# Performance Benchmark Report — M3 里程碑

**Date**: 2026-07-24  
**Hardware**: 4× 2500 MHz CPU, 1 GB RAM (Docker container)  
**Compiler**: GCC 11.4, C++17, -O2

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## Results

### BVH (Bounding Volume Hierarchy)

| Benchmark | Size | Time | Throughput |
|-----------|------|------|------------|
| Build | 500 tris | 72 µs | 6.9M tris/s |
| Build | 1000 tris | 245 µs | 4.1M tris/s |
| Build | 2000 tris | 650 µs | 3.1M tris/s |
| Ray Query | 500 tris × 1000 rays | 1.39 ms | 721K rays/s |
| Ray Query | 2000 tris × 1000 rays | 3.19 ms | 315K rays/s |

### 2D Delaunay Triangulation

| Benchmark | Size | Time | Throughput |
|-----------|------|------|------------|
| Bowyer-Watson | 100 pts | 67 µs | 1.5M pts/s |
| Bowyer-Watson | 1000 pts | 3.96 ms | 254K pts/s |
| Bowyer-Watson | 10000 pts | 671 ms | 15K pts/s |

### Curve Evaluation

| Benchmark | Size | Time | Throughput |
|-----------|------|------|------------|
| Bezier (cubic) | 10000 | 263 µs | 38.5M evals/s |
| Bezier (cubic) | 100000 | 2.66 ms | 38.1M evals/s |
| BSpline (cubic) | 10000 | 744 µs | 13.6M evals/s |
| BSpline (cubic) | 100000 | 7.33 ms | 13.8M evals/s |

### Spatial Index (KD-Tree)

| Benchmark | Size | Time | Throughput |
|-----------|------|------|------------|
| Build | 500 pts | 71 µs | 7.0M pts/s |
| Build | 2000 pts | 537 µs | 3.8M pts/s |
| kNN (k=10) | 500 pts | 64 µs | 316K q/s |
| kNN (k=10) | 2000 pts | 92 µs | 218K q/s |

### 3D Mesh Boolean

| Benchmark | Size | Time | Throughput |
|-----------|------|------|------------|
| Union | ~100 faces | 2.05 ms | 495 ops/s |
| Union | ~500 faces | 9.10 ms | 112 ops/s |
| Intersection | ~100 faces | 1.94 ms | 520 ops/s |
| Intersection | ~500 faces | 8.53 ms | 118 ops/s |

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## Summary

All 5 benchmark modules operational (143/143 tests pass). Performance scales reasonably for a C++17 geometry engine without SIMD optimization. Key areas for future improvement:

- BVH ray query: implement packet tracing / wider BVH
- Delaunay 2D: O(n²) in current Bowyer-Watson
- Boolean: clip-by-point-test is brute-force; needs exact mesh clipping