CoboCards App FAQ & Wishes Feedback
Language: English Language
Sign up for free  Login

This flashcard is just one of a free flashcard set. See all flashcards!

All main topics / Informatik / Computergrafik / Schwerpunktkolloquium: Basic Techniques, Geometry Processing, Global Illumination
52
How to compute a Discrete Harmonic Parametrization? Give three examples for weights!
Given a mesh with disk topology of points in the mesh domain , find points in the parameter domain .

A function is harmonic if its Laplace is zero, i.e.


Use a spring model: Edges of the mesh are mapped to springs. Fix parameters of mesh boundary points. Relax remaining points to equilibrium by solving

i.e.


Solve two linear systems:



To satisfy Tutte's theorem (and thus ensure a valid parametrization), use a concave boundary shape (circle, square) and have only positive spring weights.

Uniform Weights

Distributes vertices regularly in the parameter domain. No mesh structure is considered. Strong length and angular distortion.

Chordal Weights

Considers vertex distances. Low length distortion, but angular distortion is not controlled and thus high.

Cotangent Weights

In practice, low length and angular distortion. However, can lead to negative weights (violating Tutte's theorem).
New comment
Flashcard info:
Author: janisborn
Main topic: Informatik
Topic: Computergrafik
School / Univ.: RWTH Aachen
City: Aachen
Published: 18.05.2022

Cancel
Email

Password

Login    

Forgot password?
Deutsch  English