Geometric transformations in 3D and coordinate frames
Geometric transformations in 3D
and coordinate frames
Computer Graphics
CSE 167
Lecture 3
CSE 167: Computer Graphics
? 3D points as vectors
? Geometric transformations in 3D
? Coordinate frames
CSE 167, Winter 2018
2
Representing 3D points using vectors
? 3D point as 3©\vector
? 3D point using affine homogeneous
coordinates as 4©\vector
CSE 167, Winter 2018
3
Geometric transformations
? Translation
? Linear transformations
¨C Scale
¨C Rotation
? 3D rotations
? Affine transformation
¨C Linear transformation followed by translation
? Euclidean transformation
¨C Rotation followed by translation
? Composition of transformations
? Transforming normal vectors
CSE 167, Winter 2018
4
3D translation
Using
homogeneous
coordinates
CSE 167, Winter 2018
5
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