Computer Graphics · Cluster
Geometry Representation
Meshes, splines, and implicit surfaces.
- 01 Indexed Triangle Meshes and the Vertex Cache Why a triangle list repeats every vertex, what an index buffer saves in bytes, and how vertex ordering interacts with a fixed-size post-transform cache.
- 02 Consistent Orientation and Signed Volume From a Triangle Mesh How triangle winding encodes which side of a surface is outside, how to propagate it across a mesh, and how the divergence theorem turns an oriented mesh into a volume.
- 03 Half-Edge Adjacency and Constant-Time Mesh Traversal How splitting each edge into two directed halves makes neighbour queries pointer dereferences, what the structure costs in bytes, and where it refuses to apply.
- 04 Catmull-Clark Subdivision and What the Limit Surface Actually Is The three averaging rules that turn a control cage into quads, why extraordinary vertices break the bicubic patch analogy, and how to evaluate the limit without subdividing.
- 05 NURBS Knot Vectors and What Rational Weights Do How a knot vector fixes the basis, why homogeneous coordinates let one polynomial form describe exact circles, and what non-uniform spacing costs downstream.
- 06 Signed Distance Fields as an Implicit Surface How a function of position replaces a mesh, why the gradient gives the normal, how min and max build constructive solid geometry, and what storage a sampled field needs.
- 07 Marching Cubes and the Ambiguity at a Cell Face How a 256-entry lookup table turns a scalar grid into triangles, why the case count is not 256, and how a saddle on a cell face can be triangulated two incompatible ways.
- 08 Quadric Error Metrics and What an Edge Collapse Actually Costs Each vertex accumulates the planes it can see as a 4x4 symmetric matrix; collapsing an edge sums two of them, and the result predicts geometric error without measuring it.
- 09 Robust Mesh Booleans and the Exact-Arithmetic Escape Union and difference on triangle meshes fail on coplanar faces and edge-on-edge contacts, and the standard answer is to compute the intersections exactly, then round once.
- 10 Mesh Parameterization, Cuts, and the Distortion That Cannot Be Removed Mapping a surface to the plane requires cutting it into a disk, and every planar map of a curved surface must distort either angles or areas by a measurable amount.