COMPUTER GRAPHICS AND LINEAR ALGEBRA AN INTRODUCTION.

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Presentation transcript:

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 == Transforming Co-ordinate vector == Multiplication by matrices

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}

Co-ordinate vector transformation as Matrix multiplication

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)

Going from lines and points to moving images POLYGONAL MESH MOTION CAPTURE