feat(altair): implement root-locus-basic

[github-actions]

Implementation: root-locus-basic - altair

Implements the altair version of root-locus-basic.

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

Parent Issue: #4414

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🤖 impl-generate workflow

[claude]

AI Review - Attempt 1/3

Image Description

The plot shows a root locus diagram for G(s) = 1/[s(s+1)(s+2)] with three color-coded branches. Branch 1 (blue) extends along the negative real axis to the left. Branches 2 (orange) and 3 (green) curve into the upper and lower half-planes respectively, forming complex conjugate trajectories. Red cross markers indicate open-loop poles at s=0, s=−1, and s=−2 on the real axis. Red filled diamond markers with labels identify the imaginary axis crossings at jω = ±j√2 (K=6). A small gray square marks the breakaway point near s ≈ −0.42. Very faint dashed gray lines (#d0d0d0) show constant damping ratio lines radiating from the origin and natural frequency semicircular arcs (ωn = 1, 2, 3, 4). Semi-transparent thick blue segments indicate the real-axis portions of the root locus between (−1, 0) and (−∞, −2). Small colored triangle arrows on the complex branches indicate the direction of increasing gain. The title reads "root-locus-basic · altair · pyplots.ai" with subtitle "G(s) = 1 / s(s+1)(s+2) — Closed-Loop Pole Trajectories vs Gain K". A legend in the top-right identifies Branch 1/2/3. Axis labels read "Real Axis" and "Imaginary Axis". The domain is [−7, 2.5] × [−6, 6], with the main content concentrated in the center-right area, leaving significant empty space on the left.

Score: 81/100

Category	Score	Max
Visual Quality	23	30
Design Excellence	13	20
Spec Compliance	14	15
Data Quality	14	15
Code Quality	10	10
Library Mastery	7	10
Total	81	100

Visual Quality (23/30)

• VQ-01: Text Legibility (7/8) — Font sizes explicitly set throughout (title 28, axis 18/22, legend 16/18). Crossing labels at 14pt and subtitle at 17pt are slightly small but still legible.
• VQ-02: No Overlap (5/6) — Mostly clean. Some mild crowding near the origin where three poles, breakaway point, and branch convergence cluster together.
• VQ-03: Element Visibility (5/6) — Branch lines (strokeWidth=2.5), pole markers (size=400), and crossing markers (size=350) are clear. However, the damping/frequency guide lines (#d0d0d0 on white) are nearly invisible.
• VQ-04: Color Accessibility (3/4) — Blue/orange/green palette is generally distinguishable. Red accents provide good contrast for critical markers. Green branch could be confused with blue by some deuteranope viewers.
• VQ-05: Layout & Canvas (2/4) — Domain [−7, 2.5] × [−6, 6] extends far left where only faint grid lines and Branch 1's real-axis tail exist. The interesting content (branches, poles, crossings) is concentrated in roughly [−3, 1] × [−5, 5], leaving ~40% of the canvas as near-empty space.
• VQ-06: Axis Labels & Title (1/2) — "Real Axis" and "Imaginary Axis" are descriptive but could include standard notation like "Real Part (σ)" and "Imaginary Part (jω)" for a control systems audience.

Design Excellence (13/20)

• DE-01: Aesthetic Sophistication (5/8) — Custom three-color palette starting with Python Blue, clear typography hierarchy (title → subtitle → labels → annotations), red accent for critical points. Above well-configured defaults but not publication-ready.
• DE-02: Visual Refinement (4/6) — View stroke removed, default grid disabled in favor of domain-appropriate damping/frequency guide lines. Good concept but the guide lines are almost invisible (#d0d0d0 on white background).
• DE-03: Data Storytelling (4/6) — Good narrative: labeled stability crossings with gain values, direction arrows showing pole migration, breakaway point marked, subtitle explains the transfer function. The viewer can follow the stability story.

Spec Compliance (14/15)

• SC-01: Plot Type (5/5) — Correct root locus plot showing pole trajectories in the complex plane.
• SC-02: Required Features (3/4) — Covers most spec requirements: poles with × markers, continuous branches with direction arrows, real axis segments, imaginary axis crossings, damping/frequency grid. However, the spec requires "equal axis scaling to preserve geometric relationships" which is violated — x has ~147 px/unit while y has ~92 px/unit, distorting angles and circles.
• SC-03: Data Mapping (3/3) — Real part correctly mapped to x-axis, imaginary part to y-axis.
• SC-04: Title & Legend (3/3) — Title follows exact format "root-locus-basic · altair · pyplots.ai". Legend clearly identifies all three branches.

Data Quality (14/15)

• DQ-01: Feature Coverage (5/6) — Demonstrates multiple branches, breakaway point, imaginary axis crossings, real-axis segments, and direction of increasing gain. Could additionally annotate asymptote angles or centroid.
• DQ-02: Realistic Context (5/5) — Classic control systems textbook transfer function G(s) = 1/[s(s+1)(s+2)]. Neutral, educational, well-understood system with rich behavior.
• DQ-03: Appropriate Scale (4/4) — Mathematically correct: crossings at ω=√2 with K=6, breakaway at s≈−0.423, poles at 0/−1/−2. All values verified analytically.

Code Quality (10/10)

• CQ-01: KISS Structure (3/3) — Linear script: imports → data computation → layer construction → composition → save.
• CQ-02: Reproducibility (2/2) — Fully deterministic (polynomial root-finding, no randomness).
• CQ-03: Clean Imports (2/2) — All three imports (altair, numpy, pandas) are used.
• CQ-04: Code Elegance (2/2) — Well-structured with smart nearest-neighbor branch sorting. Appropriate complexity for this visualization.
• CQ-05: Output & API (1/1) — Saves as plot.png with scale_factor=3.0, plus HTML export.

Library Mastery (7/10)

• LM-01: Idiomatic Usage (4/5) — Good declarative Altair patterns: layered composition with +, proper encoding types (Q/N), detail channel for grouping, order channel for line sequencing. Could use alt.layer() for more explicit composition.
• LM-02: Distinctive Features (3/5) — Leverages Altair-specific features: interactive zoom/pan, rich tooltip encoding with formatting, HTML export, declarative detail/order channels. These would not translate trivially to other libraries.

Score Caps Applied

• None

Strengths

• Comprehensive root locus features: all major spec elements implemented (poles, branches, real-axis segments, crossings, breakaway, damping/frequency grid, direction arrows)
• Smart branch-sorting algorithm using nearest-neighbor matching ensures continuous curves
• Rich interactive features with detailed tooltips showing branch, real/imaginary parts, and gain K
• Clean, well-organized code with appropriate data computation
• Good data storytelling with labeled stability crossings and gain values

Weaknesses

• Axis scaling is not equal, distorting geometric relationships (circles appear as ellipses, angles are incorrect)
• Damping ratio and natural frequency guide lines are nearly invisible (#d0d0d0 on white)
• Layout has significant empty space on the left side; domain could be tightened
• Axis labels lack standard control systems notation (σ, jω)

Issues Found

1. SC-02 MEDIUM: Unequal axis scaling violates spec requirement for "equal axis scaling to preserve geometric relationships"
   • Fix: Adjust width/height ratio or domain ranges so that one unit on the real axis equals one unit on the imaginary axis
2. VQ-05 LOW: Canvas utilization is poor — interesting content concentrated in center-right
   • Fix: Tighten x-domain to approximately [−5, 2] or adjust to better frame the content
3. VQ-03 MINOR: Damping/frequency guide lines are nearly invisible at #d0d0d0
   • Fix: Use a slightly darker color like #b0b0b0 or #c0c0c0 so these informative lines are actually visible
4. VQ-06 MINOR: Axis labels lack standard control engineering notation
   • Fix: Use "Real Part (σ)" and "Imaginary Part (jω)" for domain-appropriate labeling

AI Feedback for Next Attempt

The main issues are (1) unequal axis scaling — the spec explicitly requires equal scaling to preserve geometric relationships, so ensure 1 unit on the real axis = 1 unit on the imaginary axis by adjusting width/height or domain ranges; (2) tighten the x-domain to reduce wasted canvas space on the left; (3) make the damping/frequency guide lines slightly more visible (e.g., #b0b0b0); and (4) use standard control notation in axis labels (σ, jω). The code quality and data are excellent — focus fixes on visual layout and spec compliance.

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 displays a root locus diagram for G(s) = 1/[s(s+1)(s+2)] with the title "root-locus-basic · altair · pyplots.ai" and a subtitle describing the transfer function. Three branches are shown in distinct colors: Branch 1 (blue, #306998) extends along the negative real axis to the left, Branch 2 (orange, #e07b39) curves upward into the upper half-plane, and Branch 3 (green, #2ca02c) curves downward into the lower half-plane. Open-loop poles are marked with red cross markers at s=0, s=−1, and s=−2 on the real axis. Imaginary axis crossings are marked with red filled diamonds labeled "jω = j√2 (K=6)" and "jω = −j√2 (K=6)". A gray filled square marks the breakaway point near s≈−0.423. Triangle direction arrows appear along the complex branches. Light dashed gray lines show damping ratio guidelines (radiating from origin) and natural frequency arcs (semicircles in the left half-plane). Semi-transparent blue segments highlight the real-axis portions of the root locus between (−1, 0) and (−∞, −2). The legend appears in the top-right corner. Axis tick labels and axis titles ("Real Axis", "Imaginary Axis") are present but appear faint/small in the rendered output. The green branch extends to the very bottom edge of the canvas.

Score: 78/100

Category	Score	Max
Visual Quality	22	30
Design Excellence	13	20
Spec Compliance	14	15
Data Quality	13	15
Code Quality	9	10
Library Mastery	7	10
Total	78	100

Visual Quality (22/30)

• VQ-01: Text Legibility (6/8) — Font sizes are explicitly set (title 28, subtitle 17, axis labels 18, axis titles 22, legend 16-18, crossing text 14). However, in the rendered output the axis tick labels and axis titles appear faint and small relative to the large canvas, reducing readability.
• VQ-02: No Overlap (5/6) — Minor overlap: the breakaway square marker sits very close to the pole cross at s=0, and the crossing label text sits near the branch lines. No major text collision.
• VQ-03: Element Visibility (5/6) — Branch lines at strokeWidth=2.5 are clearly visible. Pole crosses (size=400) and crossing diamonds (size=350) are prominent. Direction arrows are visible. Guide lines are appropriately subtle. Slightly impacted by the green branch extending to the canvas edge.
• VQ-04: Color Accessibility (3/4) — Blue/orange/green palette is generally colorblind-friendly. Red markers provide good contrast against the branch colors. However, the light gray guide lines (#d0d0d0) may be too faint for some viewers.
• VQ-05: Layout & Canvas (2/4) — Canvas is 1400×1100 (4200×3300 at 3x), which doesn't match either target format (4800×2700 or 3600×3600). The root locus data is concentrated in the center-right, leaving large empty areas in the upper-left and lower portions. The green branch is clipped at the bottom edge. Legend is isolated far from the data.
• VQ-06: Axis Labels & Title (1/2) — "Real Axis" and "Imaginary Axis" are descriptive but lack units. For the complex s-plane, units aren't strictly required, but axis titles are barely visible in the final render.

Design Excellence (13/20)

• DE-01: Aesthetic Sophistication (5/8) — Custom color palette with Python Blue as primary. Thoughtful marker differentiation (crosses for poles, diamonds for crossings, square for breakaway, triangles for direction). Subtitle with transfer function description. Clearly above defaults but not publication-ready — the guide lines and branch colors could be more refined.
• DE-02: Visual Refinement (4/6) — View stroke removed (strokeWidth=0), default grid disabled in favor of domain-specific damping/frequency guide lines. Legend well-configured with custom symbol sizes. Good attention to control-theory-specific visual conventions.
• DE-03: Data Storytelling (4/6) — The plot tells a meaningful story: pole migration from open-loop positions, stability boundary crossings clearly labeled with gain value (K=6), breakaway point marked, direction arrows showing increasing gain trajectory. Red highlighting of critical points creates visual hierarchy. The subtitle contextualizes the transfer function.

Spec Compliance (14/15)

• SC-01: Plot Type (5/5) — Correct root locus plot showing closed-loop pole trajectories in the complex plane as gain K varies.
• SC-02: Required Features (3/4) — ✅ Open-loop poles with × markers, ✅ continuous branch curves with direction arrows, ✅ real axis segments highlighted, ✅ imaginary axis crossings prominently marked, ✅ damping ratio and natural frequency guide lines. ⚠️ Axis scaling is not equal (x: [-7, 2.5] = 9.5 units, y: [-6, 6] = 12 units), and the plot is not well-centered on the origin as the spec requires.
• SC-03: Data Mapping (3/3) — Real part correctly on x-axis, imaginary part on y-axis. All data visible within the domain range.
• SC-04: Title & Legend (3/3) — Title follows exact format "root-locus-basic · altair · pyplots.ai". Legend labels "Branch 1/2/3" are clear and match the data encoding.

Data Quality (13/15)

• DQ-01: Feature Coverage (5/6) — Shows all key root locus behaviors: branches starting at open-loop poles, breakaway from real axis, migration into complex plane, imaginary axis crossing (stability boundary), and branches extending toward infinity. Missing: no zeros to demonstrate break-in behavior (but the chosen system has no zeros, which is appropriate for a basic example).
• DQ-02: Realistic Context (4/5) — G(s) = 1/[s(s+1)(s+2)] is a classic, well-known control theory example used in textbooks (e.g., Ogata, Dorf). Mathematically correct with proper breakaway at s≈−0.423 and imaginary crossing at ω=√2 for K=6.
• DQ-03: Appropriate Scale (4/4) — Gain range 0.001 to 80 adequately covers all critical transitions. Pole locations at 0, −1, −2 are standard. All computed values are mathematically verified.

Code Quality (9/10)

• CQ-01: KISS Structure (3/3) — Linear flow: imports → data generation → layer creation → composition → save. No functions or classes.
• CQ-02: Reproducibility (2/2) — Fully deterministic: uses np.roots() for polynomial root-finding with no random elements.
• CQ-03: Clean Imports (2/2) — Only altair, numpy, pandas — all actively used.
• CQ-04: Code Elegance (1/2) — Well-structured but verbose at ~300 lines. The nearest-neighbor branch sorting algorithm is necessary but could be more concise. Multiple separate DataFrames for each layer add bulk.
• CQ-05: Output & API (1/1) — Saves as plot.png with scale_factor=3.0 and plot.html. Uses current Altair 5.x API.

Library Mastery (7/10)

• LM-01: Idiomatic Usage (4/5) — Good use of Altair's declarative Grammar of Graphics: layered composition with +, encoding channels, scale/axis configuration, mark types. Tooltips are well-configured with formatted values. However, heavy manual data preparation in numpy/pandas rather than leveraging Altair's transform capabilities.
• LM-02: Distinctive Features (3/5) — Tooltips showing branch, real/imaginary parts, and gain K (valuable for root locus exploration), interactive zoom/pan via .interactive(), HTML export for full interactivity. These are meaningful Altair-specific features that add value beyond static output.

Score Caps Applied

• None — no cap conditions triggered

Strengths

• Comprehensive spec coverage with all major root locus features implemented (poles, branches, crossings, breakaway, direction arrows, guide lines)
• Good use of Altair's interactive features — tooltips showing gain K values are genuinely useful for root locus analysis
• Mathematically correct data generation with proper branch sorting algorithm
• Domain-specific guide lines (damping ratios, natural frequencies) replace generic grid effectively
• Clean visual hierarchy with red for critical points, distinct colors for branches

Weaknesses

• Axis tick labels and titles are barely visible in the rendered output despite explicit font sizes — likely a rendering/scaling issue
• Canvas size (4200×3300) doesn't match either target format (4800×2700 or 3600×3600)
• Layout has significant wasted space with data concentrated center-right; green branch clips at bottom edge
• Axis scaling is not equal as the spec requires — x spans 9.5 units vs y spans 12 units
• Code is verbose with many separate DataFrames; branch sorting algorithm could be more concise

Issues Found

1. VQ-05 LOW: Canvas dimensions don't match target formats and data-to-whitespace ratio is poor
   • Fix: Use width=1600, height=900 for 16:9 target, or adjust domain to better frame the data
2. VQ-06 LOW: Axis titles barely visible in rendered output
   • Fix: Ensure axis titles and ticks render prominently; consider increasing title padding or font weight
3. SC-02 MINOR: Axis scaling is not equal as spec requires
   • Fix: Adjust x/y domains to have equal unit ranges, e.g., [-7, 5] for x and [-6, 6] for y
4. VQ-05 LOW: Green branch clips at bottom canvas edge
   • Fix: Adjust y domain or add clipping to prevent branch from extending beyond visible area

AI Feedback for Next Attempt

Fix canvas to match target 4800×2700 (width=1600, height=900). Ensure equal axis scaling per spec requirement. Improve axis label/tick visibility — they should be prominent for a control systems plot where values matter. Tighten the domain to reduce wasted whitespace and prevent branch clipping. Consider adding axis title font weight or padding to make them stand out in the render.

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 for the transfer function G(s) = 1/s(s+1)(s+2) on a square canvas with equal axis scaling from -6 to 6. Three branches are shown in distinct colors: Branch 1 (blue) extends along the negative real axis from the origin toward negative infinity; Branch 2 (orange) curves upward from the real axis into the upper half-plane; Branch 3 (green) curves downward into the lower half-plane. Open-loop poles are marked with red cross (×) markers at s=0, s=-1, and s=-2 on the real axis. Red diamond markers indicate imaginary axis crossings at jω = ±√2 with labels "jω = j√2 (K=6)" and "jω = −j√2 (K=6)". A dark gray square marks the breakaway point near s ≈ -0.42. Light blue thick lines highlight real axis segments between (-1, 0) and from -2 to -∞. Subtle dashed gray lines show constant damping ratio guides radiating from the origin and natural frequency semicircular arcs in the left half-plane. Triangle-shaped direction arrows on the complex branches indicate the direction of increasing gain. The title reads "root-locus-basic · altair · pyplots.ai" with a subtitle describing the transfer function. A legend in the top-right identifies the three branches.

Score: 87/100

Category	Score	Max
Visual Quality	26	30
Design Excellence	14	20
Spec Compliance	15	15
Data Quality	15	15
Code Quality	10	10
Library Mastery	7	10
Total	87	100

Visual Quality (26/30)

• VQ-01: Text Legibility (7/8) — Font sizes explicitly set (title 28pt, axis titles 20pt, ticks 16pt, crossing labels 15pt). All readable; crossing labels slightly below ideal.
• VQ-02: No Overlap (5/6) — Minor visual crowding near the origin where poles, breakaway point, and real axis segments converge, but no text overlap.
• VQ-03: Element Visibility (5/6) — Branch lines (strokeWidth=2.5), pole markers (size=450), and crossing markers (size=400) are well-sized. Guide lines appropriately subtle.
• VQ-04: Color Accessibility (4/4) — Blue/orange/green branch palette is colorblind-safe. Red for critical markers provides excellent contrast against the palette.
• VQ-05: Layout & Canvas (3/4) — Square 3600×3600 canvas is appropriate for equal-scaling requirement. Axis range [-6,6] is slightly generous but necessary for damping/frequency guide lines.
• VQ-06: Axis Labels & Title (2/2) — "Real Axis (σ)" and "Imaginary Axis (jω)" with proper engineering notation.

Design Excellence (14/20)

• DE-01: Aesthetic Sophistication (6/8) — Custom palette anchored on Python Blue with complementary orange/green. Intentional color hierarchy: prominent branches, subtle gray guides, red highlights for critical points. Professional appearance clearly above defaults.
• DE-02: Visual Refinement (4/6) — View border removed, default grid disabled, guide lines rendered as subtle dashed gray. Clean white background with generous whitespace.
• DE-03: Data Storytelling (4/6) — Visual hierarchy through color contrast guides the viewer: stability boundary crossings labeled with gain values, direction arrows show increasing K, breakaway point marked. The viewer understands stability behavior at a glance.

Spec Compliance (15/15)

• SC-01: Plot Type (5/5) — Correct root locus plot showing closed-loop pole trajectories in the complex plane.
• SC-02: Required Features (4/4) — All spec features present: × markers for open-loop poles, continuous branch curves with direction arrows, real axis segments, prominent imaginary axis crossings, damping ratio and natural frequency guide lines, centered origin with equal axis scaling.
• SC-03: Data Mapping (3/3) — Real part on X-axis, imaginary part on Y-axis. All data correctly mapped and visible.
• SC-04: Title & Legend (3/3) — Title follows exact format "root-locus-basic · altair · pyplots.ai". Legend labels ("Branch 1/2/3") match data encoding.

Data Quality (15/15)

• DQ-01: Feature Coverage (6/6) — Comprehensive: multiple branches diverging from real axis, breakaway point, imaginary axis crossings, real axis locus segments, damping/frequency guide grid.
• DQ-02: Realistic Context (5/5) — Classic control systems transfer function G(s) = 1/s(s+1)(s+2). Standard textbook example, neutral and educational.
• DQ-03: Appropriate Scale (4/4) — Mathematically accurate: breakaway at s ≈ -0.42, crossing at ω = √2 for K = 6, correct polynomial root computation.

Code Quality (10/10)

• CQ-01: KISS Structure (3/3) — Follows imports → data computation → chart layers → composition → save. No functions or classes.
• CQ-02: Reproducibility (2/2) — Fully deterministic: polynomial roots computed analytically, no random data.
• CQ-03: Clean Imports (2/2) — All three imports (altair, numpy, pandas) are used.
• CQ-04: Code Elegance (2/2) — Clean and well-organized. Root computation and branch sorting are necessary complexity for this domain-specific plot. No fake UI elements.
• CQ-05: Output & API (1/1) — Saves plot.png with scale_factor=3.0 and plot.html. Current Altair API.

Library Mastery (7/10)

• LM-01: Idiomatic Usage (4/5) — Good declarative Altair patterns: layered composition with + operator, proper encoding types (Q, N), tooltip configuration, legend customization, .interactive().
• LM-02: Distinctive Features (3/5) — Leverages Altair-specific features: interactive pan/zoom with tooltips showing gain values, HTML export, multi-layer composition with independent mark types and encodings.

Score Caps Applied

• None — No score caps triggered.

Strengths

• Perfect spec compliance: all required root locus features implemented correctly (poles, branches, crossings, real axis segments, guide lines, direction arrows)
• Mathematically accurate data with proper polynomial root computation and analytical breakaway/crossing calculations
• Strong visual hierarchy: red critical points, prominent colored branches, subtle gray guide lines
• Effective use of Altair's interactive tooltips showing σ, jω, and gain K values for each point on the locus
• Clean, well-structured code with logical layer composition

Weaknesses

• DE-01/DE-02 could be pushed further with more typographic refinement (e.g., subtitle styling, annotation font choices)
• The axis range [-6, 6] leaves some unused canvas space in corners where no data exists
• Crossing labels at 15pt are slightly smaller than ideal for the canvas size

Issues Found

1. VQ-05 MINOR: Axis range [-6, 6] is generous — the interesting data is mostly within [-3, 1] × [-4, 4], leading to some wasted corner space
   • Fix: Could tighten to [-5, 3] × [-5, 5] while still showing all guide lines
2. LM-01 MINOR: Data preparation is entirely numpy-based — Altair's built-in data transformations are not leveraged
   • Fix: Not critical for this domain-specific computation which requires polynomial root finding

AI Feedback for Next Attempt

Strong implementation at 87/100 on attempt 3. The plot demonstrates excellent spec compliance, data quality, and code quality. Design excellence is good but could reach publication-level with more typographic polish and tighter axis bounds. The interactive tooltips showing gain values along the locus are a particularly effective use of Altair's capabilities.

Verdict: REJECTED

[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 displays a root locus diagram on a square canvas with equal axis scaling from -6 to 6 on both axes. Three branches are shown in distinct colors: Branch 1 (blue) runs along the negative real axis from the origin leftward toward -∞, Branch 2 (orange) curves upward into the upper half-plane, and Branch 3 (green) curves downward into the lower half-plane. Open-loop poles are marked with red cross (×) markers at s=0, s=-1, and s=-2 on the real axis. Red diamond markers indicate imaginary axis crossings at jω = ±j√2 (K=6) with bold red labels. A gray square marks the breakaway point near s ≈ -0.42. Light dashed gray lines show constant damping ratio guide lines radiating from the origin (ζ=0.4 and ζ=0.8 labeled) and natural frequency arcs (semicircles for ωn=1,2,3,4). Real axis segments of the root locus are shown as thick semi-transparent blue lines between (-1, 0) and from -2 leftward. Triangle markers indicate direction of increasing gain on the complex branches. Title reads "root-locus-basic · altair · pyplots.ai" with subtitle "G(s) = 1 / s(s+1)(s+2) · Closed-Loop Pole Trajectories vs Gain K". A legend in the top-right identifies the three branches.

Score: 86/100

Category	Score	Max
Visual Quality	27	30
Design Excellence	13	20
Spec Compliance	15	15
Data Quality	14	15
Code Quality	10	10
Library Mastery	7	10
Total	86	100

Visual Quality (27/30)

• VQ-01: Text Legibility (7/8) — Font sizes explicitly set throughout (title 28, subtitle 18, axis titles 21, tick labels 16, crossing labels 17, legend 14-16). Damping ratio labels at 12pt are slightly small but still readable.
• VQ-02: No Overlap (6/6) — All text elements are clearly separated; crossing labels don't collide with markers or branches.
• VQ-03: Element Visibility (5/6) — Branches, markers, and annotations are all clearly visible. Guide lines are intentionally subtle. Breakaway square marker could be slightly larger for emphasis.
• VQ-04: Color Accessibility (4/4) — Blue/orange/green palette is colorblind-distinguishable. Red markers provide good contrast against the branch colors.
• VQ-05: Layout & Canvas (3/4) — Square canvas with equal scaling is correct for root locus geometry. The right half-plane is largely empty (as expected for this system), but a tighter x-range could improve canvas utilization.
• VQ-06: Axis Labels & Title (2/2) — "Real Axis (σ)" and "Imaginary Axis (jω)" are descriptive with proper engineering notation.

Design Excellence (13/20)

• DE-01: Aesthetic Sophistication (5/8) — Custom color palette starting with Python Blue, thoughtful typography with subtitle showing transfer function, intentional hierarchy between data and guide elements. Above library defaults but not publication-grade.
• DE-02: Visual Refinement (4/6) — View stroke removed, grid disabled, guide lines rendered as subtle dashed overlays, axis domain/tick colors customized to gray. Good refinement, though axis spines remain.
• DE-03: Data Storytelling (4/6) — The plot tells a clear control engineering story: subtitle identifies the system, crossing labels show the critical gain K=6, breakaway point is marked, and damping/frequency guides provide design context. Visual hierarchy separates locus (prominent) from guides (subtle).

Spec Compliance (15/15)

• SC-01: Plot Type (5/5) — Correct root locus plot showing pole trajectories in the complex plane.
• SC-02: Required Features (4/4) — All spec features present: × markers for poles, continuous branch curves with direction arrows, real axis segments, imaginary axis crossing markers, damping ratio and natural frequency guide lines, equal axis scaling centered on origin.
• SC-03: Data Mapping (3/3) — X=real part, Y=imaginary part, correctly mapped with gain as parameter.
• SC-04: Title & Legend (3/3) — Title format "root-locus-basic · altair · pyplots.ai" is correct. Legend clearly identifies the three branches.

Data Quality (14/15)

• DQ-01: Feature Coverage (5/6) — Shows breakaway point, complex branch departure, imaginary axis crossing, real axis segments, and asymptotic behavior at high gain. Could show break-in point or additional systems for fuller coverage, but this single system demonstrates all key features well.
• DQ-02: Realistic Context (5/5) — Classic control systems transfer function G(s) = 1/s(s+1)(s+2), a standard textbook example that is immediately recognizable and educational.
• DQ-03: Appropriate Scale (4/4) — Poles at 0, -1, -2 with gain range from 0.001 to 80 appropriately captures breakaway (K≈0.38), crossing (K=6), and high-gain asymptotic behavior.

Code Quality (10/10)

• CQ-01: KISS Structure (3/3) — Flat structure: imports → data computation → layered chart building → save. No functions or classes.
• CQ-02: Reproducibility (2/2) — Fully deterministic: polynomial root computation with fixed coefficients, no randomness.
• CQ-03: Clean Imports (2/2) — Only altair, numpy, pandas — all used.
• CQ-04: Code Elegance (2/2) — Clean, well-organized code. Branch sorting via nearest-neighbor matching is necessary and well-implemented. Layer composition is clear.
• CQ-05: Output & API (1/1) — Saves as plot.png with scale_factor=3.0 and plot.html.

Library Mastery (7/10)

• LM-01: Idiomatic Usage (4/5) — Good use of Altair's declarative grammar: layered composition with +, typed encodings (Q/N), alt.Scale, alt.Axis, alt.Legend, alt.Title with subtitle. Tooltips and interactive() are idiomatic.
• LM-02: Distinctive Features (3/5) — Leverages Altair's layer composition, interactive exploration, tooltip encoding, and declarative scale sharing across layers. These are distinctive Altair patterns, though the heavy data computation is library-agnostic.

Score Caps Applied

• None

Strengths

• Excellent spec compliance — all required root locus features are present and correctly implemented
• Strong data storytelling with labeled crossings, breakaway point, and transfer function in subtitle
• Clean layered architecture with well-separated concerns per chart layer
• Proper engineering notation on axes and annotations
• Deterministic, mathematically correct root computation with appropriate gain range

Weaknesses

• Right half-plane is mostly empty, wasting some canvas space (inherent to the system choice)
• Damping ratio labels only shown for ζ=0.4 and ζ=0.8; ζ=0.2 and ζ=0.6 guide lines are unlabeled
• Axis spines still present; removing top/right would improve visual refinement

Issues Found

1. VQ-05 MINOR: Canvas utilization slightly suboptimal — the right half-plane is mostly unused. Could tighten x-domain or choose an asymmetric range.
2. DE-02 MINOR: Top and right axis spines still visible — removing them would give a cleaner look.

AI Feedback for Next Attempt

Strong implementation on attempt 3. All spec features are present and well-executed. The design has improved significantly with custom colors, subtle guide lines, and good data storytelling. Minor remaining improvements would be removing unnecessary spines and optimizing canvas utilization, but the implementation is solid and well above the merge threshold.

Verdict: APPROVED