position)
+        self.beam_center = self.beam_center - torch.dot(self.xray_dir, self.beam_center) * self.xray_dir
+        self.wavelength = wavelength
+
+        # If no shape information is given, assume wide-field illumination
+        if long_axis_width is None:
+            self.beam_concentration_tensor = torch.zeros((3, 3,))
+            self.max_width = np.inf
+
+        # If only one width is given, assume circular beam.
+        elif long_axis_direction is None and short_axis_width is None and short_axis_direction is None:
+            
+            self.beam_concentration_tensor = (torch.eye(3) - torch.outer(self.xray_dir, self.xray_dir)) * 1 / long_axis_width**2
+            self.max_width = long_axis_width
+
+        # If all parameters are given, full 2D beamshape
+        else:
+            raise NotImplementedError
+
+    def _intersect(
+            self,
+            positions,
+            shape_concentration_tensors,
+            rotation,
+            translation,
+            max_grain_size,
+        ):
+
+        # Rotate beam by inverse sample rotation
+        xray_propagation_direction = torch.einsum('ij,i->j', rotation, self.xray_dir )
+        beam_center = torch.einsum('ij,i->j', rotation, self.beam_center - translation ) #TODO Check how to compose translation and rotations
+        beam_concentration_tensor = torch.einsum('ij,ik,kl->il', rotation, self.beam_concentration_tensor, rotation) 
+
+        # Filter by distance to beam
+        a_minus_p = positions - beam_center[None, :]
+        proj_onto_line = torch.einsum('gi,i->g', a_minus_p, xray_propagation_direction)[:, None] * xray_propagation_direction[None, :] 
+        distance_from_beam = torch.linalg.norm(a_minus_p - proj_onto_line, axis=1)
+        grains_hit_indexvector = distance_from_beam < 3 * (self.max_width + max_grain_size) 
+
+        # Compute the overlap of the beam with each grain
+        intersection_shape_concentration_tensors = beam_concentration_tensor[None, :, :] + shape_concentration_tensors[grains_hit_indexvector, :, :]
+        B_plus_S_inv = torch.linalg.inv(intersection_shape_concentration_tensors)
+        B_b_plus_S_c = torch.einsum('ij,j->i', beam_concentration_tensor, beam_center)[None, :]\
+            + torch.einsum('gij,gj->gi', shape_concentration_tensors[grains_hit_indexvector, :, :], positions[grains_hit_indexvector, :])
+        intersection_positions = torch.einsum('gij,gj->gi', B_plus_S_inv, B_b_plus_S_c)
+        
+        # Beam intensity term.
+        #TODO This can maybe be simplified.
+        bBb = torch.einsum('i,ij,j', beam_center, beam_concentration_tensor, beam_center)
+        cSc = torch.einsum(
+            'gi,gij,gj->g', positions[grains_hit_indexvector, :],
+            shape_concentration_tensors[grains_hit_indexvector, :, :],
+            positions[grains_hit_indexvector, :]
+            )
+        C = torch.einsum('gi,gij,gj->g', B_b_plus_S_c, B_plus_S_inv, B_b_plus_S_c)
+        beam_intensity_factors = torch.exp(C - bBb - cSc)
+
+        return intersection_positions, intersection_shape_concentration_tensors, beam_intensity_factors, grains_hit_indexvector

From 953b36d28f5374d609ea1e30f0885f7e55045301 Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Tue, 26 May 2026 20:10:51 +0200
Subject: [PATCH 14/17] beam intersection implemented

---
 xrd_simulator/beam.py                   |  2 +-
 xrd_simulator/gaussian_crystal_model.py | 52 ++++++++++++++++---------
 2 files changed, 34 insertions(+), 20 deletions(-)

diff --git a/xrd_simulator/beam.py b/xrd_simulator/beam.py
index 17b4b60..dfb5317 100644
--- a/xrd_simulator/beam.py
+++ b/xrd_simulator/beam.py
@@ -497,7 +497,7 @@ def _intersect(
         # Rotate beam by inverse sample rotation
         xray_propagation_direction = torch.einsum('ij,i->j', rotation, self.xray_dir )
         beam_center = torch.einsum('ij,i->j', rotation, self.beam_center - translation ) #TODO Check how to compose translation and rotations
-        beam_concentration_tensor = torch.einsum('ij,ik,kl->il', rotation, self.beam_concentration_tensor, rotation) 
+        beam_concentration_tensor = torch.einsum('ij,ik,kl', rotation, self.beam_concentration_tensor, rotation) 
 
         # Filter by distance to beam
         a_minus_p = positions - beam_center[None, :]
diff --git a/xrd_simulator/gaussian_crystal_model.py b/xrd_simulator/gaussian_crystal_model.py
index ec0b0c3..51b642c 100644
--- a/xrd_simulator/gaussian_crystal_model.py
+++ b/xrd_simulator/gaussian_crystal_model.py
@@ -8,6 +8,7 @@
 from xrd_simulator.utils import ensure_torch
 from xrd_simulator.detector import Detector
 from xrd_simulator.laue import _get_diffraction_arcsegment
+from xrd_simulator.beam import GaussianBeam
 
 from xfab.tools import form_b_mat, genhkl_base
 from xfab import sg
@@ -52,11 +53,12 @@ def __init__(self,
         self.misorientation_tensor = misorientation_tensor
         self.strain_tensor = strain_tensor
 
-
 class GaussianPolycrystal:
 
     def __init__(self,
         grain_list: list[GaussianGrainish],
+        max_grain_size: float = 1000.0,
+        max_misorientation: float = 0.1, 
     ):
         
         phases_list = list(set([grain.phase for grain in grain_list]))
@@ -64,6 +66,8 @@ def __init__(self,
         assert n_phases == 1
 
         self.n_grains = len(grain_list)
+        self.max_grain_size = max_grain_size
+        self.max_misorientation = max_misorientation
         self.phase = phases_list[0]
 
         self.positions = torch.stack([ensure_torch(grain.position) for grain in grain_list])
@@ -76,18 +80,17 @@ def __init__(self,
 
     def render_detector_frame(
         self,
+        beam: GaussianBeam,
         detector: Detector,
-        xray_propagation_direction: npt.NDArray | Tensor,
-        wavelength: float,
         sample_orientation: npt.NDArray | Tensor = np.eye(3),
+        sample_translation: npt.NDArray | Tensor = np.zeros(3),
         sample_rotation_during_exposure: npt.NDArray | Tensor = np.zeros(3),
-        max_misorientation: float = 0.1,
-        max_grain_shape:float = 1000,
     ):
 
+        xray_propagation_direction = beam.xray_dir
+        wavelength = beam.wavelength
         sample_orientation = ensure_torch(sample_orientation)
         sample_rotation_during_exposure = ensure_torch(sample_rotation_during_exposure)
-
         
         #Rotate detector and incident beam by inverse of sample-rotation.
         xray_propagation_direction = torch.einsum('ij,i->j', sample_orientation, ensure_torch(xray_propagation_direction) )
@@ -99,13 +102,22 @@ def render_detector_frame(
         pixellengths = torch.tensor([detector.pixel_size_y, detector.pixel_size_z])
         d = torch.dot(detector_origin, detector_norm) / torch.dot(xray_propagation_direction, detector_norm)
 
+        #Compute intersection of grains and beam
+        intersection_pos, intersection_shape_concentration_tensors, beam_intensity_factors, grains_hit\
+            = beam._intersect(
+            ensure_torch(self.positions),
+            ensure_torch(self.shape_concentration_tensors),
+            sample_orientation,
+            sample_translation,
+            self.max_grain_size,
+        )
+
         # Simulate sample-rotation by adding a rotation to the grain misorientation
+        sample_rotation_during_exposure = ensure_torch(sample_rotation_during_exposure)
         rotation_vector = torch.einsum('ij,i->j', sample_orientation, sample_rotation_during_exposure)
-        smeared_misorientation_tensors = torch.linalg.inv(torch.linalg.inv(self.misori_concentration_tensors) + torch.outer(rotation_vector, rotation_vector))
+        smeared_misorientation_tensors = torch.linalg.inv(torch.linalg.inv(self.misori_concentration_tensors[grains_hit]) + torch.outer(rotation_vector, rotation_vector))
 
         #Construct some crystal and geometry information.
-        # A = form_a_mat(self.phase.unit_cell)
-        # B = 2 * np.pi * np.linalg.inv(A).T # TODO Check if the 2 pi is conventional here 
         B = form_b_mat(self.phase.unit_cell)
         
         max_angle = detector._get_wrapping_cone(xray_propagation_direction, np.mean([0, 0, 0]))
@@ -134,7 +146,8 @@ def render_detector_frame(
         for hkl, S in zip(hkl_list, structurefactors):
             for friedel_sign in [1, -1]:
 
-                # TODO reduce the number of symmetries evaluated for low-multiplicity peaks
+                #TODO reduce the number of symmetries evaluated for low-multiplicity peaks
+                #TODO Check if structure factors include multiplicity
                 symmetries = ensure_torch(self.phase.rot)
                 n_symmetries = len(self.phase.rot)
                 
@@ -142,15 +155,15 @@ def render_detector_frame(
                 h = friedel_sign * torch.tensor(B @ hkl)
                 h_norm = torch.linalg.norm(h)
                 theta_angle_unstrained = np.asin( h_norm * wavelength / 4 / np.pi )
-                p_vectors = torch.einsum('ghi,gij,sjk,k->gsh', torch.eye(3)[None,:,:] - self.strains, self.orientaions, symmetries, h)
+                p_vectors = torch.einsum('ghi,gij,sjk,k->gsh', torch.eye(3)[None,:,:] - self.strains[grains_hit], self.orientaions[grains_hit], symmetries, h)
                 p_vectors_norm = torch.linalg.norm(p_vectors, axis=-1)
                 dp = torch.einsum('i,gsi->gs', xray_propagation_direction, p_vectors) / p_vectors_norm            
-                does_diffract = torch.abs( dp + torch.sin(theta_angle_unstrained) ) <  torch.abs(3 * max_misorientation * torch.cos(theta_angle_unstrained))
+                does_diffract = torch.abs( dp + torch.sin(theta_angle_unstrained) ) <  torch.abs(3 * (self.max_misorientation+torch.linalg.norm(sample_rotation_during_exposure)) * torch.cos(theta_angle_unstrained))
 
                 # Select the relevant reflections and flatten the grain- and symetry-indexes.
-                misori_concentration_tensors = torch.tile(smeared_misorientation_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
+                misori_concentration_tensors = torch.tile(smeared_misorientation_tensors[grains_hit, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
                 p_vectors = p_vectors[does_diffract]
-                shape_concentration_tensors = torch.tile(self.shape_concentration_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
+                shape_concentration_tensors = torch.tile(intersection_shape_concentration_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
 
                 # Do pole-figure part of the calculation
                 mean_scattering_directions, partialities, azim_directions, azim_widths = _get_diffraction_arcsegment(
@@ -169,9 +182,9 @@ def render_detector_frame(
                 )
 
                 # This part involves propagation from sample to detector. unclear where it belongs
-                # --------------------------------------------------------------------------------
+                # ----------------------------------------------------------------------------------------------------------
                 # Ray-trace onto detector plane
-                pos = torch.tile(self.positions[:, None, :], (1, n_symmetries, 1,))[does_diffract]
+                pos = torch.tile(intersection_pos[:, None, :], (1, n_symmetries, 1,))[does_diffract]
                 ray_lengths = torch.einsum('xi,i->x', detector_origin[None, :] - pos, detector_norm) / torch.einsum('xi,i->x', mean_scattering_directions, detector_norm)
                 point_of_detector_intersection = pos + ray_lengths[:,None] * mean_scattering_directions
                 uv_coords = torch.einsum('xi, vi, v->xv',point_of_detector_intersection - detector_origin[None, :], W, 1/pixellengths) #TODO Tests with un-equal pixel sizes
@@ -182,18 +195,19 @@ def render_detector_frame(
                 azimuthal_smearing_tensor = torch.einsum('xu,xv->xuv',azimuthal_direction_uv, azimuthal_direction_uv)
                 detspace_splat_concentration = torch.linalg.inv( torch.linalg.inv(detectorspace_grainshape_projections) + azimuthal_smearing_tensor)
                 intensity_spread_out_factor = torch.sqrt( torch.linalg.det(detspace_splat_concentration) / torch.linalg.det(detectorspace_grainshape_projections) )  #TODO This was (organically) vibe-coded. Check on paper if there is a simplification.
-                # --------------------------------------------------------------------------------
+                # ----------------------------------------------------------------------------------------------------------
 
                 # Append to list
                 uv_corrds_list.append(uv_coords)
-                scalefactors_list.append(S * projected_thicknes_scale_factors * partialities * intensity_spread_out_factor)
+                beam_intensity_factors_insideloop = torch.tile(beam_intensity_factors[:, None], (1, n_symmetries))[does_diffract]
+                scalefactors_list.append(S * projected_thicknes_scale_factors * partialities * intensity_spread_out_factor * beam_intensity_factors_insideloop)
                 splat_concentration_tensors_list.append(detspace_splat_concentration)
 
         f = detector.render_gaussian_splats(
             torch.concat(uv_corrds_list),
             torch.concat(scalefactors_list),
             torch.concat(splat_concentration_tensors_list),
-            splat_max_size= (d * max_misorientation + max_grain_shape ) / torch.min(pixellengths)
+            splat_max_size= (d * (self.max_misorientation+torch.linalg.norm(sample_rotation_during_exposure)) + self.max_grain_size ) / torch.min(pixellengths)
         )
 
         return f

From 2a41b11d135e3bd0ab67de4941c76b94e175b9d7 Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Sat, 30 May 2026 14:58:42 +0200
Subject: [PATCH 15/17] Rotate and translate sample

---
 xrd_simulator/detector.py               |  6 +-
 xrd_simulator/gaussian_crystal_model.py | 73 +++++++++++++++++++++++--
 2 files changed, 69 insertions(+), 10 deletions(-)

diff --git a/xrd_simulator/detector.py b/xrd_simulator/detector.py
index 66388ca..702f955 100644
--- a/xrd_simulator/detector.py
+++ b/xrd_simulator/detector.py
@@ -406,9 +406,8 @@ def render_gaussian_splats(
             uv_corrds: Tensor,
             scale_factors: Tensor,
             concentration_tensors: Tensor,
-            patch_size: int = 16,
-            splat_max_size: float = 50.0 # Todo, come pu with good rule here. 
-                                         # d times max misorientation + max grainsize
+            patch_size: int = 64,
+            splat_max_size: float = 50.0,
         ):
         """ Basic 2D Gaussian rasterizer. Each gaussian has the expression:
 
@@ -437,7 +436,6 @@ def render_gaussian_splats(
         u, v = torch.meshgrid(torch.arange(shape[0]), torch.arange(shape[1]))
         f = torch.zeros(shape)
 
-        patch_size = 16
         n_patches_dim1 = (shape[0]-1)//patch_size+1
         n_patches_dim2 = (shape[1]-1)//patch_size+1
 
diff --git a/xrd_simulator/gaussian_crystal_model.py b/xrd_simulator/gaussian_crystal_model.py
index 51b642c..bbc3db3 100644
--- a/xrd_simulator/gaussian_crystal_model.py
+++ b/xrd_simulator/gaussian_crystal_model.py
@@ -9,11 +9,14 @@
 from xrd_simulator.detector import Detector
 from xrd_simulator.laue import _get_diffraction_arcsegment
 from xrd_simulator.beam import GaussianBeam
+from xrd_simulator.motion import RigidBodyMotion
 
 from xfab.tools import form_b_mat, genhkl_base
 from xfab import sg
 
 
+import time
+
 class GaussianGrainish:
     """It's not a grain, it's a grain-ish.
     
@@ -85,8 +88,12 @@ def render_detector_frame(
         sample_orientation: npt.NDArray | Tensor = np.eye(3),
         sample_translation: npt.NDArray | Tensor = np.zeros(3),
         sample_rotation_during_exposure: npt.NDArray | Tensor = np.zeros(3),
+        timing=False
     ):
 
+        if timing:
+            t0 = time.time()
+
         xray_propagation_direction = beam.xray_dir
         wavelength = beam.wavelength
         sample_orientation = ensure_torch(sample_orientation)
@@ -112,6 +119,7 @@ def render_detector_frame(
             self.max_grain_size,
         )
 
+
         # Simulate sample-rotation by adding a rotation to the grain misorientation
         sample_rotation_during_exposure = ensure_torch(sample_rotation_during_exposure)
         rotation_vector = torch.einsum('ij,i->j', sample_orientation, sample_rotation_during_exposure)
@@ -137,6 +145,7 @@ def render_detector_frame(
             self.phase._set_structure_factors(hkl_list)  #TODO Using private method
             structurefactors = ensure_torch(np.sum(self.phase.structure_factors**2, axis=1))
 
+
         # Initialize lists of 2D gaussian splat parameters
         uv_corrds_list = []
         splat_concentration_tensors_list = []
@@ -161,10 +170,12 @@ def render_detector_frame(
                 does_diffract = torch.abs( dp + torch.sin(theta_angle_unstrained) ) <  torch.abs(3 * (self.max_misorientation+torch.linalg.norm(sample_rotation_during_exposure)) * torch.cos(theta_angle_unstrained))
 
                 # Select the relevant reflections and flatten the grain- and symetry-indexes.
-                misori_concentration_tensors = torch.tile(smeared_misorientation_tensors[grains_hit, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
+                misori_concentration_tensors = torch.tile(smeared_misorientation_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
                 p_vectors = p_vectors[does_diffract]
                 shape_concentration_tensors = torch.tile(intersection_shape_concentration_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
 
+
+
                 # Do pole-figure part of the calculation
                 mean_scattering_directions, partialities, azim_directions, azim_widths = _get_diffraction_arcsegment(
                     p_vectors,
@@ -173,6 +184,8 @@ def render_detector_frame(
                     wavelength,
                 )
 
+
+
                 # Splat grain realspace shapes (Consider using the non-strained non-azimuthally shifted directions to simplify gradients later)
                 detectorspace_grainshape_projections, projected_thicknes_scale_factors = self.splat_grainshapes(
                     mean_scattering_directions,
@@ -203,6 +216,10 @@ def render_detector_frame(
                 scalefactors_list.append(S * projected_thicknes_scale_factors * partialities * intensity_spread_out_factor * beam_intensity_factors_insideloop)
                 splat_concentration_tensors_list.append(detspace_splat_concentration)
 
+        if timing:
+            print(f'Splatting took {time.time()-t0}')
+            t0 = time.time()
+
         f = detector.render_gaussian_splats(
             torch.concat(uv_corrds_list),
             torch.concat(scalefactors_list),
@@ -210,15 +227,19 @@ def render_detector_frame(
             splat_max_size= (d * (self.max_misorientation+torch.linalg.norm(sample_rotation_during_exposure)) + self.max_grain_size ) / torch.min(pixellengths)
         )
 
+        if timing:
+            print(f'Rasterization took {time.time()-t0}')
+            t0 = time.time()
+
         return f
     
 
     def splat_grainshapes(
-            self,
-            mean_scattering_directions: Tensor,
-            shape_concentration_tensors: Tensor,
-            W: Tensor,
-            pixellengths: Tensor,
+        self,
+        mean_scattering_directions: Tensor,
+        shape_concentration_tensors: Tensor,
+        W: Tensor,
+        pixellengths: Tensor,
     ):
         """ Project the laoratory space shape-concentration-tensors of a range of grains along a the scattering directions
         into 2D detector pixels space.
@@ -260,6 +281,46 @@ def splat_grainshapes(
 
         return projected_shape_pixelunits, 1/torch.sqrt(dSd)
 
+
+    def transform(
+            self,
+            rigid_body_motion : RigidBodyMotion,
+            time : float = 1.0,
+        ):
+        """Transform the polycrystal by performing a rigid body motion.
+
+        This updates all the sample-information in-place.
+
+        Parameters
+        ----------
+        rigid_body_motion : RigidBodyMotion
+            Rigid body motion object describing the polycrystal transformation
+            as a function of time on the domain ``time=[0, 1]``.
+        time : float
+            Time between ``[0, 1]`` at which to call the rigid body motion.
+        """
+
+        # Get rotation matrix and translation vector.
+        Rot_mat = rigid_body_motion.rotator.get_rotation_matrix(
+            rigid_body_motion.rotation_angle * time
+        )
+        translation_vector = rigid_body_motion.translation * time
+
+        # Rotate vectors:
+        self.positions = torch.einsum('ij,gj->gi', Rot_mat, self.positions-self.origin[None,:])+self.origin[None,:]
+
+        # Rotate compose rotations
+        self.orientaions = torch.einsum('ij,gjk->gik', Rot_mat, self.orientaions)
+
+        #Rotate tensors
+        self.shape_concentration_tensors = torch.einsum('ij,gjk,lk ->gil', Rot_mat, self.shape_concentration_tensors, Rot_mat)
+        self.misori_concentration_tensors = torch.einsum('ij,gjk,lk ->gil', Rot_mat, self.misori_concentration_tensors, Rot_mat)
+        self.strains = torch.einsum('ij,gjk,lk ->gil', Rot_mat, self.strains, Rot_mat)
+        
+        #Translate
+        self.positions = self.positions + translation_vector[None, :] 
+
+
     # ------------------------------------------------------------------------------------------
     # The methods below here are for computing polefigures, not needed for diffraction patterns.
     # ------------------------------------------------------------------------------------------

From 9dca9da15897146c84c6ec73753f92178a8e1249 Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Sun, 31 May 2026 10:58:22 +0200
Subject: [PATCH 16/17] Use same symmetry handling as main workflow

---
 xrd_simulator/gaussian_crystal_model.py | 147 +++++++++++-------------
 xrd_simulator/polycrystal.py            |   2 +-
 2 files changed, 67 insertions(+), 82 deletions(-)

diff --git a/xrd_simulator/gaussian_crystal_model.py b/xrd_simulator/gaussian_crystal_model.py
index bbc3db3..3b21369 100644
--- a/xrd_simulator/gaussian_crystal_model.py
+++ b/xrd_simulator/gaussian_crystal_model.py
@@ -119,7 +119,6 @@ def render_detector_frame(
             self.max_grain_size,
         )
 
-
         # Simulate sample-rotation by adding a rotation to the grain misorientation
         sample_rotation_during_exposure = ensure_torch(sample_rotation_during_exposure)
         rotation_vector = torch.einsum('ij,i->j', sample_orientation, sample_rotation_during_exposure)
@@ -127,94 +126,80 @@ def render_detector_frame(
 
         #Construct some crystal and geometry information.
         B = form_b_mat(self.phase.unit_cell)
-        
         max_angle = detector._get_wrapping_cone(xray_propagation_direction, np.mean([0, 0, 0]))
         self.phase._setup_diffracting_planes(wavelength=wavelength, min_bragg_angle=0.0, max_bragg_angle=max_angle)  #TODO Using private method
         
-        sg_obj = sg.sg(sgname=self.phase.sgname)
-        hkl_list = genhkl_base(
-            self.phase.unit_cell,
-            sg_obj.syscond,
-            0.0, np.sin(max_angle) / wavelength,
-            sg_obj.crystal_system,
-            sg_obj.Laue,
-        )
-        if self.phase.path_to_cif_file is None:
-            structurefactors = torch.ones(hkl_list.shape[0])
+        # Get miller indicies and structure factors
+        miller_indices = self.phase.miller_indices
+        if self.phase.structure_factors is not None:
+            structure_factors = torch.sum(
+                ensure_torch(self.phase.structure_factors) ** 2, axis=1
+            )
+            miller_indices = miller_indices[structure_factors > 1e-6]
+            structure_factors = structure_factors[structure_factors > 1e-6]
         else:
-            self.phase._set_structure_factors(hkl_list)  #TODO Using private method
-            structurefactors = ensure_torch(np.sum(self.phase.structure_factors**2, axis=1))
-
-
+            # If no structure factors provided, use uniform intensity (all ones)
+            structure_factors = torch.ones(miller_indices.shape[0])
+        
         # Initialize lists of 2D gaussian splat parameters
         uv_corrds_list = []
         splat_concentration_tensors_list = []
         scalefactors_list = []
 
-        # Loop over reflection orders
-        for hkl, S in zip(hkl_list, structurefactors):
-            for friedel_sign in [1, -1]:
-
-                #TODO reduce the number of symmetries evaluated for low-multiplicity peaks
-                #TODO Check if structure factors include multiplicity
-                symmetries = ensure_torch(self.phase.rot)
-                n_symmetries = len(self.phase.rot)
-                
-                # Cheap test to discard reflections far from Bragg-condition
-                h = friedel_sign * torch.tensor(B @ hkl)
-                h_norm = torch.linalg.norm(h)
-                theta_angle_unstrained = np.asin( h_norm * wavelength / 4 / np.pi )
-                p_vectors = torch.einsum('ghi,gij,sjk,k->gsh', torch.eye(3)[None,:,:] - self.strains[grains_hit], self.orientaions[grains_hit], symmetries, h)
-                p_vectors_norm = torch.linalg.norm(p_vectors, axis=-1)
-                dp = torch.einsum('i,gsi->gs', xray_propagation_direction, p_vectors) / p_vectors_norm            
-                does_diffract = torch.abs( dp + torch.sin(theta_angle_unstrained) ) <  torch.abs(3 * (self.max_misorientation+torch.linalg.norm(sample_rotation_during_exposure)) * torch.cos(theta_angle_unstrained))
-
-                # Select the relevant reflections and flatten the grain- and symetry-indexes.
-                misori_concentration_tensors = torch.tile(smeared_misorientation_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
-                p_vectors = p_vectors[does_diffract]
-                shape_concentration_tensors = torch.tile(intersection_shape_concentration_tensors[:, None, :, :], (1, n_symmetries, 1, 1))[does_diffract]
-
-
-
-                # Do pole-figure part of the calculation
-                mean_scattering_directions, partialities, azim_directions, azim_widths = _get_diffraction_arcsegment(
-                    p_vectors,
-                    misori_concentration_tensors,
-                    xray_propagation_direction,
-                    wavelength,
-                )
-
-
-
-                # Splat grain realspace shapes (Consider using the non-strained non-azimuthally shifted directions to simplify gradients later)
-                detectorspace_grainshape_projections, projected_thicknes_scale_factors = self.splat_grainshapes(
-                    mean_scattering_directions,
-                    shape_concentration_tensors,
-                    W,
-                    pixellengths,
-                )
-
-                # This part involves propagation from sample to detector. unclear where it belongs
-                # ----------------------------------------------------------------------------------------------------------
-                # Ray-trace onto detector plane
-                pos = torch.tile(intersection_pos[:, None, :], (1, n_symmetries, 1,))[does_diffract]
-                ray_lengths = torch.einsum('xi,i->x', detector_origin[None, :] - pos, detector_norm) / torch.einsum('xi,i->x', mean_scattering_directions, detector_norm)
-                point_of_detector_intersection = pos + ray_lengths[:,None] * mean_scattering_directions
-                uv_coords = torch.einsum('xi, vi, v->xv',point_of_detector_intersection - detector_origin[None, :], W, 1/pixellengths) #TODO Tests with un-equal pixel sizes
-
-                # Do smearing due to angular divergence
-                azimuthal_direction_uv = torch.einsum('xi,ui->xu', azim_directions, W) / pixellengths[None, :] * ray_lengths[:, None] * azim_widths[:, None]\
-                    / (1 - torch.einsum('xi,ui->xu', mean_scattering_directions, W)**2)
-                azimuthal_smearing_tensor = torch.einsum('xu,xv->xuv',azimuthal_direction_uv, azimuthal_direction_uv)
-                detspace_splat_concentration = torch.linalg.inv( torch.linalg.inv(detectorspace_grainshape_projections) + azimuthal_smearing_tensor)
-                intensity_spread_out_factor = torch.sqrt( torch.linalg.det(detspace_splat_concentration) / torch.linalg.det(detectorspace_grainshape_projections) )  #TODO This was (organically) vibe-coded. Check on paper if there is a simplification.
-                # ----------------------------------------------------------------------------------------------------------
-
-                # Append to list
-                uv_corrds_list.append(uv_coords)
-                beam_intensity_factors_insideloop = torch.tile(beam_intensity_factors[:, None], (1, n_symmetries))[does_diffract]
-                scalefactors_list.append(S * projected_thicknes_scale_factors * partialities * intensity_spread_out_factor * beam_intensity_factors_insideloop)
-                splat_concentration_tensors_list.append(detspace_splat_concentration)
+        # Loop over hkl tuples
+        for hkl, S in zip(miller_indices, structure_factors):
+
+            # Cheap test to discard reflections far from Bragg-condition
+            h = torch.tensor(B @ hkl)
+            h_norm = torch.linalg.norm(h)
+            theta_angle_unstrained = np.asin( h_norm * wavelength / 4 / np.pi )
+            p_vectors = torch.einsum('ghi,gij,j->gh', torch.eye(3)[None,:,:] - self.strains[grains_hit], self.orientaions[grains_hit], h)
+            p_vectors_norm = torch.linalg.norm(p_vectors, axis=-1)
+            dp = torch.einsum('i,gi->g', xray_propagation_direction, p_vectors) / p_vectors_norm            
+            does_diffract = torch.abs( dp + torch.sin(theta_angle_unstrained) ) <  torch.abs(3 * (self.max_misorientation+torch.linalg.norm(sample_rotation_during_exposure)) * torch.cos(theta_angle_unstrained))
+
+            # Select the relevant reflections and flatten the grain- and symetry-indexes.
+            misori_concentration_tensors = smeared_misorientation_tensors[does_diffract]
+            p_vectors = p_vectors[does_diffract]
+            shape_concentration_tensors = intersection_shape_concentration_tensors[does_diffract]
+
+            # Do pole-figure part of the calculation
+            mean_scattering_directions, partialities, azim_directions, azim_widths = _get_diffraction_arcsegment(
+                p_vectors,
+                misori_concentration_tensors,
+                xray_propagation_direction,
+                wavelength,
+            )
+
+            # Splat grain realspace shapes (Consider using the non-strained non-azimuthally shifted directions to simplify gradients later)
+            detectorspace_grainshape_projections, projected_thicknes_scale_factors = self.splat_grainshapes(
+                mean_scattering_directions,
+                shape_concentration_tensors,
+                W,
+                pixellengths,
+            )
+
+            # This part involves propagation from sample to detector. unclear where it belongs
+            # ----------------------------------------------------------------------------------------------------------
+            # Ray-trace onto detector plane
+            pos = intersection_pos[does_diffract]
+            ray_lengths = torch.einsum('xi,i->x', detector_origin[None, :] - pos, detector_norm) / torch.einsum('xi,i->x', mean_scattering_directions, detector_norm)
+            point_of_detector_intersection = pos + ray_lengths[:,None] * mean_scattering_directions
+            uv_coords = torch.einsum('xi, vi, v->xv',point_of_detector_intersection - detector_origin[None, :], W, 1/pixellengths) #TODO Tests with un-equal pixel sizes
+
+            # Do smearing due to angular divergence
+            azimuthal_direction_uv = torch.einsum('xi,ui->xu', azim_directions, W) / pixellengths[None, :] * ray_lengths[:, None] * azim_widths[:, None]\
+                / (1 - torch.einsum('xi,ui->xu', mean_scattering_directions, W)**2)
+            azimuthal_smearing_tensor = torch.einsum('xu,xv->xuv',azimuthal_direction_uv, azimuthal_direction_uv)
+            detspace_splat_concentration = torch.linalg.inv( torch.linalg.inv(detectorspace_grainshape_projections) + azimuthal_smearing_tensor)
+            intensity_spread_out_factor = torch.sqrt( torch.linalg.det(detspace_splat_concentration) / torch.linalg.det(detectorspace_grainshape_projections) )  #TODO This was (organically) vibe-coded. Check on paper if there is a simplification.
+            # ----------------------------------------------------------------------------------------------------------
+
+            # Append to list
+            uv_corrds_list.append(uv_coords)
+            beam_intensity_factors_insideloop = beam_intensity_factors[does_diffract]
+            scalefactors_list.append(S * projected_thicknes_scale_factors * partialities * intensity_spread_out_factor * beam_intensity_factors_insideloop)
+            splat_concentration_tensors_list.append(detspace_splat_concentration)
 
         if timing:
             print(f'Splatting took {time.time()-t0}')
@@ -224,7 +209,7 @@ def render_detector_frame(
             torch.concat(uv_corrds_list),
             torch.concat(scalefactors_list),
             torch.concat(splat_concentration_tensors_list),
-            splat_max_size= (d * (self.max_misorientation+torch.linalg.norm(sample_rotation_during_exposure)) + self.max_grain_size ) / torch.min(pixellengths)
+            splat_max_size= (d * (self.max_misorientation+torch.linalg.norm(sample_rotation_during_exposure)) + self.max_grain_size ) / torch.min(pixellengths) * 1.41
         )
 
         if timing:
diff --git a/xrd_simulator/polycrystal.py b/xrd_simulator/polycrystal.py
index 2458a2d..1ab0d40 100644
--- a/xrd_simulator/polycrystal.py
+++ b/xrd_simulator/polycrystal.py
@@ -280,7 +280,7 @@ def _compute_peaks(self, beam, rigid_body_motion, verbose=True):
 
         peaks = torch.empty(
             (0, 10)
-        )  # We create a dataframe to store all the relevant values for each individual reflection inr an organized manner
+        )  # We create a dataframe to store all the relevant values for each individual reflection in an organized manner
 
         # For each phase of the sample, we compute all reflections at once in a vectorized manner
         for i, phase in enumerate(phases):

From 377908543ebf7dbf5d8954870b6412d3d811223e Mon Sep 17 00:00:00 2001
From: MACarlsen <madscarlsen@zohomail.eu>
Date: Sun, 31 May 2026 15:19:37 +0200
Subject: [PATCH 17/17] vectorized hkl loop

---
 xrd_simulator/gaussian_crystal_model.py | 130 ++++++++++++------------
 1 file changed, 66 insertions(+), 64 deletions(-)

diff --git a/xrd_simulator/gaussian_crystal_model.py b/xrd_simulator/gaussian_crystal_model.py
index 3b21369..3d5865f 100644
--- a/xrd_simulator/gaussian_crystal_model.py
+++ b/xrd_simulator/gaussian_crystal_model.py
@@ -125,12 +125,12 @@ def render_detector_frame(
         smeared_misorientation_tensors = torch.linalg.inv(torch.linalg.inv(self.misori_concentration_tensors[grains_hit]) + torch.outer(rotation_vector, rotation_vector))
 
         #Construct some crystal and geometry information.
-        B = form_b_mat(self.phase.unit_cell)
+        B = torch.Tensor(form_b_mat(self.phase.unit_cell))
         max_angle = detector._get_wrapping_cone(xray_propagation_direction, np.mean([0, 0, 0]))
         self.phase._setup_diffracting_planes(wavelength=wavelength, min_bragg_angle=0.0, max_bragg_angle=max_angle)  #TODO Using private method
         
         # Get miller indicies and structure factors
-        miller_indices = self.phase.miller_indices
+        miller_indices = torch.Tensor(self.phase.miller_indices)
         if self.phase.structure_factors is not None:
             structure_factors = torch.sum(
                 ensure_torch(self.phase.structure_factors) ** 2, axis=1
@@ -141,74 +141,76 @@ def render_detector_frame(
             # If no structure factors provided, use uniform intensity (all ones)
             structure_factors = torch.ones(miller_indices.shape[0])
         
-        # Initialize lists of 2D gaussian splat parameters
-        uv_corrds_list = []
-        splat_concentration_tensors_list = []
-        scalefactors_list = []
-
-        # Loop over hkl tuples
-        for hkl, S in zip(miller_indices, structure_factors):
-
-            # Cheap test to discard reflections far from Bragg-condition
-            h = torch.tensor(B @ hkl)
-            h_norm = torch.linalg.norm(h)
-            theta_angle_unstrained = np.asin( h_norm * wavelength / 4 / np.pi )
-            p_vectors = torch.einsum('ghi,gij,j->gh', torch.eye(3)[None,:,:] - self.strains[grains_hit], self.orientaions[grains_hit], h)
-            p_vectors_norm = torch.linalg.norm(p_vectors, axis=-1)
-            dp = torch.einsum('i,gi->g', xray_propagation_direction, p_vectors) / p_vectors_norm            
-            does_diffract = torch.abs( dp + torch.sin(theta_angle_unstrained) ) <  torch.abs(3 * (self.max_misorientation+torch.linalg.norm(sample_rotation_during_exposure)) * torch.cos(theta_angle_unstrained))
-
-            # Select the relevant reflections and flatten the grain- and symetry-indexes.
-            misori_concentration_tensors = smeared_misorientation_tensors[does_diffract]
-            p_vectors = p_vectors[does_diffract]
-            shape_concentration_tensors = intersection_shape_concentration_tensors[does_diffract]
-
-            # Do pole-figure part of the calculation
-            mean_scattering_directions, partialities, azim_directions, azim_widths = _get_diffraction_arcsegment(
-                p_vectors,
-                misori_concentration_tensors,
-                xray_propagation_direction,
-                wavelength,
-            )
+        # Test to find the reflections close to the bragg condition
+        h = torch.einsum('ij,hj->hi', B, miller_indices)
+        p_vectors = torch.einsum('ghi,gij,kj->gkh', torch.eye(3)[None,:,:] - self.strains[grains_hit], self.orientaions[grains_hit], h)
+        p_vectors_norm = torch.linalg.norm(p_vectors, axis=-1)
+        theta_angle = torch.asin( p_vectors_norm * wavelength / 4 / np.pi )
+        dp = torch.einsum('i,ghi->gh', xray_propagation_direction, p_vectors) / p_vectors_norm 
+        does_diffract = torch.abs( dp + torch.sin(theta_angle) ) / torch.cos(theta_angle)\
+            <  torch.abs(6 * (self.max_misorientation + torch.linalg.norm(sample_rotation_during_exposure)))
+        grain_does_diffract, hkl_does_diffract = torch.where(does_diffract)
+
+        # Select the relevant reflections and flatten the grain- and symetry-indexes.
+        misori_concentration_tensors = smeared_misorientation_tensors[grain_does_diffract]
+        p_vectors = p_vectors[does_diffract]
+        shape_concentration_tensors = intersection_shape_concentration_tensors[grain_does_diffract]
 
-            # Splat grain realspace shapes (Consider using the non-strained non-azimuthally shifted directions to simplify gradients later)
-            detectorspace_grainshape_projections, projected_thicknes_scale_factors = self.splat_grainshapes(
-                mean_scattering_directions,
-                shape_concentration_tensors,
-                W,
-                pixellengths,
-            )
+        if timing:
+            print(f'Bragg-condition filterin took {time.time()-t0}')
+            t0 = time.time()
+
+        # Do pole-figure part of the calculation
+        mean_scattering_directions, partialities, azim_directions, azim_widths = _get_diffraction_arcsegment(
+            p_vectors,
+            misori_concentration_tensors,
+            xray_propagation_direction,
+            wavelength,
+        )
+
+        if timing:
+            print(f'Reciprocal space part took {time.time()-t0}')
+            t0 = time.time()
+
+        # Splat grain realspace shapes (Consider using the non-strained non-azimuthally shifted directions to simplify gradients later)
+        detectorspace_grainshape_projections, projected_thicknes_scale_factors = self.splat_grainshapes(
+            mean_scattering_directions,
+            shape_concentration_tensors,
+            W,
+            pixellengths,
+        )
+
+        if timing:
+            print(f'Realspace proj took {time.time()-t0}')
+            t0 = time.time()
 
-            # This part involves propagation from sample to detector. unclear where it belongs
-            # ----------------------------------------------------------------------------------------------------------
-            # Ray-trace onto detector plane
-            pos = intersection_pos[does_diffract]
-            ray_lengths = torch.einsum('xi,i->x', detector_origin[None, :] - pos, detector_norm) / torch.einsum('xi,i->x', mean_scattering_directions, detector_norm)
-            point_of_detector_intersection = pos + ray_lengths[:,None] * mean_scattering_directions
-            uv_coords = torch.einsum('xi, vi, v->xv',point_of_detector_intersection - detector_origin[None, :], W, 1/pixellengths) #TODO Tests with un-equal pixel sizes
-
-            # Do smearing due to angular divergence
-            azimuthal_direction_uv = torch.einsum('xi,ui->xu', azim_directions, W) / pixellengths[None, :] * ray_lengths[:, None] * azim_widths[:, None]\
-                / (1 - torch.einsum('xi,ui->xu', mean_scattering_directions, W)**2)
-            azimuthal_smearing_tensor = torch.einsum('xu,xv->xuv',azimuthal_direction_uv, azimuthal_direction_uv)
-            detspace_splat_concentration = torch.linalg.inv( torch.linalg.inv(detectorspace_grainshape_projections) + azimuthal_smearing_tensor)
-            intensity_spread_out_factor = torch.sqrt( torch.linalg.det(detspace_splat_concentration) / torch.linalg.det(detectorspace_grainshape_projections) )  #TODO This was (organically) vibe-coded. Check on paper if there is a simplification.
-            # ----------------------------------------------------------------------------------------------------------
-
-            # Append to list
-            uv_corrds_list.append(uv_coords)
-            beam_intensity_factors_insideloop = beam_intensity_factors[does_diffract]
-            scalefactors_list.append(S * projected_thicknes_scale_factors * partialities * intensity_spread_out_factor * beam_intensity_factors_insideloop)
-            splat_concentration_tensors_list.append(detspace_splat_concentration)
+        # This part involves propagation from sample to detector. unclear where it belongs
+        # ----------------------------------------------------------------------------------------------------------
+        # Ray-trace onto detector plane
+        pos = intersection_pos[grain_does_diffract]
+        ray_lengths = torch.einsum('xi,i->x', detector_origin[None, :] - pos, detector_norm) / torch.einsum('xi,i->x', mean_scattering_directions, detector_norm)
+        point_of_detector_intersection = pos + ray_lengths[:,None] * mean_scattering_directions
+        uv_coords = torch.einsum('xi,vi,v->xv',point_of_detector_intersection - detector_origin[None, :], W, 1/pixellengths) #TODO Tests with un-equal pixel sizes
+
+        # Do smearing due to angular divergence
+        azimuthal_direction_uv = torch.einsum('xi,ui->xu', azim_directions, W) / pixellengths[None, :] * ray_lengths[:, None] * azim_widths[:, None]\
+            / (1 - torch.einsum('xi,ui->xu', mean_scattering_directions, W)**2)
+        azimuthal_smearing_tensor = torch.einsum('xu,xv->xuv',azimuthal_direction_uv, azimuthal_direction_uv)
+        detspace_splat_concentration = torch.linalg.inv( torch.linalg.inv(detectorspace_grainshape_projections) + azimuthal_smearing_tensor)
+        intensity_spread_out_factor = torch.sqrt( torch.linalg.det(detspace_splat_concentration) / torch.linalg.det(detectorspace_grainshape_projections) )  #TODO This was (organically) vibe-coded. Check on paper if there is a simplification.
+        # ----------------------------------------------------------------------------------------------------------
+
+        scalefactors = structure_factors[hkl_does_diffract] * projected_thicknes_scale_factors * partialities * intensity_spread_out_factor * beam_intensity_factors[grain_does_diffract]
+        does_diffract = scalefactors > 1e-10 * torch.max(scalefactors)
 
         if timing:
-            print(f'Splatting took {time.time()-t0}')
+            print(f'Raytracing took {time.time()-t0}')
             t0 = time.time()
 
         f = detector.render_gaussian_splats(
-            torch.concat(uv_corrds_list),
-            torch.concat(scalefactors_list),
-            torch.concat(splat_concentration_tensors_list),
+            uv_coords[does_diffract],
+            scalefactors[does_diffract],
+            detspace_splat_concentration[does_diffract],
             splat_max_size= (d * (self.max_misorientation+torch.linalg.norm(sample_rotation_during_exposure)) + self.max_grain_size ) / torch.min(pixellengths) * 1.41
         )
 
@@ -292,7 +294,7 @@ def transform(
         translation_vector = rigid_body_motion.translation * time
 
         # Rotate vectors:
-        self.positions = torch.einsum('ij,gj->gi', Rot_mat, self.positions-self.origin[None,:])+self.origin[None,:]
+        self.positions = torch.einsum('ij,gj->gi', Rot_mat, self.positions-rigid_body_motion.origin[None,:])+rigid_body_motion.origin[None,:]
 
         # Rotate compose rotations
         self.orientaions = torch.einsum('ij,gjk->gik', Rot_mat, self.orientaions)