feat(letsplot): implement smith-chart-basic (#3871)

## Implementation: `smith-chart-basic` - letsplot

Implements the **letsplot** version of `smith-chart-basic`.

**File:** `plots/smith-chart-basic/implementations/letsplot.py`

**Parent Issue:** #3792

---
:robot: *[impl-generate
workflow](https://github.com/MarkusNeusinger/pyplots/actions/runs/21047489117)*

---------

Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>
Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

Author: github-actions[bot]

plots/smith-chart-basic/implementations/letsplot.py

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+""" pyplots.ai
+smith-chart-basic: Smith Chart for RF/Impedance
+Library: letsplot 4.8.2 | Python 3.13.11
+Quality: 91/100 | Created: 2026-01-15
+"""
+
+import numpy as np
+import pandas as pd
+from lets_plot import (
+    LetsPlot,
+    aes,
+    coord_fixed,
+    element_rect,
+    element_text,
+    geom_path,
+    geom_point,
+    geom_text,
+    ggplot,
+    ggsize,
+    labs,
+    layer_tooltips,
+    theme,
+    theme_void,
+)
+from lets_plot.export import ggsave
+
+
+LetsPlot.setup_html()
+
+# Reference impedance
+Z0 = 50  # ohms
+
+# Generate example impedance data: simulated antenna impedance sweep
+np.random.seed(42)
+n_points = 60
+freq = np.linspace(1e9, 6e9, n_points)  # 1-6 GHz
+
+# Simulate realistic antenna impedance that varies with frequency
+# Creates a trajectory that traverses both upper (inductive) and lower (capacitive) regions
+t = np.linspace(0, 2.5 * np.pi, n_points)
+# Resistance transitions from low to high across frequency sweep
+r_base = 20 + 80 * (1 - np.exp(-t / 2.5))  # Resistance varies 20-100 ohms
+# Reactance oscillates between inductive (+) and capacitive (-) regions
+x_base = 50 * np.sin(t) * np.exp(-t / 6)  # Stronger reactance swing
+z_real = r_base + 3 * np.random.randn(n_points)
+z_imag = x_base + 2 * np.random.randn(n_points)
+
+# Normalize impedance
+z_norm_real = z_real / Z0
+z_norm_imag = z_imag / Z0
+
+# Convert normalized impedance to reflection coefficient (gamma)
+# gamma = (Z - Z0) / (Z + Z0) = (z_norm - 1) / (z_norm + 1)
+z_norm = z_norm_real + 1j * z_norm_imag
+gamma = (z_norm - 1) / (z_norm + 1)
+gamma_real = np.real(gamma)
+gamma_imag = np.imag(gamma)
+
+# Create dataframe for impedance locus with full data for tooltips
+df_locus = pd.DataFrame(
+    {
+        "gamma_real": gamma_real,
+        "gamma_imag": gamma_imag,
+        "freq_ghz": freq / 1e9,
+        "z_real": z_real,
+        "z_imag": z_imag,
+        "vswr": (1 + np.abs(gamma)) / (1 - np.abs(gamma)),
+    }
+)
+
+# Build Smith chart grid data - constant resistance circles
+# Formula: circle centered at (r/(r+1), 0) with radius 1/(r+1)
+grid_data = []
+r_values = [0, 0.2, 0.5, 1, 2, 5]
+for r in r_values:
+    center_x = r / (r + 1)
+    radius = 1 / (r + 1)
+    theta = np.linspace(0, 2 * np.pi, 100)
+    x = center_x + radius * np.cos(theta)
+    y = radius * np.sin(theta)
+    # Clip to unit circle
+    mask = (x**2 + y**2) <= 1.001
+    for i in np.where(mask)[0]:
+        grid_data.append({"x": x[i], "y": y[i], "type": "resistance", "group": f"r_{r}"})
+
+# Build Smith chart grid data - constant reactance arcs
+# Formula: circle centered at (1, 1/x) with radius |1/x|
+x_values = [0.2, 0.5, 1, 2, 5]
+for xv in x_values:
+    for sign in [1, -1]:
+        x_val = sign * xv
+        center_y = 1 / x_val
+        radius = abs(1 / x_val)
+        theta = np.linspace(0, 2 * np.pi, 100)
+        x = 1 + radius * np.cos(theta)
+        y = center_y + radius * np.sin(theta)
+        # Keep only points inside unit circle
+        mask = (x**2 + y**2) <= 1.001
+        for i in np.where(mask)[0]:
+            grid_data.append({"x": x[i], "y": y[i], "type": "reactance", "group": f"x_{x_val}"})
+
+df_grid = pd.DataFrame(grid_data)
+
+# Unit circle (outer boundary)
+theta_circle = np.linspace(0, 2 * np.pi, 200)
+df_boundary = pd.DataFrame({"x": np.cos(theta_circle), "y": np.sin(theta_circle)})
+
+# Real axis (horizontal line through center)
+df_axis = pd.DataFrame({"x": [-1, 1], "y": [0, 0]})
+
+# Key frequency labels at start, middle, and end (reduced to avoid overlap)
+label_indices = [0, n_points // 2, n_points - 1]
+df_labels = pd.DataFrame(
+    {
+        "x": [gamma_real[i] for i in label_indices],
+        "y": [gamma_imag[i] for i in label_indices],
+        "label": [f"{freq[i] / 1e9:.1f} GHz" for i in label_indices],
+    }
+)
+
+# Start/end marker dataframes with labels for legend
+df_start = df_locus.head(1).copy()
+df_start["marker"] = "Start (1.0 GHz)"
+df_end = df_locus.tail(1).copy()
+df_end["marker"] = "End (6.0 GHz)"
+
+# Center point (matched condition Z = Z0)
+df_center = pd.DataFrame({"x": [0], "y": [0]})
+
+# Legend data for markers (positioned outside chart area)
+df_legend = pd.DataFrame(
+    {
+        "x": [1.15, 1.15],
+        "y": [0.15, -0.15],
+        "color": ["#22C55E", "#DC2626"],
+        "label": ["Start (1.0 GHz)", "End (6.0 GHz)"],
+    }
+)
+
+# Create the Smith chart plot
+plot = (
+    ggplot()
+    # Outer boundary circle
+    + geom_path(aes(x="x", y="y"), data=df_boundary, color="#333333", size=1.5)
+    # Real axis
+    + geom_path(aes(x="x", y="y"), data=df_axis, color="#333333", size=0.8)
+    # Grid lines - resistance circles
+    + geom_path(
+        aes(x="x", y="y", group="group"),
+        data=df_grid[df_grid["type"] == "resistance"],
+        color="#306998",
+        size=0.6,
+        alpha=0.5,
+    )
+    # Grid lines - reactance arcs
+    + geom_path(
+        aes(x="x", y="y", group="group"),
+        data=df_grid[df_grid["type"] == "reactance"],
+        color="#306998",
+        size=0.6,
+        alpha=0.5,
+    )
+    # Impedance locus curve
+    + geom_path(aes(x="gamma_real", y="gamma_imag"), data=df_locus, color="#FFD43B", size=2.5)
+    # Interactive points with hover tooltips showing impedance data
+    + geom_point(
+        aes(x="gamma_real", y="gamma_imag"),
+        data=df_locus,
+        color="#FFD43B",
+        size=4,
+        alpha=0.8,
+        tooltips=layer_tooltips()
+        .line("Freq: @freq_ghz GHz")
+        .line("Z: @z_real + j@z_imag Ω")
+        .line("VSWR: @vswr")
+        .format("z_real", ".1f")
+        .format("z_imag", ".1f")
+        .format("vswr", ".2f"),
+    )
+    # Start marker (green)
+    + geom_point(aes(x="gamma_real", y="gamma_imag"), data=df_start, color="#22C55E", size=10)
+    # End marker (red)
+    + geom_point(aes(x="gamma_real", y="gamma_imag"), data=df_end, color="#DC2626", size=10)
+    # Center point (matched condition)
+    + geom_point(aes(x="x", y="y"), data=df_center, color="#333333", size=6, shape=3)
+    # Frequency labels along trajectory
+    + geom_text(aes(x="x", y="y", label="label"), data=df_labels, size=14, nudge_x=0.08, nudge_y=0.08, color="#333333")
+    # Legend markers (outside chart)
+    + geom_point(aes(x="x", y="y"), data=df_legend[df_legend["label"].str.contains("Start")], color="#22C55E", size=8)
+    + geom_point(aes(x="x", y="y"), data=df_legend[df_legend["label"].str.contains("End")], color="#DC2626", size=8)
+    + geom_text(aes(x="x", y="y", label="label"), data=df_legend, size=12, hjust=0, nudge_x=0.05, color="#333333")
+    # Styling
+    + labs(title="smith-chart-basic · letsplot · pyplots.ai")
+    + theme_void()
+    + theme(
+        plot_title=element_text(size=24, hjust=0.5),
+        plot_background=element_rect(fill="white"),
+        panel_background=element_rect(fill="white"),
+    )
+    + coord_fixed(ratio=1, xlim=(-1.3, 1.8), ylim=(-1.3, 1.3))  # Extend x to accommodate legend
+    + ggsize(1200, 1200)  # Square aspect for Smith chart
+)
+
+# Save outputs
+ggsave(plot, "plot.png", path=".", scale=3)
+ggsave(plot, "plot.html", path=".")