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|Session Name:||Math for Game Programmers: Harmonic Functions and Mean-Value|
|Company Name(s):||Gaslamp Games|
|Track / Format:||Programming|
|Overview:||In this session, Nicholas Vining of Gaslamp Games will discuss two useful parameterizations for procedural geometry, with applications in mesh manipulation and UV generation. Mean value coordinates are a generalization of Barycentric coordinates which allow a vertex in a planar triangulation to be expressed as a convex combination of its neighbors. Harmonic functions are twice-continuously differentiable over a manifold, useful when texturing complex meshes of unknown topology and genus with surface details (rust, cracks). Nicholas will go over how he constructs them by discretizing the Laplace operator using cotangent weights, then solving a constrained least-squares optimization.|