3D Depth Sorting for Triangle Rendering in Scratch
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Colomando_3D
Posted on August 4, 2025 • Expert
🎨 3D depth sorting for triangle rendering
I’m working on a 3D renderer where I draw each individual filled triangle using costume blocks. How do I implement depth sorting to know which triangles to draw first?
I need to figure out the correct rendering order so that triangles in the back don’t appear in front of triangles that should be closer to the camera. Any help with the sorting algorithm would be appreciated! 🎯
Graphics3D_Expert
Replied 1 hour later • ⭐ Best Answer
Excellent question @Colomando_3D! Depth sorting is crucial for proper 3D rendering. Let me show you how to implement a complete depth sorting system for triangle rendering:
📊 3D Depth Sorting Flow
Here’s how the depth sorting process works:
🎯 Step 1: Triangle Data Structure
First, set up your triangle data storage system:
// Triangle data structure setup when green flag clicked // Initialize triangle storage lists delete all of [triangle x1 v] delete all of [triangle y1 v] delete all of [triangle z1 v] delete all of [triangle x2 v] delete all of [triangle y2 v] delete all of [triangle z2 v] delete all of [triangle x3 v] delete all of [triangle y3 v] delete all of [triangle z3 v] delete all of [triangle depth v] delete all of [triangle color v] delete all of [triangle id v] // Camera position set [camera x v] to [0] set [camera y v] to [0] set [camera z v] to [-10]
📐 Step 2: Calculate Triangle Centroid and Depth
Calculate the centroid (center point) of each triangle for depth sorting:
// Calculate triangle centroid and depth define calculate triangle depth (triangle index) // Get triangle vertices set [x1 v] to (item (triangle index) of [triangle x1 v]) set [y1 v] to (item (triangle index) of [triangle y1 v]) set [z1 v] to (item (triangle index) of [triangle z1 v]) set [x2 v] to (item (triangle index) of [triangle x2 v]) set [y2 v] to (item (triangle index) of [triangle y2 v]) set [z2 v] to (item (triangle index) of [triangle z2 v]) set [x3 v] to (item (triangle index) of [triangle x3 v]) set [y3 v] to (item (triangle index) of [triangle y3 v]) set [z3 v] to (item (triangle index) of [triangle z3 v]) // Calculate centroid set [centroid x v] to (((x1) + (x2) + (x3)) / [3]) set [centroid y v] to (((y1) + (y2) + (y3)) / [3]) set [centroid z v] to (((z1) + (z2) + (z3)) / [3]) // Calculate distance from camera set [dx v] to ((centroid x) - (camera x)) set [dy v] to ((centroid y) - (camera y)) set [dz v] to ((centroid z) - (camera z)) set [depth v] to ([sqrt v] of (((dx) * (dx)) + (((dy) * (dy)) + ((dz) * (dz))))) // Store depth replace item (triangle index) of [triangle depth v] with (depth)
🔄 Step 3: Sorting Algorithm Implementation
Implement a bubble sort algorithm for depth sorting:
// Bubble sort for depth sorting define sort triangles by depth set [triangle count v] to (length of [triangle depth v]) set [sorted v] to [false] repeat until <(sorted) = [true]> set [sorted v] to [true] repeat ((triangle count) - [1]) set [i v] to (counter) set [j v] to ((counter) + [1]) // Compare depths (farther triangles first) if <(item (i) of [triangle depth v]) < (item (j) of [triangle depth v])> then // Swap all triangle data swap triangle data (i) (j) set [sorted v] to [false] end end end define swap triangle data (index1) (index2) // Swap all triangle properties set [temp v] to (item (index1) of [triangle x1 v]) replace item (index1) of [triangle x1 v] with (item (index2) of [triangle x1 v]) replace item (index2) of [triangle x1 v] with (temp) // Repeat for all other properties (y1, z1, x2, y2, z2, x3, y3, z3, depth, color, id) // ... (similar swaps for all properties)
⚡ Step 4: Optimized Quick Sort (Better Performance)
For better performance with many triangles, use quick sort:
// Quick sort implementation define quick sort triangles (low) (high) if <(low) < (high)> then partition triangles (low) (high) set [pivot v] to (partition result) quick sort triangles (low) ((pivot) - [1]) quick sort triangles ((pivot) + [1]) (high) end define partition triangles (low) (high) set [pivot depth v] to (item (high) of [triangle depth v]) set [i v] to ((low) - [1]) repeat ((high) - (low)) set [j v] to ((low) + ((counter) - [1])) if <(item (j) of [triangle depth v]) > (pivot depth)> then change [i v] by [1] swap triangle data (i) (j) end end change [i v] by [1] swap triangle data (i) (high) set [partition result v] to (i)
🎨 Step 5: Rendering Pipeline
Complete rendering system with depth sorting:
// Complete rendering pipeline define render frame // Clear screen erase all // Update all triangle depths repeat (length of [triangle depth v]) calculate triangle depth (counter) end // Sort triangles by depth (farthest first) quick sort triangles [1] (length of [triangle depth v]) // Render triangles in sorted order repeat (length of [triangle depth v]) render triangle (counter) end define render triangle (index) // Get triangle data set [x1 v] to (item (index) of [triangle x1 v]) set [y1 v] to (item (index) of [triangle y1 v]) set [x2 v] to (item (index) of [triangle x2 v]) set [y2 v] to (item (index) of [triangle y2 v]) set [x3 v] to (item (index) of [triangle x3 v]) set [y3 v] to (item (index) of [triangle y3 v]) set [color v] to (item (index) of [triangle color v]) // Project 3D to 2D (perspective projection) project 3d to 2d (x1) (y1) (item (index) of [triangle z1 v]) set [screen x1 v] to (projected x) set [screen y1 v] to (projected y) project 3d to 2d (x2) (y2) (item (index) of [triangle z2 v]) set [screen x2 v] to (projected x) set [screen y2 v] to (projected y) project 3d to 2d (x3) (y3) (item (index) of [triangle z3 v]) set [screen x3 v] to (projected x) set [screen y3 v] to (projected y) // Draw filled triangle set pen color to (color) draw filled triangle (screen x1) (screen y1) (screen x2) (screen y2) (screen x3) (screen y3)
🔧 Step 6: Advanced Depth Testing
For more accurate depth sorting, implement per-pixel depth testing:
// Advanced depth buffer system when green flag clicked // Initialize depth buffer set [screen width v] to [480] set [screen height v] to [360] delete all of [depth buffer v] repeat ((screen width) * (screen height)) add [999999] to [depth buffer v] // Far plane end define set depth buffer (x) (y) (depth) set [buffer index v] to (((y) * (screen width)) + (x)) if <(depth) < (item (buffer index) of [depth buffer v])> then replace item (buffer index) of [depth buffer v] with (depth) set [depth test passed v] to [true] else set [depth test passed v] to [false] end define draw pixel with depth (x) (y) (depth) (color) set depth buffer (x) (y) (depth) if <(depth test passed) = [true]> then set pen color to (color) go to x: (x) y: (y) pen down pen up end
🎮 Step 7: Complete Example Usage
Here’s how to use the complete system:
// Example usage when green flag clicked // Add some test triangles add triangle (0) (0) (0) (100) (0) (0) (50) (100) (0) [#ff0000] add triangle (0) (0) (50) (100) (0) (50) (50) (100) (50) [#00ff00] add triangle (0) (0) (100) (100) (0) (100) (50) (100) (100) [#0000ff] forever // Rotate camera around scene change [camera angle v] by [1] set [camera x v] to (([cos v] of (camera angle)) * [200]) set [camera z v] to (([sin v] of (camera angle)) * [200]) // Render frame render frame wait [0.033] seconds // ~30 FPS end define add triangle (x1) (y1) (z1) (x2) (y2) (z2) (x3) (y3) (z3) (color) add (x1) to [triangle x1 v] add (y1) to [triangle y1 v] add (z1) to [triangle z1 v] add (x2) to [triangle x2 v] add (y2) to [triangle y2 v] add (z2) to [triangle z2 v] add (x3) to [triangle x3 v] add (y3) to [triangle y3 v] add (z3) to [triangle z3 v] add [0] to [triangle depth v] add (color) to [triangle color v] add (length of [triangle id v]) to [triangle id v]
This system will correctly sort your triangles from back to front, ensuring proper depth rendering! The key is calculating the centroid depth and sorting before rendering. 🎨
AwesomeLlama_Graphics
Replied 30 minutes later
@Graphics3D_Expert fantastic comprehensive answer! I’d add that for simple cases, you can also use the painter’s algorithm approach:
// Simple painter's algorithm define simple depth sort // Just sort by average Z coordinate repeat (length of [triangle depth v]) set [avg z v] to (((item (counter) of [triangle z1 v]) + (item (counter) of [triangle z2 v]) + (item (counter) of [triangle z3 v])) / [3]) replace item (counter) of [triangle depth v] with (avg z) end // Sort by Z (farthest first) sort triangles by depth
This works well for most cases and is much simpler to implement! 🎯
Colomando_3D
Replied 15 minutes later
@Graphics3D_Expert @AwesomeLlama_Graphics This is exactly what I needed! Thank you both! 🎉
The centroid-based approach makes perfect sense, and I love the complete pipeline you’ve provided. Going to implement the quick sort version for better performance with my triangle meshes!
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