Math for Game Programmers - Harmonic Functions and Mean-Value

Explore two useful parameterizations for procedural geometry in this 2017 GDC talk by Nicholas Vining from Gaslamp Games. Delve into harmonic functions and mean-value coordinates, discovering their applications in mesh manipulation and UV generation. Learn about smooth Laplace functions, the strong maximum principle, and continuous Laplacian. Understand least squares methods, Lagrange multipliers, and barycentric coordinates. Examine convexity, the Lagrange property, and mean valid coordinate weights. Gain insights into real-time harmonic mesh applications and additional resources for further study. Note that due to technical issues, the audio may have occasional skips, so enabling closed captions is recommended for a better viewing experience.

Intro
Title
Overview
Harmonic Functions
Smooth
Laplace
Strong Maximum Principle
Continuous Laplacian
Last Year
Least Squares
Lagrange Multiplier
Barycentric coordinates
Convexity
Lagrange Property
Mean valid coordinate weights
Other Applications
Summary
References
Harmonic Mesh
RealTime Harmonic Mesh
CRC Press
Book