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COMPUTER GRAPHICS AND LINEAR ALGEBRA

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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COMPUTER GRAPHICS AND LINEAR ALGEBRA

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  1. COMPUTER GRAPHICS AND LINEAR ALGEBRA AN INTRODUCTION

  2. 1. Representing image on computer Points on Screen == Co-ordinate vectors

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

  4. Picture with points joined together

  5. 1. Moving the images Moving a point == Transforming Co-ordinate vector == Multiplication by matrices

  6. 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}

  7. Co-ordinate vector transformation as Matrix multiplication

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

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

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

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