Improve profile computation memory efficiency

Profile functions (compute_density_profile, compute_speed_profile,
compute_profiles) no longer require pre-computed grid intersections.
When grid_intersections_area is not provided, intersections are computed
per frame internally, avoiding the allocation of the full
(grid_cells × pedestrians) matrix.

- Add _compute_frame_grid_intersection helper for single-frame intersection
- Change _compute_grid_polygon_intersection to process frame-by-frame
  using NumPy instead of a single broadcast
- Make grid_intersections_area optional in compute_density_profile and
  compute_speed_profile (on-the-fly when omitted)
- Simplify compute_profiles to delegate to _compute_density_for_frame and
  _compute_speed_for_frame per frame with shared intersection
- Extract _compute_density_for_frame and _compute_speed_for_frame as
  single-dispatch helpers; compute_density_profile and compute_speed_profile
  also delegate here, eliminating duplicated method branches
- Move frame-invariant quantities (bounds, grid centers) out of the
  per-frame loop to avoid redundant recomputation
- Update user guide to use the simpler API without
  compute_grid_cell_polygon_intersection_area

Author: schroedtert

notebooks/user_guide.ipynb

@@ -3499,25 +3499,12 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "from pedpy import (\n",
-    "    compute_grid_cell_polygon_intersection_area,\n",
-    "    get_grid_cells,\n",
-    ")\n",
-    "\n",
     "grid_size = 0.4\n",
-    "grid_cells, _, _ = get_grid_cells(walkable_area=walkable_area, grid_size=grid_size)\n",
     "\n",
-    "min_frame_profiles = 250  # We use here just an excerpt of the\n",
-    "max_frame_profiles = 400  # trajectory data to reduce compute time\n",
+    "min_frame_profiles = 500  # We use here just an excerpt of the\n",
+    "max_frame_profiles = 1000  # trajectory data to reduce compute time\n",
     "\n",
-    "profile_data = profile_data[profile_data.frame.between(min_frame_profiles, max_frame_profiles)]\n",
-    "\n",
-    "# Compute the grid intersection area for the resorted profile data (they have the same sorting)\n",
-    "# for usage in multiple calls to not run the compute heavy operation multiple times\n",
-    "(\n",
-    "    grid_cell_intersection_area,\n",
-    "    resorted_profile_data,\n",
-    ") = compute_grid_cell_polygon_intersection_area(data=profile_data, grid_cells=grid_cells)"
+    "profile_data = profile_data[profile_data.frame.between(min_frame_profiles, max_frame_profiles)]"
    ]
   },
   {
@@ -3567,14 +3554,29 @@
    },
    "outputs": [],
    "source": [
-    "from pedpy import plot_measurement_setup\n",
+    "from pedpy import PEDPY_ORANGE, get_grid_cells, plot_measurement_setup\n",
     "\n",
-    "plot_measurement_setup(\n",
+    "ax = plot_measurement_setup(\n",
     "    walkable_area=walkable_area,\n",
     "    measurement_areas=[profile_measurement_area],\n",
     "    ma_line_width=2,\n",
     "    ma_alpha=0.2,\n",
     ").set_aspect(\"equal\")\n",
+    "\n",
+    "grid_size = 0.4\n",
+    "grid_cells_measurement_area, _, _ = get_grid_cells(\n",
+    "    axis_aligned_measurement_area=profile_measurement_area,\n",
+    "    grid_size=grid_size,\n",
+    ")\n",
+    "grid_cells = [MeasurementArea(cell) for cell in grid_cells_measurement_area]\n",
+    "plot_measurement_setup(\n",
+    "    measurement_areas=grid_cells,\n",
+    "    ma_line_color=PEDPY_ORANGE,\n",
+    "    ma_line_width=0.3,\n",
+    "    ma_alpha=0,\n",
+    "    axes=ax,\n",
+    ").set_aspect(\"equal\")\n",
+    "\n",
     "plt.show()"
    ]
   },
@@ -3667,17 +3669,15 @@
     "from pedpy import SpeedMethod, compute_speed_profile\n",
     "\n",
     "voronoi_speed_profile = compute_speed_profile(\n",
-    "    data=resorted_profile_data,\n",
+    "    data=profile_data,\n",
     "    walkable_area=walkable_area,\n",
-    "    grid_intersections_area=grid_cell_intersection_area,\n",
     "    grid_size=grid_size,\n",
     "    speed_method=SpeedMethod.VORONOI,\n",
     ")\n",
     "\n",
     "arithmetic_speed_profile = compute_speed_profile(\n",
-    "    data=resorted_profile_data,\n",
+    "    data=profile_data,\n",
     "    walkable_area=walkable_area,\n",
-    "    grid_intersections_area=grid_cell_intersection_area,\n",
     "    grid_size=grid_size,\n",
     "    speed_method=SpeedMethod.ARITHMETIC,\n",
     ")\n",
@@ -3770,19 +3770,17 @@
     "from pedpy import AxisAlignedMeasurementArea, SpeedMethod, compute_speed_profile\n",
     "\n",
     "voronoi_speed_profile = compute_speed_profile(\n",
-    "    data=resorted_profile_data_measurement_area,\n",
+    "    data=profile_data,\n",
     "    walkable_area=walkable_area,\n",
     "    axis_aligned_measurement_area=profile_measurement_area,\n",
-    "    grid_intersections_area=grid_cell_intersection_area_measurement_area,\n",
     "    grid_size=grid_size,\n",
     "    speed_method=SpeedMethod.VORONOI,\n",
     ")\n",
     "\n",
     "arithmetic_speed_profile = compute_speed_profile(\n",
-    "    data=resorted_profile_data_measurement_area,\n",
+    "    data=profile_data,\n",
     "    walkable_area=walkable_area,\n",
     "    axis_aligned_measurement_area=profile_measurement_area,\n",
-    "    grid_intersections_area=grid_cell_intersection_area_measurement_area,\n",
     "    grid_size=grid_size,\n",
     "    speed_method=SpeedMethod.ARITHMETIC,\n",
     ")\n",
@@ -3916,16 +3914,13 @@
    "source": [
     "from pedpy import DensityMethod, compute_density_profile\n",
     "\n",
-    "# here it is important to use the resorted data, as it needs to be in the same ordering as \"grid_cell_intersection_area\"\n",
     "voronoi_density_profile = compute_density_profile(\n",
-    "    data=resorted_profile_data,\n",
+    "    data=profile_data,\n",
     "    walkable_area=walkable_area,\n",
-    "    grid_intersections_area=grid_cell_intersection_area,\n",
     "    grid_size=grid_size,\n",
     "    density_method=DensityMethod.VORONOI,\n",
     ")\n",
     "\n",
-    "# here the unsorted data can be used\n",
     "classic_density_profile = compute_density_profile(\n",
     "    data=profile_data,\n",
     "    walkable_area=walkable_area,\n",
@@ -4005,17 +4000,14 @@
    "source": [
     "from pedpy import DensityMethod, compute_density_profile\n",
     "\n",
-    "# here it is important to use the resorted data, as it needs to be in the same ordering as \"grid_cell_intersection_area\"\n",
     "voronoi_density_profile = compute_density_profile(\n",
-    "    data=resorted_profile_data_measurement_area,\n",
+    "    data=profile_data,\n",
     "    walkable_area=walkable_area,\n",
     "    axis_aligned_measurement_area=profile_measurement_area,\n",
-    "    grid_intersections_area=grid_cell_intersection_area_measurement_area,\n",
     "    grid_size=grid_size,\n",
     "    density_method=DensityMethod.VORONOI,\n",
     ")\n",
     "\n",
-    "# here the unsorted data can be used\n",
     "classic_density_profile = compute_density_profile(\n",
     "    data=profile_data,\n",
     "    walkable_area=walkable_area,\n",