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106
Characterize linear, affine and projective transforms!
Linear Maps
A map
which is
additive:
homogenous:
Representable by a transformation matrix
:

Linear map preserve the origin.
Affine Maps
A map
which is
composed of a linear map
and a translation:

Affine transformations can be represented as a matrix-vector product by using extended coordinates:

Affine maps preserve collinearity of points and distance ratios.
Projective Maps
Represented by a matrix-vector product using homogeneous coordinates.
Projective maps preserve cross ratios:

A map

additive:

homogenous:

Representable by a transformation matrix


Linear map preserve the origin.
Affine Maps
A map

composed of a linear map


Affine transformations can be represented as a matrix-vector product by using extended coordinates:

Affine maps preserve collinearity of points and distance ratios.
Projective Maps
Represented by a matrix-vector product using homogeneous coordinates.
Projective maps preserve cross ratios:


Flashcard info:
Author: janisborn
Main topic: Informatik
Topic: Computergrafik
School / Univ.: RWTH Aachen
City: Aachen
Published: 18.05.2022