A Hands-On Introduction to
Discrete Differential Operators on Polygon Meshes

Introduction

Sven D. Wagner

TU Dortmund

Astrid Bunge

AutoForm Engineering

Mario Botsch

TU Dortmund

🚀 by Decker

Solve PDEs on discrete surface meshes and volume meshes

images/vw.png Surface mesh images/bunny-tets.png Volume mesh

Solve PDEs on discrete surface meshes and volume meshes

We focus on surface meshes

images/vw.png Surface mesh images/bunny-tets.png Volume mesh

Gradient (direction of steepest ascent) \[ \small \grad f(u,v) \;=\; \vector{ \pdiff{f}{u} \\ \pdiff{f}{v} } \]
Divergence (magnitude of source or sink) \[ \small \func{div}\of{\vec{f}(u,v)} \;=\; \func{div} \vector{f_1(u,v) \\ f_2(u,v)} \;=\; \pdiff{f_1}{u} + \pdiff{f_2}{v} \]
Laplace (difference to average of local neighborhood) \[ \small \laplace f(u,v) \;=\; \func{div} \grad f \;=\; \frac{\partial^2 f}{\partial u^2} + \frac{\partial^2 f}{\partial v^2} \]

images/vw.png Surface Meshes: ~~Triangles~~ Polygons images/bunny-tets.png Volume Meshes: ~~Tetrahedra~~ Polyhedra

Part 1: Triangle Meshes (09:00–10:30)
- Introduction
- Laplacian on Triangle Meshes
- Coding: Parameterization
- Robust Laplacians on Triangle Meshes
- Coding: Parameterization

Part 2: Polygon Meshes (10:45–12:15)
- Laplacian on Polygon Meshes
- Coding: Smoothing
- Robust Polygon Laplacian
- Coding: Geodesics in Heat
- Other Polygon Laplacians

Please ask question at any time!