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Explain how to transform geometry according to camera position and projection to the screen!
Concatenation of three matrices:
Look-at transform
Given a camera position
, a desired viewing direction 
and an up vector 
, we compute a orthogonal coordinate system as follows:
Now, the matrix transforming points from camera space to world space is given by
The look-at transform is the inverse of this, transforming points from world space to local camera space:
Frustum transform
Transforms points from a frustum defined by the near / far plane distance of the camera
and the extents of the near plane rectangle 
into the unit cube 
. 
maps points on the near plane to 
and points on the far plane to 
.
Viewport transform
Transforms from the unit cube to pixel coordinates on a
screen:
Look-at transform
Given a camera position
, a desired viewing direction and an up vector , we compute a orthogonal coordinate system as follows:Now, the matrix transforming points from camera space to world space is given by
The look-at transform is the inverse of this, transforming points from world space to local camera space:
Frustum transform
Transforms points from a frustum defined by the near / far plane distance of the camera
and the extents of the near plane rectangle into the unit cube . maps points on the near plane to and points on the far plane to .Viewport transform
Transforms from the unit cube to pixel coordinates on a
screen:
Flashcard info:
Author: janisborn
Main topic: Informatik
Topic: Computergrafik
School / Univ.: RWTH Aachen
City: Aachen
Published: 18.05.2022