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Introduction to Geometric Computing - Sherif Ghali

Introduction to Geometric Computing


Published: 11th July 2008
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Computing is quickly making much of geometry intriguing not only for philosophers and mathematicians, but also for scientists and engineers. What is the core set of topics that a practitioner needs to study before embarking on the design and implementation of a geometric system in a specialized discipline? This book attempts to find the answer. Every programmer tackling a geometric computing problem encounters design decisions that need to be solved. This book reviews the geometric theory then applies it in an attempt to find that elusive "right" design.

From the reviews: "This textbook is excellent for students and programmers working in geometric computing. ! The main theme of the book is the definition of coordinate-free geometric software layers for Euclidean, spherical, projective, and oriented projective geometries. ! The reader can learn the way of designing libraries for Euclidean, spherical, projective, and oriented projective geometries. ! The author also presents the classical raster graphics algorithms that are traditionally introduced in an undergraduate computer graphics course." (Attila Fazekas, Zentralblatt MATH, Vol. 1154, 2009)

Euclidean geometryp. 1
2D computational Euclidean geometryp. 3
Geometric predicatesp. 17
3D computational Euclidean geometryp. 27
Affine transformationsp. 35
Affine intersectionsp. 51
Genericity in geometric computingp. 61
Numerical precisionp. 69
Non-Euclidean geometriesp. 85
1D computational spherical geometryp. 87
2D computational spherical geometryp. 93
Rotations and quaternionsp. 101
Projective geometryp. 109
Homogeneous coordinates for projective geometryp. 119
Barycentric coordinatesp. 143
Oriented projective geometryp. 149
Oriented projective intersectionsp. 157
Coordinate-free geometryp. 169
Homogeneous coordinates for Euclidean geometryp. 171
Coordinate-free geometric computingp. 175
Introduction to CGALp. 183
Raster graphicsp. 191
Segment scan conversionp. 193
Polygon-point containmentp. 201
Illumination and shadingp. 205
Raster-based visibilityp. 209
Ray tracingp. 213
Tree and graph drawingp. 217
Tree drawingp. 219
Graph drawingp. 227
Geometric and solid modelingp. 235
Boundary representationsp. 237
The halfedge data structure and Euler operatorsp. 245
BSP trees in Euclidean and spherical geometriesp. 255
Geometry-free geometric computingp. 265
Constructive solid geometryp. 277
Vector visibilityp. 285
Visibility from Euclidean to spherical spacesp. 287
Visibility in spacep. 293
Appendicesp. 297
The PostScript languagep. 299
OpenGLp. 309
The GLOW toolkitp. 319
Bibliographyp. 331
Indexp. 335
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9781848001145
ISBN-10: 1848001142
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 340
Published: 11th July 2008
Publisher: Springer London Ltd
Country of Publication: GB
Dimensions (cm): 25.4 x 20.3  x 2.03
Weight (kg): 0.72