Computer graphics and linear algebra
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COMPUTER GRAPHICS AND LINEAR ALGEBRA. AN INTRODUCTION. 1. Representing image on computer. Points on Screen == Co -ordinate vectors. Example {0, 0}, {1, 1}, {2, 2}, {3, 3}, , {4, 2}, {5, 1}, {6, 0}. Picture with points joined together. 1. Moving the images. Moving a point

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1 representing image on computer
1. Representing image on computer

Points on Screen

== Co-ordinate vectors


Example 0 0 1 1 2 2 3 3 4 2 5 1 6 0
Example{0, 0}, {1, 1}, {2, 2}, {3, 3}, , {4, 2}, {5, 1}, {6, 0}



1 moving the images
1. Moving the images

Moving a point

== Transforming Co-ordinate vector

== Multiplication by matrices


Transformation of co ordinate vectors
Transformation of co-ordinate vectors

  • Original: {0, 0}, {1, 1}, {2, 2}, {3, 3}, , {4, 2}, {5, 1}, {6, 0}

  • Multiply each x-co-ordinate by 2, keeping y the same

  • New: {0, 0}, {2, 1}, {4, 2}, {6, 3}, {8, 2}, {10, 1}, {12, 0}



Image of transformed vectors 0 0 2 1 4 2 6 3 8 2 10 1 12 0
Image of transformed vectors{0, 0}, {2, 1}, {4, 2}, {6, 3}, {8, 2}, {10, 1}, {12, 0}


The two images in same picture blue original red new
The two images in same picture(blue: original, red: new)


Going from lines and points to moving images
Going from lines and points to moving images

  • POLYGONAL MESH

  • MOTION CAPTURE


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