feat(pygal): implement root-locus-basic

[github-actions]

Implementation: root-locus-basic - pygal

Implements the pygal version of root-locus-basic.

File: plots/root-locus-basic/implementations/pygal.py

Parent Issue: #4414

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🤖 impl-generate workflow

[claude]

AI Review - Attempt 1/3

Image Description

The plot displays a root locus diagram on a white background. A blue curve traces the closed-loop pole migration through the complex plane — two branches depart from near the origin along the real axis, then split into the upper and lower half-planes, curving rightward and crossing the imaginary axis around ±1.6j. Red circular markers indicate open-loop poles at s = 0, -1, -2, and -4 on the real axis. A green circular marker shows the open-loop zero at s = -3. Orange markers highlight the imaginary-axis (stability boundary) crossings at approximately ±1.6j. Dashed gray lines radiate from the origin representing constant damping ratio guides (ζ = 0.2, 0.4, 0.6, 0.8), and dashed gray semicircles represent constant natural frequency guides (ωn = 1–5). The real-axis locus segments are shown in gray but are barely distinguishable. The title reads "root-locus-basic · pygal · pyplots.ai" and axis labels are "Real Axis (σ)" and "Imaginary Axis (jω)". A legend at the bottom lists all seven series.

Score: 79/100

Category	Score	Max
Visual Quality	23	30
Design Excellence	11	20
Spec Compliance	14	15
Data Quality	14	15
Code Quality	10	10
Library Mastery	7	10
Total	79	100

Visual Quality (23/30)

• VQ-01: Text Legibility (7/8) — Font sizes explicitly set (title=52, label=40, major_label=36, legend=28). All readable, though legend text is slightly small relative to the large canvas.
• VQ-02: No Overlap (5/6) — No significant overlaps. Legend items at bottom are somewhat tightly packed but still readable.
• VQ-03: Element Visibility (4/6) — Root locus branches and markers are clearly visible, but real-axis locus segments (gray on white) are very difficult to distinguish from the background/axis line. Guide lines are appropriately subtle.
• VQ-04: Color Accessibility (2/4) — Red for poles and green for zero is a classic red-green pairing that is problematic for colorblind viewers. Blue and orange are fine.
• VQ-05: Layout & Canvas (3/4) — Good proportions, plot fills canvas well. Minor asymmetry with more empty space on the left side.
• VQ-06: Axis Labels & Title (2/2) — "Real Axis (σ)" and "Imaginary Axis (jω)" are descriptive with proper mathematical notation.

Design Excellence (11/20)

• DE-01: Aesthetic Sophistication (5/8) — Custom color palette, explicit typography, clean white background. Above well-configured defaults but not publication-level polish.
• DE-02: Visual Refinement (3/6) — White background, subtle dashed guide lines, custom grid styling. Some refinement visible but pygal's default chrome (spines, grid dots) remains.
• DE-03: Data Storytelling (3/6) — Stability boundary markers in orange create a focal point. Guide lines provide engineering context. The hierarchy between main locus and reference lines is clear, but no additional emphasis on key features like breakaway points.

Spec Compliance (14/15)

• SC-01: Plot Type (5/5) — Correct root locus plot showing pole migration in the complex plane.
• SC-02: Required Features (3/4) — Open-loop poles/zeros marked (as circles, not ×/○ — pygal limitation). Continuous locus curves present. Real-axis segments shown. jω crossings marked. Damping ratio and natural frequency guides included. Missing: arrows indicating direction of increasing gain.
• SC-03: Data Mapping (3/3) — Real part on x-axis, imaginary on y-axis. Axes show full data range.
• SC-04: Title & Legend (3/3) — Title follows exact format. Legend labels are descriptive and match data series.

Data Quality (14/15)

• DQ-01: Feature Coverage (5/6) — Shows breakaway from real axis, complex conjugate branch migration, stability boundary crossing. Missing explicit breakaway point annotation.
• DQ-02: Realistic Context (5/5) — Transfer function G(s) = (s+3)/[s(s+1)(s+2)(s+4)] is a plausible control systems example with 4 poles and 1 zero.
• DQ-03: Appropriate Scale (4/4) — Gain range 0–500, axis range [-6,3]×[-5,5] are appropriate for the pole/zero locations.

Code Quality (10/10)

• CQ-01: KISS Structure (3/3) — Linear imports → data → plot → save structure. No functions or classes.
• CQ-02: Reproducibility (2/2) — Fully deterministic (polynomial roots, no randomness).
• CQ-03: Clean Imports (2/2) — numpy, pygal, Style — all used.
• CQ-04: Code Elegance (2/2) — Clean pole-tracking algorithm with nearest-neighbor assignment. Appropriate complexity for the visualization.
• CQ-05: Output & API (1/1) — Saves as plot.png using render_to_png. Current API.

Library Mastery (7/10)

• LM-01: Idiomatic Usage (4/5) — Good use of XY chart type, allow_interruptions for multi-segment lines, stroke_style dicts for per-series customization, label dicts for tooltip content.
• LM-02: Distinctive Features (3/5) — Uses pygal-specific allow_interruptions for line breaks (None separators), stroke_style dictionaries, label metadata in data points, legend_at_bottom_columns layout, and dual HTML+PNG export.

Score Caps Applied

• None

Strengths

• Excellent data engineering: polynomial root computation with intelligent pole-tracking across gain sweep
• Comprehensive feature set: damping ratio guides, natural frequency semicircles, stability boundary markers
• Clean, deterministic code with well-structured data generation
• Good use of pygal's allow_interruptions for multi-segment rendering

Weaknesses

• Real-axis locus segments are nearly invisible (gray on white background)
• Red-green color pairing for poles vs zeros is not colorblind-safe
• No arrows indicating direction of increasing gain (spec requirement)
• Design could benefit from stronger visual hierarchy and more refined styling

Issues Found

1. VQ-03 MEDIUM: Real-axis locus segments barely visible — gray stroke on white background blends in
   • Fix: Use a more visible color or increase stroke width for real-axis segments
2. VQ-04 LOW: Red-green color pairing for poles vs zeros fails colorblind accessibility
   • Fix: Replace green with a colorblind-safe alternative (e.g., teal #00897b or purple #7b1fa2)
3. SC-02 LOW: Missing arrows showing direction of increasing gain on locus branches
   • Fix: Add small arrow markers (▶) at intervals along locus branches, or annotate gain direction
4. DE-01 MEDIUM: Styling is above defaults but lacks the polish for publication quality
   • Fix: Refine color palette, add more visual weight differentiation between primary data and guides

AI Feedback for Next Attempt

Improve real-axis locus visibility by using a darker/bolder color or thicker stroke. Replace the red-green pole/zero color pairing with colorblind-safe alternatives. Add directional arrows or gain annotations along the locus branches to satisfy the spec requirement. Consider strengthening the visual hierarchy between primary locus curves and reference guide lines.

Verdict: REJECTED

[github-actions]

🔧 Repair Attempt 1/3

Applied fixes based on AI review feedback.

Status: Repair completed, re-triggering review...

---

🤖 impl-repair

[claude]

AI Review - Attempt 2/3

Image Description

The plot shows a root locus diagram on a white background with the title "root-locus-basic · pygal · pyplots.ai" at the top. The x-axis is labeled "Real Axis (σ)" ranging from -6.00 to 3.00, and the y-axis is labeled "Imaginary Axis (jω)" ranging from -5.00 to 5.00. A blue continuous curve traces the root locus branches that depart from the real axis near the origin and curve upward/downward into the right half-plane. Four red dots mark open-loop poles at s = 0, -1, -2, -4 on the real axis. One green dot marks the open-loop zero at s = -3. Two orange dots mark the stability boundary (jω axis crossings) at approximately ±1.6j. Light gray dashed lines radiate from the origin showing constant damping ratio (ζ) guide lines, and gray dashed semicircles show constant natural frequency (ωn) arcs. A legend at the bottom displays 8 series across 4 columns. The real-axis locus segments are not visually distinguishable from the x-axis line. Gain direction markers are not visible in the rendered plot.

Score: 76/100

Category	Score	Max
Visual Quality	22	30
Design Excellence	11	20
Spec Compliance	13	15
Data Quality	13	15
Code Quality	10	10
Library Mastery	7	10
Total	76	100

Visual Quality (22/30)

• VQ-01: Text Legibility (7/8) — Font sizes explicitly set (title=52, labels=40, major_label=36, legend=28). All text readable at full resolution.
• VQ-02: No Overlap (5/6) — Legend at bottom with 4 columns is slightly cramped with 8 series; some legend text with special characters (ζ, ωn) is tight but readable.
• VQ-03: Element Visibility (3/6) — Root locus curve and pole/zero markers are clearly visible, but real-axis locus segments are indistinguishable from the x-axis line (dark gray stroke at y=0 blends with axis). Gain direction markers are not visible in the rendered PNG.
• VQ-04: Color Accessibility (2/4) — Red (#c62828) for poles and green/teal (#00897b) for zeros is a red-green distinction that may be problematic for colorblind users, despite using teal rather than pure green.
• VQ-05: Layout & Canvas (3/4) — Plot fills most of the canvas with reasonable margins. Slightly more whitespace on left side than needed.
• VQ-06: Axis Labels & Title (2/2) — "Real Axis (σ)" and "Imaginary Axis (jω)" with proper engineering notation.

Design Excellence (11/20)

• DE-01: Aesthetic Sophistication (5/8) — Custom color palette with intentional color choices for each element type. Clean white background. Thoughtful styling above defaults but not publication-level.
• DE-02: Visual Refinement (3/6) — Subtle grid with light guide colors, dashed guide lines for ζ and ωn. Custom stroke widths. Some refinement visible but guide lines could be more polished.
• DE-03: Data Storytelling (3/6) — Color differentiation between poles (red), zeros (green), stability boundary (orange), and locus (blue) creates visual hierarchy. Guide lines add interpretive context. However, no emphasis on critical gain values or breakaway points.

Spec Compliance (13/15)

• SC-01: Plot Type (5/5) — Correct root locus plot using XY chart type.
• SC-02: Required Features (2/4) — Poles marked ✅, zeros marked ✅, locus branches ✅, jω crossings marked ✅, damping ratio guides ✅, natural frequency semicircles ✅. However: gain direction arrows are not visible in rendered output; real-axis segments are indistinguishable from axis; equal axis scaling not preserved (9-unit x-range vs 10-unit y-range on 16:9 canvas distorts geometry).
• SC-03: Data Mapping (3/3) — Real/imaginary parts correctly mapped to x/y axes.
• SC-04: Title & Legend (3/3) — Title follows exact format "root-locus-basic · pygal · pyplots.ai". Legend labels are descriptive and meaningful.

Data Quality (13/15)

• DQ-01: Feature Coverage (5/6) — Shows complex branch departure, jω crossings, multiple poles/zeros. Missing visible breakaway point emphasis.
• DQ-02: Realistic Context (4/5) — Standard control systems transfer function G(s) = (s+3)/[s(s+1)(s+2)(s+4)] — a textbook-quality example with meaningful pole-zero configuration.
• DQ-03: Appropriate Scale (4/4) — Gain range 0-500, pole locations at 0,-1,-2,-4, zero at -3 — all physically sensible for a control system.

Code Quality (10/10)

• CQ-01: KISS Structure (3/3) — Linear flow: imports → transfer function → gain sweep → locus computation → chart creation → save. No functions or classes.
• CQ-02: Reproducibility (2/2) — Fully deterministic: specific polynomial coefficients, no random data.
• CQ-03: Clean Imports (2/2) — numpy, pygal, Style — all used.
• CQ-04: Code Elegance (2/2) — Well-structured with clear comments. Pole-tracking algorithm with nearest-neighbor matching is appropriate complexity for root locus.
• CQ-05: Output & API (1/1) — Saves as plot.png using render_to_png().

Library Mastery (7/10)

• LM-01: Idiomatic Usage (4/5) — Good use of pygal.XY, Style class, allow_interruptions for multi-branch line breaks, stroke_style for per-series customization, dict-based data points with labels.
• LM-02: Distinctive Features (3/5) — Uses allow_interruptions (pygal-specific pattern for line breaks), tooltip labels via dict data points, concurrent SVG+PNG export. But doesn't leverage pygal's interactive SVG capabilities deeply.

Score Caps Applied

• None

Strengths

• Excellent code quality: clean, well-commented, deterministic, with sophisticated pole-tracking algorithm
• Good use of pygal's allow_interruptions for multi-branch rendering
• Comprehensive feature set: damping ratio guides, natural frequency semicircles, stability boundary markers
• Proper engineering notation on axes (σ, jω)
• Custom color palette with distinct colors for each element type

Weaknesses

• Real-axis locus segments are invisible — they blend with the x-axis line because they're plotted at y=0 with a color too similar to the axis
• Gain direction markers are not visible in the rendered PNG
• Red-green color choice for poles vs zeros is not optimal for colorblind accessibility
• Axis scaling is not equal — the 16:9 canvas with different x/y ranges distorts geometric relationships important for root locus interpretation

Issues Found

1. VQ-03 LOW: Real-axis locus segments invisible — dark gray line at y=0 blends with x-axis
   • Fix: Use a distinctly different approach — thicker stroke, brighter/contrasting color, or slight y-offset to make segments visible above the axis line
2. VQ-03 LOW: Gain direction markers not visible in rendered plot
   • Fix: Increase dots_size for gain direction series significantly (e.g., 24+), or use a contrasting color
3. VQ-04 LOW: Red-green colorblind issue for poles vs zeros
   • Fix: Change zero marker color to blue (#1565C0) or purple (#6A1B9A) instead of teal/green
4. SC-02 PARTIAL: Equal axis scaling not preserved
   • Fix: Consider using square canvas (3600×3600) or adjusting x/y ranges to match the aspect ratio

AI Feedback for Next Attempt

Focus on visibility of real-axis locus segments and gain direction markers — these are core spec requirements that are currently invisible. Use a brighter, contrasting color or thicker stroke for real-axis segments, and increase gain direction marker size significantly. Switch zero marker color from teal to blue or purple for better colorblind accessibility. Consider square canvas for equal axis scaling.

Verdict: REJECTED

[github-actions]

🔧 Repair Attempt 2/3

Applied fixes based on AI review feedback.

Status: Repair completed, re-triggering review...

---

🤖 impl-repair

[claude]

AI Review - Attempt 3/3

Image Description

The plot displays a root locus diagram on a white background with the title "root-locus-basic · pygal · pyplots.ai" at the top. The x-axis is labeled "Real Axis (σ)" ranging from -6.00 to 4.00, and the y-axis is labeled "Imaginary Axis (jω)" ranging from -5.00 to 5.00, on a square 3600×3600 canvas preserving equal axis scaling. A blue continuous curve traces the root locus branches — two branches depart from the real axis near the breakaway point between -1 and -2, curving upward and downward into the right half-plane and exiting the plot at the edges. Two other branches move along the real axis. Four red circular dots mark open-loop poles at s = 0, -1, -2, -4. A purple dot marks the open-loop zero at s = -3, though it is partially obscured by the dense cluster of blue locus points in that region. An orange line with width=14 clearly shows real-axis locus segments on the intervals [0, -1], [-2, -3], and [-4, -6]. Two orange dots mark the stability boundary (jω axis crossings) at approximately ±1.6j. Dark blue dots of size 26 mark gain direction along the locus branches at K = 5, 15, 40, 100, 250. Light gray dashed lines radiate from the origin showing constant damping ratio (ζ = 0.2, 0.4, 0.6, 0.8) guide lines, and gray dashed semicircles show constant natural frequency (ωn = 1, 2, 3, 4, 5) arcs. A legend at the bottom displays 8 series across 3 columns.

Score: 79/100

Category	Score	Max
Visual Quality	23	30
Design Excellence	11	20
Spec Compliance	14	15
Data Quality	14	15
Code Quality	10	10
Library Mastery	7	10
Total	79	100

Visual Quality (23/30)

• VQ-01: Text Legibility (7/8) — Font sizes explicitly set (title=52, labels=40, major_label=36, legend=28). All text clearly readable at full resolution.
• VQ-02: No Overlap (4/6) — Legend at bottom with 3 columns is adequate but tight with 8 series and special characters (ζ, ωn). Near the real axis around -3, blue locus dots cluster over the purple zero marker.
• VQ-03: Element Visibility (4/6) — Root locus curve, poles (red), stability boundary (orange), and gain direction markers (dark blue) are all clearly visible. Real-axis locus is now prominent as a thick orange line. However, the open-loop zero (purple) is partially lost in the dense cluster of blue locus points near -3.
• VQ-04: Color Accessibility (3/4) — Improved from attempt 2: purple (#6A1B9A) for zeros vs red (#c62828) for poles is colorblind-friendly. Orange tones for real-axis locus and stability boundary provide good contrast against blue locus.
• VQ-05: Layout & Canvas (3/4) — Square canvas preserves geometric relationships important for root locus interpretation. Plot fills most of the canvas with reasonable margins.
• VQ-06: Axis Labels & Title (2/2) — "Real Axis (σ)" and "Imaginary Axis (jω)" with proper engineering notation.

Design Excellence (11/20)

• DE-01: Aesthetic Sophistication (5/8) — Custom color palette with intentional choices for each element type (blue locus, red poles, purple zero, orange segments/boundaries). Clean white background. Thoughtful styling above defaults but not publication-level.
• DE-02: Visual Refinement (3/6) — Subtle grid with light guide colors (#e8e8e8), dashed guide lines for ζ and ωn with custom dash patterns. Custom stroke widths differentiate primary data from guides. Some refinement visible but not fully polished.
• DE-03: Data Storytelling (3/6) — Color differentiation and size variation create visual hierarchy: thick orange real-axis locus, prominent red poles, large gain direction markers. Guide lines add interpretive context for control engineers. However, no emphasis on critical gain values or breakaway points.

Spec Compliance (14/15)

• SC-01: Plot Type (5/5) — Correct root locus plot using pygal.XY chart type.
• SC-02: Required Features (3/4) — Poles marked ✅, zeros marked ✅, locus branches as continuous curves ✅, gain direction indicators ✅, real-axis locus segments ✅, jω crossings marked ✅, damping ratio guides ✅, natural frequency semicircles ✅, equal axis scaling ✅. Marker shapes are all circles (pygal limitation prevents × and ○ shapes); direction shown as dots rather than arrows.
• SC-03: Data Mapping (3/3) — Real/imaginary parts correctly mapped to x/y axes. All data visible within axis range.
• SC-04: Title & Legend (3/3) — Title follows exact format "root-locus-basic · pygal · pyplots.ai". Legend labels are descriptive with (×) and (○) notation.

Data Quality (14/15)

• DQ-01: Feature Coverage (5/6) — Shows complex branch departure, jω crossings, multiple poles and one zero, real-axis segments. Missing visible breakaway point emphasis.
• DQ-02: Realistic Context (5/5) — Standard control systems transfer function G(s) = (s+3)/[s(s+1)(s+2)(s+4)] — a textbook-quality example with meaningful pole-zero configuration that demonstrates all important root locus features.
• DQ-03: Appropriate Scale (4/4) — Gain range 0-500 with variable density, pole locations at 0, -1, -2, -4, zero at -3 — all physically sensible for a control system.

Code Quality (10/10)

• CQ-01: KISS Structure (3/3) — Linear flow: imports → transfer function → gain sweep → locus computation → chart creation → save. No functions or classes.
• CQ-02: Reproducibility (2/2) — Fully deterministic: specific polynomial coefficients, no random data.
• CQ-03: Clean Imports (2/2) — numpy, pygal, Style — all used.
• CQ-04: Code Elegance (2/2) — Well-structured with clear comments. Pole-tracking algorithm with nearest-neighbor matching is appropriate complexity. Variable-density gain sweep is a nice touch.
• CQ-05: Output & API (1/1) — Saves as plot.png using render_to_png() and also generates HTML.

Library Mastery (7/10)

• LM-01: Idiomatic Usage (4/5) — Good use of pygal.XY, Style class, allow_interruptions for multi-branch line breaks, stroke_style for per-series customization, dict-based data points with tooltip labels.
• LM-02: Distinctive Features (3/5) — Uses allow_interruptions (pygal-specific pattern for rendering multi-segment lines with None separators), tooltip labels via dict data points, concurrent SVG+PNG export via render_to_file.

Score Caps Applied

• None

Strengths

• Excellent code quality: clean, well-commented, deterministic, with sophisticated nearest-neighbor pole-tracking algorithm
• Comprehensive feature set covering all spec requirements: damping ratio guides, natural frequency semicircles, stability boundary markers, real-axis locus segments
• Good use of pygal's allow_interruptions for multi-branch/multi-segment rendering
• Proper engineering notation on axes (σ, jω) with units
• Custom color palette with colorblind-safe choices (purple zeros, red poles)
• Variable-density gain sweep provides finer resolution near critical points
• Square canvas preserves geometric relationships (fixed from attempt 2)
• Real-axis locus and gain direction markers now clearly visible (fixed from attempt 2)

Weaknesses

• Open-loop zero marker (purple) is partially obscured by dense cluster of blue locus points near s = -3
• Design could be more polished — guide lines and overall aesthetic are functional but not publication-ready
• No visual emphasis on breakaway/break-in points which are important root locus features
• Legend with 8 entries is dense; guide lines (ζ, ωn) could potentially be unlabeled to reduce legend clutter

Issues Found

1. VQ-03 MINOR: Open-loop zero at s = -3 is partially hidden by blue locus points clustering in that area
   • Fix: Increase z-order or size of zero marker, or reduce locus point density near known features
2. VQ-02 MINOR: Legend with 8 series in 3 columns is somewhat crowded
   • Fix: Consider combining ζ and ωn guide lines or using fewer legend columns
3. DE-02 MODERATE: Visual refinement could be improved for a more polished appearance
   • Fix: Further refine grid styling, add more generous spacing, polish guide line presentation

AI Feedback for Next Attempt

The implementation has improved significantly from attempt 2: real-axis locus segments are now clearly visible, gain direction markers are prominent, colorblind accessibility is improved with purple zeros, and equal axis scaling is preserved on the square canvas. The main remaining issue is the open-loop zero marker being partially obscured by locus points. Design excellence could be elevated with more polished guide line presentation and reduced legend clutter.

Verdict: APPROVED

[github-actions]

🔧 Repair Attempt 3/3

Applied fixes based on AI review feedback.

Status: Repair completed, re-triggering review...

---

🤖 impl-repair

[claude]

AI Review - Attempt 3/3

Image Description

The plot shows a root locus diagram on a square canvas with title "root-locus-basic · pygal · pyplots.ai". The x-axis is labeled "Real Axis (σ)" ranging from -6.0 to 4.0, and the y-axis "Imaginary Axis (jω)" from -5.0 to 5.0. Light gray dashed guide lines radiate from the origin representing constant damping ratio (ζ) values, and gray dashed semicircles in the left half-plane represent constant natural frequency (ωn) values. A vivid blue root locus curve traces pole migration — two symmetric branches depart from the real axis and curve through the right half-plane. A dark red/orange horizontal line marks real-axis locus segments. Red circular dots mark open-loop poles at s = 0, -1, -2, -4. A violet/purple dot marks the open-loop zero at s = -3. A large green dot highlights the breakaway point between s = -1 and s = -2. Two amber/orange dots mark jω-axis crossings (stability boundary) at approximately ±1.5j. Small blue dots along the locus indicate gain direction markers. The legend at the bottom shows 9 series in 4 columns. The background is a subtle off-white (#fafafa).

Score: 82/100

Category	Score	Max
Visual Quality	24	30
Design Excellence	13	20
Spec Compliance	14	15
Data Quality	14	15
Code Quality	10	10
Library Mastery	7	10
Total	82	100

Visual Quality (24/30)

• VQ-01: Text Legibility (7/8) — Font sizes explicitly set (title=52, labels=40, major_labels=36, legend=26). All text readable, though legend text is slightly small relative to plot area.
• VQ-02: No Overlap (4/6) — Legend at bottom is crowded with 9 series in 4 columns. Some markers near real axis cluster together (poles, zeros, breakaway, gain markers all near same y=0 line).
• VQ-03: Element Visibility (5/6) — Locus branches are clear. Poles, zeros, breakaway, and stability boundary are distinct sizes and colors. However, gain direction markers are small dots that blend with locus branch dots.
• VQ-04: Color Accessibility (3/4) — Good palette: blue locus, red poles, violet zero, green breakaway, amber stability. Red vs violet distinction could be difficult for some colorblind types (protanopia).
• VQ-05: Layout & Canvas (3/4) — Square 3600×3600 canvas is appropriate for this symmetric plot. Plot fills space well. Minor wasted space on the right side (range extends to 4.0 but locus data doesn't fully use it).
• VQ-06: Axis Labels & Title (2/2) — "Real Axis (σ)" and "Imaginary Axis (jω)" are descriptive with proper notation.

Design Excellence (13/20)

• DE-01: Aesthetic Sophistication (5/8) — Custom color palette with intentional choices (warm background tint, color-coded series with clear hierarchy). Above default styling but not publication-quality — markers are all circles due to pygal limitations.
• DE-02: Visual Refinement (4/6) — Guide lines rendered as subtle dashed gray. Background uses off-white tones. Custom stroke widths differentiate elements. Good attention to detail with allow_interruptions for clean line breaks.
• DE-03: Data Storytelling (4/6) — Plot tells a clear story: pole migration from open-loop positions, breakaway highlighted in green, stability boundary in amber creates clear visual hierarchy. Color and size variation guide the viewer through the analysis.

Spec Compliance (14/15)

• SC-01: Plot Type (5/5) — Correct root locus plot in the complex plane.
• SC-02: Required Features (3/4) — All major features present: poles, zeros, locus branches, real-axis segments, stability boundary crossings, damping/frequency guide lines. However, poles should be × markers and zeros should be ○ markers per spec — shown as circles (pygal limitation). Direction arrows are dots, not arrows.
• SC-03: Data Mapping (3/3) — Real/imaginary axes correctly assigned. Data spans appropriate range. Equal axis scaling preserved.
• SC-04: Title & Legend (3/3) — Title "root-locus-basic · pygal · pyplots.ai" matches required format. Legend labels are descriptive ("Poles (×)", "Zero (○)", etc.).

Data Quality (14/15)

• DQ-01: Feature Coverage (6/6) — Transfer function G(s) = (s+3)/[s(s+1)(s+2)(s+4)] with 4 poles and 1 zero provides rich behavior: multiple branches, breakaway point, stability boundary crossing, asymptotic behavior.
• DQ-02: Realistic Context (4/5) — Standard control systems transfer function. Realistic and neutral engineering context. Slightly generic (textbook example) rather than a named real-world system.
• DQ-03: Appropriate Scale (4/4) — Poles at 0, -1, -2, -4 and zero at -3 are sensible. Gain range 0-500 captures all important behavior.

Code Quality (10/10)

• CQ-01: KISS Structure (3/3) — Linear flow: imports → transfer function setup → gain sweep → chart creation → save. No functions or classes.
• CQ-02: Reproducibility (2/2) — Fully deterministic: polynomial roots computation with no random elements.
• CQ-03: Clean Imports (2/2) — numpy, pygal, Style — all used.
• CQ-04: Code Elegance (2/2) — Well-structured with clear comments. Pole tracking algorithm uses nearest-neighbor matching — necessary complexity. Variable density gain sweep is a smart engineering choice.
• CQ-05: Output & API (1/1) — Saves as plot.png via render_to_png. Also generates HTML.

Library Mastery (7/10)

• LM-01: Idiomatic Usage (4/5) — Good use of pygal XY chart, Style customization, allow_interruptions for discontinuous series, stroke_style for line customization, dots_size for marker sizing, label dictionaries for tooltips.
• LM-02: Distinctive Features (3/5) — Uses allow_interruptions (pygal-specific for discontinuous data), built-in tooltip labels, HTML export alongside PNG, legend_at_bottom_columns layout, truncate_legend=-1.

Score Caps Applied

• None

Strengths

• Excellent data engineering: variable-density gain sweep, nearest-neighbor pole tracking, and numerical breakaway/crossing detection
• Rich feature set: guide lines for ζ and ωn, real-axis locus segments, breakaway point, stability boundary — all spec requirements addressed
• Thoughtful color hierarchy: background guides in gray, locus in blue, critical points in distinct warm colors (green, amber, red)
• Clean, well-commented code with appropriate complexity for the mathematical content

Weaknesses

• Legend is crowded with 9 series in 4 columns at bottom — some entries hard to distinguish at the small legend font size
• Marker shapes limited to circles (pygal limitation) — spec requests × for poles and ○ for zeros
• Gain direction "arrows" are just dots — no actual directional indication visible in the PNG output
• Some clustering of markers near the real axis makes individual elements harder to distinguish

Issues Found

1. VQ-02 MODERATE: Legend crowded with 9 series in 4 columns
   • Fix: Consider reducing legend entries by combining guide series or using fewer legend columns
2. SC-02 MINOR: Markers are all circles instead of × and ○ as spec requires
   • Note: This is a fundamental pygal limitation — the library does not support custom marker shapes in XY charts

AI Feedback for Next Attempt

Score of 82 on attempt 3/3 meets the ≥50 threshold for final merge. The implementation demonstrates strong engineering of the root locus computation and good use of pygal's features. The main limitations are inherent to pygal (no custom marker shapes, no arrow markers). Legend crowding could be improved by consolidating guide line series or adjusting font sizes.

Verdict: REJECTED