feat(pygal): implement line-parametric (#5080)

## Implementation: `line-parametric` - pygal

Implements the **pygal** version of `line-parametric`.

**File:** `plots/line-parametric/implementations/pygal.py`

**Parent Issue:** #4424

---
:robot: *[impl-generate
workflow](https://github.com/MarkusNeusinger/pyplots/actions/runs/23339035335)*

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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/line-parametric/implementations/pygal.py

@@ -0,0 +1,173 @@
+""" pyplots.ai
+line-parametric: Parametric Curve Plot
+Library: pygal 3.1.0 | Python 3.14.3
+Quality: 80/100 | Created: 2026-03-20
+"""
+
+import numpy as np
+import pygal
+from pygal.style import Style
+
+
+# Data — parametric curves with parameter t
+n_points = 1000
+
+# Lissajous figure: x = sin(3t), y = sin(2t), t ∈ [0, 2π]
+t_liss = np.linspace(0, 2 * np.pi, n_points)
+lissajous_x = np.sin(3 * t_liss)
+lissajous_y = np.sin(2 * t_liss)
+
+# Spiral: x = t·cos(t), y = t·sin(t), t ∈ [0, 4π], normalized to [-1,1]
+t_spiral = np.linspace(0, 4 * np.pi, n_points)
+raw_spiral_x = t_spiral * np.cos(t_spiral)
+raw_spiral_y = t_spiral * np.sin(t_spiral)
+spiral_max = max(np.abs(raw_spiral_x).max(), np.abs(raw_spiral_y).max())
+spiral_x = raw_spiral_x / spiral_max
+spiral_y = raw_spiral_y / spiral_max
+
+# Split each curve into 4 segments for smooth color gradient
+n_segs = 4
+seg_size = n_points // n_segs
+
+# Lissajous gradient: deep blue → steel blue → burnt orange → warm amber
+liss_colors = ["#08306b", "#2171b5", "#d94701", "#fd8d3c"]
+liss_labels = ["Lissajous  0 → π/2", "Lissajous  π/2 → π", "Lissajous  π → 3π/2", "Lissajous  3π/2 → 2π"]
+
+# Spiral gradient: deep purple → orchid → teal → forest green
+spi_colors = ["#4a1486", "#807dba", "#006d5b", "#41ab5d"]
+spi_labels = ["Spiral  0 → π", "Spiral  π → 2π", "Spiral  2π → 3π", "Spiral  3π → 4π"]
+
+all_colors = liss_colors + spi_colors + ["#d62728", "#d62728", "#1a1a1a", "#1a1a1a"]
+
+# Style — polished design with explicit font sizing
+font = "DejaVu Sans, Helvetica, Arial, sans-serif"
+
+custom_style = Style(
+    background="white",
+    plot_background="#f7f7f7",
+    foreground="#2d2d2d",
+    foreground_strong="#1a1a1a",
+    foreground_subtle="#d9d9d9",
+    guide_stroke_color="#e8e8e8",
+    major_guide_stroke_color="#d0d0d0",
+    colors=tuple(all_colors),
+    font_family=font,
+    title_font_family=font,
+    title_font_size=52,
+    label_font_size=36,
+    major_label_font_size=32,
+    legend_font_size=30,
+    legend_font_family=font,
+    value_font_size=28,
+    tooltip_font_size=28,
+    tooltip_font_family=font,
+    opacity=0.95,
+    opacity_hover=1.0,
+    stroke_opacity=1.0,
+    stroke_opacity_hover=1.0,
+    stroke_width=8,
+)
+
+
+# Custom tooltip formatter showing parameter value
+def fmt_tooltip(x, y, t_val, curve):
+    return f"{curve}: t={t_val:.2f}  →  ({x:.3f}, {y:.3f})"
+
+
+# Chart — square 3600×3600 for geometric accuracy
+chart = pygal.XY(
+    width=3600,
+    height=3600,
+    style=custom_style,
+    title="line-parametric · pygal · pyplots.ai",
+    x_title="Horizontal Position x(t)",
+    y_title="Vertical Position y(t)",
+    show_legend=True,
+    legend_at_bottom=True,
+    legend_at_bottom_columns=4,
+    legend_box_size=22,
+    stroke=True,
+    show_dots=False,
+    show_x_guides=True,
+    show_y_guides=True,
+    x_value_formatter=lambda v: f"{v:.1f}",
+    value_formatter=lambda v: f"{v:.1f}",
+    margin_bottom=200,
+    margin_left=100,
+    margin_right=80,
+    margin_top=80,
+    truncate_legend=-1,
+    print_values=False,
+    xrange=(-1.3, 1.3),
+    range=(-1.3, 1.3),
+    js=[],
+    include_x_axis=True,
+    dots_size=0,
+)
+
+# Lissajous — 4 segments for smooth cool-to-warm gradient
+for k in range(n_segs):
+    start = k * seg_size
+    end = min((k + 1) * seg_size + 1, n_points)
+    seg_data = [
+        {
+            "value": (float(lissajous_x[i]), float(lissajous_y[i])),
+            "label": fmt_tooltip(lissajous_x[i], lissajous_y[i], t_liss[i], "Lissajous"),
+        }
+        for i in range(start, end)
+    ]
+    chart.add(
+        liss_labels[k], seg_data, stroke_style={"width": 10, "linecap": "round", "linejoin": "round"}, show_dots=False
+    )
+
+# Spiral — 4 segments for smooth purple-to-green gradient
+for k in range(n_segs):
+    start = k * seg_size
+    end = min((k + 1) * seg_size + 1, n_points)
+    seg_data = [
+        {
+            "value": (float(spiral_x[i]), float(spiral_y[i])),
+            "label": fmt_tooltip(spiral_x[i], spiral_y[i], t_spiral[i], "Spiral"),
+        }
+        for i in range(start, end)
+    ]
+    chart.add(
+        spi_labels[k], seg_data, stroke_style={"width": 8, "linecap": "round", "linejoin": "round"}, show_dots=False
+    )
+
+# Start points — large red dots at t=0, offset slightly so both are visible
+# Lissajous starts at (0, 0), Spiral starts at (0, 0) — show side by side
+chart.add(
+    "▶ Lissajous start",
+    [{"value": (float(lissajous_x[0]), float(lissajous_y[0])), "label": "Lissajous t=0"}],
+    stroke=False,
+    dots_size=30,
+    show_dots=True,
+)
+chart.add(
+    "▶ Spiral start",
+    [{"value": (float(spiral_x[0]) + 0.03, float(spiral_y[0]) + 0.03), "label": "Spiral t=0 (origin)"}],
+    stroke=False,
+    dots_size=26,
+    show_dots=True,
+)
+
+# End points — dark square markers at curve endpoints (distinct positions)
+chart.add(
+    "◼ Lissajous end",
+    [{"value": (float(lissajous_x[-1]), float(lissajous_y[-1])), "label": "Lissajous t=2π"}],
+    stroke=False,
+    dots_size=26,
+    show_dots=True,
+)
+chart.add(
+    "◼ Spiral end",
+    [{"value": (float(spiral_x[-1]), float(spiral_y[-1])), "label": "Spiral t=4π"}],
+    stroke=False,
+    dots_size=26,
+    show_dots=True,
+)
+
+# Save
+chart.render_to_png("plot.png")
+chart.render_to_file("plot.html")