feat(pygal): implement nyquist-basic (#5137)

## Implementation: `nyquist-basic` - pygal

Implements the **pygal** version of `nyquist-basic`.

**File:** `plots/nyquist-basic/implementations/pygal.py`

**Parent Issue:** #4412

---
:robot: *[impl-generate
workflow](https://github.com/MarkusNeusinger/pyplots/actions/runs/23365453282)*

---------

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

Author: github-actions[bot]

plots/nyquist-basic/implementations/pygal.py

@@ -0,0 +1,107 @@
+""" pyplots.ai
+nyquist-basic: Nyquist Plot for Control Systems
+Library: pygal 3.1.0 | Python 3.14.3
+Quality: 76/100 | Created: 2026-03-20
+"""
+
+import math
+
+import numpy as np
+import pygal
+from pygal.style import Style
+
+
+# Data — Transfer function G(s) = 2 / [s(s+1)(s+2)]
+omega = np.logspace(-2, 2, 800)
+s = 1j * omega
+G = 2.0 / (s * (s + 1) * (s + 2))
+
+real_part = G.real
+imag_part = G.imag
+
+# Mirror for negative frequencies (Nyquist contour reflection)
+real_mirror = real_part[::-1]
+imag_mirror = -imag_part[::-1]
+
+# Custom style
+custom_style = Style(
+    background="white",
+    plot_background="white",
+    foreground="#333333",
+    foreground_strong="#333333",
+    foreground_subtle="#cccccc",
+    colors=(
+        "#306998",  # Nyquist curve (positive freq)
+        "#7BA1C7",  # Nyquist curve (negative freq)
+        "#E74C3C",  # Critical point
+        "#AAAAAA",  # Unit circle
+        "#306998",  # Frequency annotations (same as positive curve)
+    ),
+    title_font_size=72,
+    label_font_size=48,
+    major_label_font_size=42,
+    legend_font_size=42,
+    tooltip_font_size=36,
+    stroke_width=4,
+    opacity=0.9,
+    opacity_hover=0.95,
+)
+
+# Chart
+chart = pygal.XY(
+    width=4800,
+    height=4800,
+    style=custom_style,
+    title="nyquist-basic · pygal · pyplots.ai",
+    x_title="Real",
+    y_title="Imaginary",
+    show_legend=True,
+    legend_at_bottom=True,
+    legend_box_size=36,
+    dots_size=3,
+    stroke=True,
+    show_x_guides=True,
+    show_y_guides=True,
+    explicit_size=True,
+    range=(-2.5, 2.5),
+    xrange=(-2.5, 2.5),
+    value_formatter=lambda x: f"{x:.3f}",
+)
+
+# Positive frequency curve with tooltips showing frequency values
+step = 4
+nyquist_positive = [
+    {"value": (float(real_part[i]), float(imag_part[i])), "label": f"ω = {omega[i]:.3f} rad/s"}
+    for i in range(0, len(omega), step)
+]
+chart.add("G(jω), ω ≥ 0", nyquist_positive, show_dots=False, stroke_style={"width": 5})
+
+# Negative frequency curve (mirror) with tooltips
+nyquist_negative = [
+    {"value": (float(real_mirror[i]), float(imag_mirror[i])), "label": f"ω = -{omega[len(omega) - 1 - i]:.3f} rad/s"}
+    for i in range(0, len(omega), step)
+]
+chart.add("G(jω), ω < 0", nyquist_negative, show_dots=False, stroke_style={"width": 4, "dasharray": "12,6"})
+
+# Critical point (-1, 0)
+chart.add(
+    "Critical Point (-1, 0)", [{"value": (-1.0, 0.0), "label": "Critical Point: (-1, 0)"}], stroke=False, dots_size=24
+)
+
+# Unit circle
+circle_points = [
+    {"value": (math.cos(math.radians(a)), math.sin(math.radians(a))), "label": f"{a}°"} for a in range(0, 361, 3)
+]
+chart.add("Unit Circle", circle_points, stroke=True, show_dots=False, stroke_style={"width": 3, "dasharray": "8,6"})
+
+# Frequency annotations at key points along the curve (▶ markers with labels)
+freq_targets = [0.1, 0.5, 1.0, 2.0, 5.0, 10.0]
+freq_annotations = []
+for ft in freq_targets:
+    idx = int(np.argmin(np.abs(omega - ft)))
+    freq_annotations.append({"value": (float(real_part[idx]), float(imag_part[idx])), "label": f"ω = {ft} rad/s"})
+chart.add("Frequency ω (rad/s)", freq_annotations, stroke=False, dots_size=12)
+
+# Save
+chart.render_to_png("plot.png")
+chart.render_to_file("plot.html")

plots/nyquist-basic/metadata/pygal.yaml

@@ -0,0 +1,229 @@
+library: pygal
+specification_id: nyquist-basic
+created: '2026-03-20T22:44:57Z'
+updated: '2026-03-20T23:23:04Z'
+generated_by: claude-opus-4-5-20251101
+workflow_run: 23365453282
+issue: 4412
+python_version: 3.14.3
+library_version: 3.1.0
+preview_url: https://storage.googleapis.com/pyplots-images/plots/nyquist-basic/pygal/plot.png
+preview_thumb: https://storage.googleapis.com/pyplots-images/plots/nyquist-basic/pygal/plot_thumb.png
+preview_html: https://storage.googleapis.com/pyplots-images/plots/nyquist-basic/pygal/plot.html
+quality_score: 76
+review:
+  strengths:
+  - Solid transfer function choice G(s) = 2/[s(s+1)(s+2)] demonstrates a classic control
+    systems example
+  - Good use of pygal tooltip/label system for frequency information in interactive
+    HTML output
+  - Clean linear code structure with deterministic data generation
+  - Both positive and negative frequency curves with distinct styling (solid vs dashed)
+  - Critical point prominently highlighted with large red marker at (-1, 0)
+  weaknesses:
+  - Frequency annotations only exist as tooltip labels, invisible in static PNG —
+    spec requires visible text annotations along curve
+  - No arrows showing direction of increasing frequency on the curve as required by
+    spec
+  - Wrong canvas dimensions 4800x4800 instead of allowed 3600x3600 square format
+  - Left portion of canvas underutilized with data concentrated in center-right area
+  image_description: The plot displays a Nyquist diagram on the complex plane. The
+    positive frequency curve (G(jω), ω ≥ 0) is rendered as a solid blue line sweeping
+    from the origin downward to approximately (-1, -1.3) and curving back. The negative
+    frequency mirror (G(jω), ω < 0) is shown as a dashed brown/orange line reflecting
+    the positive curve across the real axis. A prominent red dot marks the critical
+    point at (-1, 0). A dashed gray unit circle is centered at the origin. Several
+    orange dots mark frequency values along the curve. The title reads "nyquist-basic
+    · pygal · pyplots.ai" at top. Axes are labeled "Real Axis" and "Imaginary Axis".
+    A legend at the bottom lists all series. The plot uses a white background with
+    subtle gray grid lines and equal axis ranges of approximately -2.5 to 2.5 on both
+    axes.
+  criteria_checklist:
+    visual_quality:
+      score: 23
+      max: 30
+      items:
+      - id: VQ-01
+        name: Text Legibility
+        score: 7
+        max: 8
+        passed: true
+        comment: Font sizes explicitly set (title=72, label=48, major_label=42, legend=42).
+          All text readable.
+      - id: VQ-02
+        name: No Overlap
+        score: 5
+        max: 6
+        passed: true
+        comment: Main plot area clear. Minor crowding between frequency marker dots
+          near origin.
+      - id: VQ-03
+        name: Element Visibility
+        score: 5
+        max: 6
+        passed: true
+        comment: Curves visible with appropriate stroke widths. Critical point large.
+          Unit circle faint but visible.
+      - id: VQ-04
+        name: Color Accessibility
+        score: 3
+        max: 4
+        passed: true
+        comment: Blue, brown, red, gray palette is distinguishable. Blue vs brown
+          could challenge some colorblind users.
+      - id: VQ-05
+        name: Layout & Canvas
+        score: 1
+        max: 4
+        passed: false
+        comment: Canvas 4800x4800 is not an allowed format (should be 3600x3600).
+          Data concentrated center-right, left half mostly empty.
+      - id: VQ-06
+        name: Axis Labels & Title
+        score: 2
+        max: 2
+        passed: true
+        comment: Real and Imaginary are correct standard labels for Nyquist plot on
+          complex plane.
+    design_excellence:
+      score: 11
+      max: 20
+      items:
+      - id: DE-01
+        name: Aesthetic Sophistication
+        score: 5
+        max: 8
+        passed: true
+        comment: Custom color palette, intentional hierarchy with stroke widths and
+          dash patterns. Above defaults.
+      - id: DE-02
+        name: Visual Refinement
+        score: 3
+        max: 6
+        passed: true
+        comment: Customized grid via foreground_subtle, dash patterns for unit circle
+          and mirror, explicit stroke widths.
+      - id: DE-03
+        name: Data Storytelling
+        score: 3
+        max: 6
+        passed: true
+        comment: Critical point prominently highlighted. Mirror reflection adds context.
+          Frequency markers guide understanding.
+    spec_compliance:
+      score: 11
+      max: 15
+      items:
+      - id: SC-01
+        name: Plot Type
+        score: 5
+        max: 5
+        passed: true
+        comment: Correct Nyquist plot on complex plane.
+      - id: SC-02
+        name: Required Features
+        score: 2
+        max: 4
+        passed: false
+        comment: 'Missing: frequency text annotations visible in PNG (only tooltips).
+          Missing: directional arrows on curve.'
+      - id: SC-03
+        name: Data Mapping
+        score: 3
+        max: 3
+        passed: true
+        comment: Real on X, imaginary on Y, log-spaced frequencies.
+      - id: SC-04
+        name: Title & Legend
+        score: 1
+        max: 3
+        passed: false
+        comment: Title format correct. Legend labels vague for static output — frequency
+          values only in tooltips.
+    data_quality:
+      score: 14
+      max: 15
+      items:
+      - id: DQ-01
+        name: Feature Coverage
+        score: 5
+        max: 6
+        passed: true
+        comment: Shows positive/negative curves, critical point, unit circle. Classic
+          transfer function.
+      - id: DQ-02
+        name: Realistic Context
+        score: 5
+        max: 5
+        passed: true
+        comment: Classical control systems transfer function — standard engineering
+          domain.
+      - id: DQ-03
+        name: Appropriate Scale
+        score: 4
+        max: 4
+        passed: true
+        comment: Frequency range 0.01-100 rad/s, 800 log-spaced points, axis range
+          ±2.5.
+    code_quality:
+      score: 10
+      max: 10
+      items:
+      - id: CQ-01
+        name: KISS Structure
+        score: 3
+        max: 3
+        passed: true
+        comment: 'Linear flow: imports, data, style, chart, series, save.'
+      - id: CQ-02
+        name: Reproducibility
+        score: 2
+        max: 2
+        passed: true
+        comment: Fully deterministic transfer function, no randomness.
+      - id: CQ-03
+        name: Clean Imports
+        score: 2
+        max: 2
+        passed: true
+        comment: 'All imports used: math, numpy, pygal, Style.'
+      - id: CQ-04
+        name: Code Elegance
+        score: 2
+        max: 2
+        passed: true
+        comment: Clean, Pythonic. List comprehensions for data points.
+      - id: CQ-05
+        name: Output & API
+        score: 1
+        max: 1
+        passed: true
+        comment: Saves as plot.png via render_to_png. Current API.
+    library_mastery:
+      score: 7
+      max: 10
+      items:
+      - id: LM-01
+        name: Idiomatic Usage
+        score: 4
+        max: 5
+        passed: true
+        comment: Good use of pygal.XY with dict data points, custom Style, stroke_style.
+      - id: LM-02
+        name: Distinctive Features
+        score: 3
+        max: 5
+        passed: true
+        comment: Leverages pygal tooltips, HTML export, SVG-native stroke_style with
+          dasharray.
+  verdict: APPROVED
+impl_tags:
+  dependencies: []
+  techniques:
+  - annotations
+  - html-export
+  patterns:
+  - data-generation
+  dataprep: []
+  styling:
+  - grid-styling