Cutting Up Curved Things (With Math)
8 days ago
- #3D Rendering
- #Computer Graphics
- #Tessellation
- GPUs render only triangles, not curved surfaces directly.
- Tessellation converts curved surfaces into triangle meshes for rendering.
- A triangle mesh consists of vertices (points in space) and indices (defining triangles).
- Mathematical representations of surfaces (like cylinders) are sampled to create these meshes.
- Sampling involves laying a grid in parameter space (u, v) and evaluating points on the surface.
- More samples result in smoother surfaces but require more triangles and computational power.
- Flat faces can be triangulated easily using fan triangulation for convex polygons.
- Cylinders and spheres require specific sampling strategies to handle their curvature.
- Holes in surfaces complicate triangulation and require merging boundaries before processing.
- Ear clipping is used to triangulate complex polygons with holes.
- The output is a triangle mesh format compatible with GPUs, STL files, and physics engines.
- The illusion of smooth surfaces is created by densely packed triangles that appear seamless.