Lecture 10:
Transform 3
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Lecture 10: Transforms and Matrix Inverses, Slides of Computer Graphics
Various transforms including scaling, rotation, and translation matrices. It also explains the concept of homogeneous coordinates and their relation to 3d points and vectors. The inverse of a matrix and how it can be used to undo transformations. Exercises and solutions for matrix inverses and transposes.
Typology: Slides
2012/2013
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Lecture 10:
Transform 3
Write out the basic forms for a 2D: Scaling matrix Rotation matrix Translation matrix
Why is Translation transform affine but not linear?
What are homogeneous coordinates? What is the basic form of a 3D point in homogeneous coordinates? What about a 3D vector?
Refresher
Exercise - Solution
Questions?
Matrix Inverse
Matrix Inverse
Matrix Inverse
Is to think of an inverse as an “undo”
For example, if A scales by a factor of 2 and rotates 135 degrees, then A-1^ will rotate by -135 degrees and scale by 0.
One Way To Think About Inverses…
Rectangle(B) (^) A*B A-1^ *B (^) A-1 (^) AB
Finding Inverse Matrices…
Inverse Rotation Matrix
Questions?
Matrix Transpose
Neat Fact about Rotation Matrix
Questions?