EmbeddingGemma 2: an open, lightweight multimodal embedding model
deepmind.google·6d ago
AI Engineering
Hacker News·Aug 28·5 min read
Hilariously Fast Volume Computation with the Divergence Theorem
TL;DR
A new algorithm leverages the Divergence Theorem for rapid volume computation of simple, closed, triangulated 3D meshes, significantly speeding up the process.
✦ Why It Matters
Implement this algorithm to enhance volume computation speed in your 3D modeling or simulation projects today.
Key Takeaways
- Utilize the Divergence Theorem for volume calculations.
- Implement the algorithm for real-time 3D graphics applications.
- Optimize triangle processing to achieve linear time complexity.
- Explore existing literature for similar algorithms to enhance understanding.
How It Works
The algorithm defines volume as a surface integral derived from a function with a divergence of one. By parametrizing each triangle and calculating the cross product of its vertices, the algorithm simplifies the volume computation to a series of efficient arithmetic operations, avoiding complex numerical methods.