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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:
Karteninfo:
Autor: janisborn
Oberthema: Informatik
Thema: Computergrafik
Schule / Uni: RWTH Aachen
Ort: Aachen
Veröffentlicht: 18.05.2022