This flashcard is just one of a free flashcard set. See all flashcards!
53
How can you estimate the distortion introduced by a parametrization?
Given a parametrization
consider the Jacobian of
at some point 
:
and its Singular Value Decomposition
and 
are orthonormal, i.e. rotation matrices. 
is a diagonal matrix and corresponds to an axis-aligned scaling. 
thus can be interpreted as a concatenation of a rotation, a scaling and again a rotation. The distortion at can thus be inferred from 
and 
:
consider the Jacobian of
at some point :and its Singular Value Decomposition
and are orthonormal, i.e. rotation matrices. is a diagonal matrix and corresponds to an axis-aligned scaling. thus can be interpreted as a concatenation of a rotation, a scaling and again a rotation. The distortion at can thus be inferred from and :- Conformal / angle preserving:
- Area preserving:
- Isometry:
Flashcard info:
Author: janisborn
Main topic: Informatik
Topic: Computergrafik
School / Univ.: RWTH Aachen
City: Aachen
Published: 18.05.2022