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Computer Graphics and Applications of Matrix Methods: Three Dimensional Computer Graphics and Projections (UMAP)

Sister Mary K. Keller

 Mathematics Topic:Linear Algebra Application Areas:Computer Graphics Prerequisites:Matrix multiplication, calculate with trigonometric functions sine & cosine; elementary concepts of three dimensional coordinate geometry

| ©1983 by COMAP, Inc. | 43 pages |

In this unit, matrix concepts are used to create "pictures" on a display device that is controlled by a computer program. Students identify the transformation in two dimensional space affected by multiplying homogeneous coordinates by a matrix, distinguish among several types of projections and their transforming matrices, construct matrices for rotation and translation of figures in space.

1. COMPUTER GRAPHICS
1.1 An Introduction to Computer Graphics
1.2 The Test Pattern
1.3 The Matrix of Coordinates
1.4 Example Transformations
1.5 Rotations in a Plane
1.6 Translations in a Plane
1.7 A New Representation of Two Dimensional Systems
1.8 Scaling
1.9 Combining Rotation and Translation
1.10 Experiment
1.11 Perspective
1.12 Homogeneous Coordinates
1.13 Model Exam (Unit 106)

2. APPLICATIONS OF MATRIX METHODS: THREE DIMENSIONAL COMPUTER GRAPHICS AND PROJECTIONS
2.1 Challenge Problem
2.2 Homogeneous Coordinates in Three Dimensional Space
2.3 Graphing Points in Three Dimensional Space
2.4 Rotations in Three Dimensional Space
2.5 Experiments
2.6 Projections in Three Dimensional Space
2.7 Types of Perspective Projection
2.8 Project for Computer Graphics in Three Dimensions
2.9 Model Exam (Unit 110)

3. ANSWERS TO MODEL EXAM (Unit 106)

4. ANSWERS TO MODEL EXAM (Unit 110)

APPENDIX A

APPENDIX B