From a856f1b2cb9c5ce83c12f11a87b2cb87e411f037 Mon Sep 17 00:00:00 2001 From: Matthew Dingle Date: Sun, 25 Jan 2026 19:38:16 +1030 Subject: [PATCH 1/4] v2: Complete refactoring with bug fixes, tests, and documentation ## Bug Fixes - Fixed grid row calculation using wrong spacing variable (was hex_horizontal_spacing, now hex_vertical_spacing) - Fixed closest_palette_color returning None when all colors avoided (added fallback logic) - Fixed progress bar overshoot (update by actual chunk size, not hardcoded value) - Removed ineffective cache (was using only avg_rgb as key but patterns are position-dependent) ## New Features - Comprehensive test suite with 68 tests (tests/test_regression.py, tests/test_geometry.py) - Algorithm documentation (docs/ALGORITHM.md) with detailed mathematical descriptions - Clean v2/ architecture with modular components: - config.py: All constants and configuration values - color.py: ColorPalette class for palette generation and color selection - geometry.py: HexagonGrid and HexagonMask classes - layers.py: LayerRenderer for multi-layer hexagon patterns - processor.py: Main HexagonProcessor orchestration - hexify.py: CLI entry point for v2 ## Code Quality - Added type hints to hexagon_processor.py and hexify.py - Added Google-style docstrings to all classes and functions - Added input validation for palette colors, process count, chunk size - Created py.typed marker file for PEP 561 compliance - Updated .gitignore with Python-specific entries ## Testing - Test fixtures for gradient, color blocks, and fire images - Reference outputs for regression testing - Both pixel-perfect and tolerance-based comparison tests - Palette consistency and output dimension tests Co-Authored-By: Claude Opus 4.5 --- .gitignore | 27 +- docs/ALGORITHM.md | 520 +++++++++++ fire/f09f0b_palette.png | Bin 0 -> 545 bytes fire/output.png | Bin 0 -> 7312931 bytes hexagon_processor.py | 829 +++++++++++++----- hexify.py | 435 +++++++-- py.typed | 0 tests/__init__.py | 1 + tests/conftest.py | 67 ++ tests/create_fixtures.py | 58 ++ tests/fixtures/checkerboard_64x64.png | Bin 0 -> 971 bytes tests/fixtures/color_blocks_64x64.png | Bin 0 -> 326 bytes tests/fixtures/fire_64x64.png | Bin 0 -> 10864 bytes tests/fixtures/fire_64x64/166be1_palette.png | Bin 0 -> 557 bytes tests/fixtures/fire_64x64/output.png | Bin 0 -> 88060 bytes tests/fixtures/gradient_32x48.png | Bin 0 -> 621 bytes tests/fixtures/gradient_64x64.png | Bin 0 -> 495 bytes tests/fixtures/solid_gray_64x64.png | Bin 0 -> 221 bytes tests/generate_reference_outputs.py | 83 ++ .../ref_color_blocks_64x64_c16.png | Bin 0 -> 84635 bytes .../ref_color_blocks_64x64_c16_palette.npy | Bin 0 -> 512 bytes .../reference_outputs/ref_fire_64x64_c16.png | Bin 0 -> 207664 bytes .../ref_fire_64x64_c16_palette.npy | Bin 0 -> 512 bytes .../ref_gradient_32x48_c16.png | Bin 0 -> 65798 bytes .../ref_gradient_32x48_c16_palette.npy | Bin 0 -> 512 bytes .../ref_gradient_64x64_c16.png | Bin 0 -> 177003 bytes .../ref_gradient_64x64_c16_palette.npy | Bin 0 -> 512 bytes .../ref_gradient_64x64_c8.png | Bin 0 -> 165774 bytes .../ref_gradient_64x64_c8_palette.npy | Bin 0 -> 320 bytes tests/test_geometry.py | 550 ++++++++++++ tests/test_regression.py | 521 +++++++++++ v2/__init__.py | 35 + v2/color.py | 238 +++++ v2/config.py | 126 +++ v2/geometry.py | 266 ++++++ v2/hexify.py | 334 +++++++ v2/layers.py | 342 ++++++++ v2/processor.py | 284 ++++++ 38 files changed, 4425 insertions(+), 291 deletions(-) create mode 100644 docs/ALGORITHM.md create mode 100644 fire/f09f0b_palette.png create mode 100644 fire/output.png create mode 100644 py.typed create mode 100644 tests/__init__.py create mode 100644 tests/conftest.py create mode 100644 tests/create_fixtures.py create mode 100644 tests/fixtures/checkerboard_64x64.png create mode 100644 tests/fixtures/color_blocks_64x64.png create mode 100644 tests/fixtures/fire_64x64.png create mode 100644 tests/fixtures/fire_64x64/166be1_palette.png create mode 100644 tests/fixtures/fire_64x64/output.png create mode 100644 tests/fixtures/gradient_32x48.png create mode 100644 tests/fixtures/gradient_64x64.png create mode 100644 tests/fixtures/solid_gray_64x64.png create mode 100644 tests/generate_reference_outputs.py create mode 100644 tests/reference_outputs/ref_color_blocks_64x64_c16.png create mode 100644 tests/reference_outputs/ref_color_blocks_64x64_c16_palette.npy create mode 100644 tests/reference_outputs/ref_fire_64x64_c16.png create mode 100644 tests/reference_outputs/ref_fire_64x64_c16_palette.npy create mode 100644 tests/reference_outputs/ref_gradient_32x48_c16.png create mode 100644 tests/reference_outputs/ref_gradient_32x48_c16_palette.npy create mode 100644 tests/reference_outputs/ref_gradient_64x64_c16.png create mode 100644 tests/reference_outputs/ref_gradient_64x64_c16_palette.npy create mode 100644 tests/reference_outputs/ref_gradient_64x64_c8.png create mode 100644 tests/reference_outputs/ref_gradient_64x64_c8_palette.npy create mode 100644 tests/test_geometry.py create mode 100644 tests/test_regression.py create mode 100644 v2/__init__.py create mode 100644 v2/color.py create mode 100644 v2/config.py create mode 100644 v2/geometry.py create mode 100644 v2/hexify.py create mode 100644 v2/layers.py create mode 100644 v2/processor.py diff --git a/.gitignore b/.gitignore index bf3e0b6..ae332d5 100644 --- a/.gitignore +++ b/.gitignore @@ -1 +1,26 @@ -Hexify/Ilya/ +Hexify/Ilya/ + +# Python +__pycache__/ +*.py[cod] +*$py.class +*.so + +# pytest +.pytest_cache/ + +# Virtual environments +venv/ +.venv/ +ENV/ +env/ + +# IDE +.idea/ +.vscode/ +*.swp +*.swo + +# OS +.DS_Store +Thumbs.db diff --git a/docs/ALGORITHM.md b/docs/ALGORITHM.md new file mode 100644 index 0000000..d3357e2 --- /dev/null +++ b/docs/ALGORITHM.md @@ -0,0 +1,520 @@ +# Hexify Image Processing Algorithm + +## Table of Contents +1. [Overview](#overview) +2. [Input/Output](#inputoutput) +3. [Hexagonal Grid System](#hexagonal-grid-system) +4. [7-Layer Concentric System](#7-layer-concentric-system) +5. [Color Selection](#color-selection) +6. [Zone Angle Calculation](#zone-angle-calculation) +7. [Mathematical Formulas](#mathematical-formulas) + +--- + +## Overview + +Hexify is an image processing algorithm that transforms input images into a stylized mosaic composed of hexagonal cells. Each hexagonal cell contains a sophisticated 7-layer concentric pattern that represents the average color of the corresponding region in the source image. + +The algorithm achieves a unique aesthetic by: +- Dividing the output into a tessellated hexagonal grid +- Creating 7 concentric hexagonal layers within each cell +- Using alternating black/white and colored layers +- Implementing a 12-zone pie pattern for colored layers +- Intelligently selecting colors from a generated palette + +``` +Input Image Output Image ++-------------+ +---------------------------+ +| | | /\ /\ /\ /\ | +| Original | =========> | / \ / \ / \ / \ | +| Photo | Hexify | /hex \/ hex\/ hex\/ hex\ | +| | | \ 7L /\ 7L /\ 7L /\ 7L / | ++-------------+ | \ / \ / \ / \ / | + +---------------------------+ +``` + +--- + +## Input/Output + +### Input +- **Image**: Any standard image (RGB format) +- **Palette Size**: Number of colors to extract (default: 16) +- **Chunk Size**: Processing batch size (default: 32) + +### Output +- **Scaled Image**: 16x the resolution of the input +- **Format**: RGB image with hexagonal cell patterns + +### Scaling Factor + +``` +Output Resolution = Input Resolution x 16 + +Example: + Input: 1920 x 1080 pixels + Output: 30720 x 17280 pixels +``` + +### Hexagon Dimensions + +| Property | Value | Formula | +|----------|-------|---------| +| Hex Width | 256 px | Fixed | +| Hex Height | 222 px | `256 * (sqrt(3)/2)` | +| Hex Radius | 128 px | `256 / 2` | +| Horizontal Spacing | 192 px | `256 * 0.75` | +| Vertical Spacing | 222 px | Same as height | + +--- + +## Hexagonal Grid System + +### Grid Layout + +The hexagonal grid uses an offset coordinate system where odd columns are shifted vertically by half the hex height: + +``` +Column: 0 1 2 3 4 + +-----+ +-----+ +-----+ +-----+ +-----+ +Row 0 | 0,0 | | | | 0,2 | | | | 0,4 | + +-----+ | | +-----+ | | +-----+ + +-----+ +-----+ +Row 1 | 1,1 | | 1,3 | + +-----+ +-----+ + +-----+ +-----+ +-----+ +Row 1 | 1,0 | | 1,2 | | 1,4 | + +-----+ +-----+ +-----+ +``` + +### Center Calculation + +For each hexagon at grid position (row, col): + +```python +center_x = hex_horizontal_spacing * col +center_y = hex_vertical_spacing * row + (0.5 * hex_vertical_spacing if col % 2 else 0) +``` + +### Hexagon Mask Creation + +Hexagons are oriented with a flat top (orientation = pi/2): + +``` + ____ + / \ + / \ + \ / + \____/ +``` + +The mask is created using `RegularPolygon` with 6 vertices and the specified radius. + +--- + +## 7-Layer Concentric System + +Each hexagonal cell contains 7 concentric hexagonal layers, numbered from inside (1) to outside (7): + +``` +Cross-section view of a hexagonal cell: + + Layer 7 (outermost) - Black/White + +---------------------------+ + | Layer 6 - Colored (12 zones) + | +----------------------+ | + | | Layer 5 - Black/White| | + | | +------------------+ | | + | | | Layer 4 - Colored| | | + | | | +--------------+ | | | + | | | | L3 - B/W | | | | + | | | | +----------+ | | | | + | | | | | L2 Color | | | | | + | | | | | +------+ | | | | | + | | | | | | L1 | | | | | | + | | | | | | B/W | | | | | | + | | | | | +------+ | | | | | + | | | | +----------+ | | | | + | | | +--------------+ | | | + | | +------------------+ | | + | +----------------------+ | + +---------------------------+ +``` + +### Layer Types + +| Layer | Type | Description | +|-------|------|-------------| +| 7 | Odd | Outermost, solid black or white | +| 6 | Even | Colored 12-zone pie pattern | +| 5 | Odd | Solid black or white | +| 4 | Even | Colored 12-zone pie pattern | +| 3 | Odd | Solid black or white | +| 2 | Even | Colored 12-zone pie pattern | +| 1 | Odd | Innermost, solid black or white | + +### Odd Layers (1, 3, 5, 7) - Black/White + +Odd layers are filled with either pure black (0, 0, 0) or pure white (255, 255, 255) based on the average brightness of the cell: + +```python +brightness = mean(avg_rgb) +bw_color = (0, 0, 0) if brightness < 128 else (255, 255, 255) +``` + +**Layer Radii (Fixed Proportions)**: +```python +layer_radius[i] = outer_radius * (i / 7) + +Layer 7: radius * (7/7) = 100% of hex radius +Layer 5: radius * (5/7) = ~71% of hex radius +Layer 3: radius * (3/7) = ~43% of hex radius +Layer 1: radius * (1/7) = ~14% of hex radius +``` + +### Even Layers (2, 4, 6) - Colored Pie Patterns + +Even layers contain a 12-zone pie pattern with two alternating colors. The layer diameter varies based on brightness: + +**Layer 6 Diameter**: +```python +diameter = 256 - abs(brightness - 128) * (256 - 192) / 128 + +When brightness = 128 (mid-gray): diameter = 256 (maximum) +When brightness = 0 or 255: diameter = 192 (minimum) +``` + +**Layers 4 and 2 Diameter**: +```python +diameter = (layer_radii[i + 1] * 2) - abs(brightness - 128) * 64 / 128 +``` + +This creates a visual effect where: +- Mid-brightness cells have larger colored layers +- Very dark or very bright cells have smaller colored layers + +--- + +## Color Selection + +### Palette Generation + +1. **Downscale** large images to max 1 million pixels for efficiency +2. **K-Means Clustering** extracts the dominant colors: + ```python + kmeans = KMeans(n_clusters=num_palette_colors, random_state=42) + palette = kmeans.cluster_centers_ + ``` +3. **Sort** palette by brightness for consistency +4. **Round** and **hash** for caching purposes + +### Color 1 Selection (Primary Color) + +The closest palette color to the average RGB of the layer region: + +```python +color_1 = closest_palette_color(avg_rgb, palette, avoid_rgb) +``` + +Colors used in previous layers are avoided to increase variety. + +### Color 2 Selection (Secondary Color) + +Color 2 is selected to minimize the difference between the weighted average of all colors in the layer and the target average RGB: + +```python +mixed_rgb = (color_1_area * color_1 + color_2_area * color_2 + bw_area * bw_color) / total_area +color_2 = argmin(|avg_rgb - mixed_rgb|) +``` + +This ensures that when you "squint" at the output, the colors blend to approximate the original image. + +--- + +## Zone Angle Calculation + +### 12-Zone Pie Pattern + +Each even layer is divided into 12 alternating zones radiating from the center: + +``` + Zone 1 + _____|_____ + / | \ + Z12 / Z2 | Z2 \ Z2 + / _____|_____ \ + / / | \ \ + Z11| | Center| | Z3 + | |______|_______| | + Z10 \ \ | / / Z4 + \ \_____|_____/ / + Z9 \ Z8 | Z8 / Z5 + \____|____/ + Z7 + Z6 +``` + +### Even vs Odd Zone Angles + +The angular width of zones alternates: +- **Even zones** (2, 4, 6, 8, 10, 12): Use `even_angle` +- **Odd zones** (1, 3, 5, 7, 9, 11): Use `odd_angle` + +```python +# Total must equal 360 degrees +6 * even_angle + 6 * odd_angle = 360 +# Therefore: +even_angle + odd_angle = 60 degrees +``` + +### Calculating Zone Angles + +The angle split is determined by how close Color 1 is to the target: + +```python +# Distance from Color 1 to target +dist_1 = |color_1 - avg_rgb| + +# Distance to nearest adjacent palette color +color_adj = closest_color_to(color_1) in palette +dist_adj = |color_1 - color_adj| + +# Percentage determines angle split +percentage_off = min(dist_1, dist_adj) / max(dist_1, dist_adj) + +even_angle = percentage_off * 60 # Range: 0 to 60 degrees +odd_angle = 60 - even_angle # Range: 60 to 0 degrees +``` + +**Effect**: +- When Color 1 is an exact match: `even_angle = 0`, Color 1 zones are minimal +- When Color 1 is far from target: `even_angle = 60`, Color 1 zones are maximal + +### Zone Vertex Calculation + +For each zone, three key points define the triangular shape: + +``` + p2 + /\ + / \ + / p3 \ + /______\ + p1 center + +Where: +- center: (radius, radius) - the hexagon center +- p1: Starting point on hexagon edge +- p2: Ending point on hexagon edge +- p3: Apex point for odd zones (creates extra triangle fill) +``` + +**Calculating p1 and p2**: +```python +start_angle = angle_offset +end_angle = start_angle + zone_angle + +p1 = (center + hex_radius * cos(start_angle), + center + hex_radius * sin(start_angle)) + +p2 = (center + hex_radius * cos(end_angle), + center + hex_radius * sin(end_angle)) +``` + +**Calculating p3 (Apex for Odd Zones)**: +```python +# Midpoint of p1-p2 +p12 = ((p1.x + p2.x) / 2, (p1.y + p2.y) / 2) + +# Half-distance between p1 and p2 +d = distance(p1, p2) / 2 + +# Length of shorter leg (30-60-90 triangle geometry) +length_of_shorter_leg = d / sqrt(3) + +# Perpendicular offset from midpoint +dx = (p12.x - p1.x) / distance(p1, p12) +dy = (p12.y - p1.y) / distance(p1, p12) +p3 = (p12.x + length_of_shorter_leg * dy, + p12.y - length_of_shorter_leg * dx) +``` + +The initial angle offset ensures zones align properly with the hexagon edges: +```python +angle_offset = 30 - (even_angle / 2) +``` + +--- + +## Mathematical Formulas + +### Hexagon Area Formula + +For a regular hexagon with radius `r` (center to vertex): + +``` +A = (3 * sqrt(3) / 2) * r^2 + +Derivation: +- A hexagon consists of 6 equilateral triangles +- Each triangle has side length r +- Area of equilateral triangle = (sqrt(3) / 4) * r^2 +- Total area = 6 * (sqrt(3) / 4) * r^2 = (3 * sqrt(3) / 2) * r^2 +``` + +**In code**: +```python +hex_area = 3 * math.sqrt(3) * (hex_radius ** 2) / 2 +``` + +### Layer Diameter Calculations + +**Layer 6 (Outermost Colored Layer)**: +``` +diameter = 256 - |brightness - 128| * (256 - 192) / 128 + = 256 - |brightness - 128| * 64 / 128 + = 256 - |brightness - 128| / 2 + +Range: [192, 256] pixels +Maximum when brightness = 128 +Minimum when brightness = 0 or 255 +``` + +**Layers 4 and 2**: +``` +diameter = 2 * layer_radii[i+1] - |brightness - 128| * 64 / 128 + +Where layer_radii[i+1] is the radius of the next outer odd layer +``` + +### Zone Area Calculations + +For a pie slice (circular sector approximation): + +``` +zone_area = 0.5 * r^2 * theta + +Where: +- r = layer radius +- theta = zone angle in radians +``` + +**Total Even Zone Area** (6 zones): +```python +even_area = 6 * (0.5 * hex_radius^2 * radians(even_angle)) +``` + +**Total Odd Zone Area** (6 zones): +```python +odd_area = 6 * (0.5 * hex_radius^2 * radians(odd_angle)) +``` + +### Color Mixing Weighted Average + +The weighted average formula for selecting Color 2: + +``` +mixed_rgb = (A1 * C1 + A2 * C2 + Abw * Cbw) / (A1 + A2 + Abw) + +Where: +- A1 = Total area of Color 1 zones (even zones) +- C1 = Color 1 RGB values +- A2 = Total area of Color 2 zones (odd zones) +- C2 = Color 2 RGB values (candidate) +- Abw = Area of black/white layer above +- Cbw = Black or white RGB (0,0,0 or 255,255,255) +``` + +**Goal**: Find C2 that minimizes: +``` +|avg_rgb - mixed_rgb| +``` + +This Euclidean distance minimization ensures the blended appearance matches the original. + +### Euclidean Distance (Color Matching) + +``` +distance = sqrt((r1-r2)^2 + (g1-g2)^2 + (b1-b2)^2) +``` + +**In code**: +```python +distance = np.linalg.norm(color_1 - color_2) +``` + +--- + +## Implementation Notes + +### Caching System + +Hexagon patterns are cached by their average RGB values to avoid redundant computation: + +```python +cache_key = (int(avg_r), int(avg_g), int(avg_b)) +``` + +This significantly improves performance for images with many similar-colored regions. + +### Parallel Processing + +The algorithm processes hexagons in chunks using `ProcessPoolExecutor`: +- Hexagons are grouped into chunks (default size: 32) +- Each chunk is processed by a separate worker process +- Results are composited onto the output image + +### Point Clipping + +Zone vertices that fall outside the hexagon boundary are clipped to the nearest edge: + +```python +def clip_point_to_hexagon(point, hex_coords): + if point is inside hexagon: + return point + else: + return nearest_point_on_hexagon_edge(point) +``` + +This ensures all zone triangles render correctly within the hexagonal cell boundary. + +--- + +## Quick Reference + +| Constant | Value | Description | +|----------|-------|-------------| +| Scale Factor | 16x | Output resolution multiplier | +| Hex Width | 256 px | Base hexagon width | +| Hex Height | ~222 px | Based on sqrt(3)/2 ratio | +| Layers | 7 | Concentric hexagon layers | +| Zones per Layer | 12 | Pie slices in colored layers | +| Brightness Threshold | 128 | Black vs white determination | + +--- + +## Pseudocode Summary + +``` +function hexify(input_image): + output = create_blank_image(input.size * 16) + palette = kmeans_extract_colors(input_image, n=16) + + for each hexagon_center in grid: + avg_rgb = sample_input_region(hexagon_center / 16) + bw_color = BLACK if mean(avg_rgb) < 128 else WHITE + + # Draw layers from outside to inside + for layer in [7, 6, 5, 4, 3, 2, 1]: + if layer is odd: + draw_solid_hexagon(layer, bw_color) + else: + color_1 = closest_palette_color(avg_rgb) + color_2 = select_complementary_color(avg_rgb, color_1) + angles = calculate_zone_angles(avg_rgb, color_1) + draw_12_zone_pattern(layer, color_1, color_2, angles) + + composite(output, hexagon_pattern) + + return output +``` diff --git a/fire/f09f0b_palette.png b/fire/f09f0b_palette.png new file mode 100644 index 0000000000000000000000000000000000000000..cdddc62f7b7a019c81aa6aa4f98a17a6fb571679 GIT binary patch literal 545 zcmeAS@N?(olHy`uVBq!ia0y~yU;;8395~p3WX}Hc`+<~IiEBhjaDG}zd16s2gKuI< zK~8>2PG*uqS!z*nW`3Tro}q!Bg^of-Nl8JmmA-y1T!mhKQM&%Y=+bjQQ#cDeB8wRq 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