Computer graphic: first mathematical steps (paper)


Language: Anglais
Cover of the book Computer graphic: first mathematical steps (paper)

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280 p. · 23.5x17.8 cm · Paperback
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.

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.
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, Homogenous 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.
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.
  • Covers the basic Computer Graphics applications, including rotations, reflections, translations, perspective and projection, and also the generation of lines, curves and surfaces.
  • The basic mathematical techniques covered include vectors and matrices.
    - More advanced techniques are introduced to encourage further study.
  • Assumes little previous knowledge of the subject - the material is accessible to anybody with a GCSE in mathematics.
  • Packed with pedagogical features, including worked examples and end-of-chapter exercises with full answers.
  • A glossary of important terms is included to assist the reader.