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Table of contents:
Computer Graphics - First Mathematical Steps will help students to master basic Computer Graphics and the mathematical concepts which underlie this subject. They will be led to develop their own skills, and appreciate Computer Graphics techniques in both two and three dimensions. The presentation of the text is methodical, systematic and gently paced - everything translates into numbers and simple ideas. Sometimes students experience difficulty in understanding some of the mathematics in standard Computer Graphics books; this book can serve as a good introduction to more advanced texts. It starts from first principles and is sympathetically written for those with a limited mathematical background. Computer Graphics - First Mathematical Steps is suitable for supporting undergraduate programmes in Computers and also the newer areas of Computer Graphics and Visualization. It is appropriate for post-graduate conversion courses which develop expertise in Computer Graphics and CAD. It can also be used for enrichment topics for high-flying pre-college students, and for refresher/enhancement courses for computer graphics technicians.
Contents:
I -POINTS, LINES AND PLANAR CURVES: VECTOR ALGEBRA 1
Shapes Inside a Computer 2
Points in a Plane: Position Vectors 3
Angles Between Lines
- Introducing the Third Dimension: Scalar Products 4
Finding Normals to Planes: Vector Products 5
Following a Line: Parameters 6
Lines in Space: Vector Equations 7
Lines and Common Curves: Parametric and Cartesian Forms II - TRANSFORMATIONS: MATRIX ALGEBRA 8
Tools for Transformations: Matrices 9
Moving In a Plane (I): Scaling, Reflection and Rotation 10
Moving in a Plane (II): Combining Transformations
- Translations 11
Sizing Things Up
- Homogeneous Vectors 12
Useful Manoeuvers: 'Non-Standard' Rotations and Reflections, and the Viewing Transformations 13
Into the Third Dimension: Moving Along Rays, Points at Infinity, and Three-Dimensional Transformations 14
Points of View: Single Point Perspective, and Projection 15
A Greater Sense of Perspective: Two Point and Three Point Perspective III SPACE, CURVES AND SURFACES: DIFFERENTIATION 16
Slopes of Lines and Planar Curves: Gradient Functions 17
Slopes of Space Curves: Tangents and Normals 18
Curve Fitting: Interpolation and Shape Functions 19
Planes and Surfaces: Biparametric Forms, Sweeps and Revolutions 20
Wire Frame Surfaces, Surface Tangents and Normals: Partial Differentiation 21
Piecewise Surfaces: Quadrilateral Patches 22
Computer Graphics: Next Steps Books for Further Reading Appendices
Brief Description:
Starting from the first principles of computer graphics, this work includes rotations, reflections, translations, perspective and projection, and the generation of lines, curves and surfaces. More advanced techniques are introduced to encourage further study.
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