This book sets out the fundamental elements of the theory of computational geometry and computer-aided design in a mathematically rigorous manner. Splines and Bézier curves are first tackled, leading to Bézier surfaces, triangulation, and box splines. The final chapter is devoted to algebraic geometry and provides a firm theoretical basis for anyone wishing to seriously develop and investigate CAD systems.
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Editorial Reviews
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"...the principal advantage of this work is that it complements a fairly complete presentation of the standard material with material like triangulations and results from algebraic geometry, which is usually not included in such books, although it is important for CAD research and development. The author even goes one step further and discusses recently published results and techniques (such as base points and box splines), even though CAD systems do not use them yet." N. Sapidis, Computing Reviews
Language Notes
Text: English (translation)
Original Language: French
Original Language: French
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First Sentence:
1.1.1 Notation Let Pk denote the vector space (over the field R) of polynomials of degree k in one variable. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
polyhedral splines, knot sequence, control polygon, spline surfaces, spline curves, algebraic set, affine map, circumscribed circle, divided differences Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proposition Let, Definition Let, Proof Let, Corollary Let, Example Let, Lemma Let, Proof One, Proof Recall, Remark One, Theorem Let New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
1.1.1 Notation Let Pk denote the vector space (over the field R) of polynomials of degree k in one variable. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
polyhedral splines, knot sequence, control polygon, spline surfaces, spline curves, algebraic set, affine map, circumscribed circle, divided differences Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proposition Let, Definition Let, Proof Let, Corollary Let, Example Let, Lemma Let, Proof One, Proof Recall, Remark One, Theorem Let New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 9
books:
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2
books
cite this book:
- Computational Geometry for Design and Manufacture by I. D. Faux in Back Matter
- Multivariate Splines (CBMS-NSF Regional Conference Series in Applied Mathematics) by Charles K. Chui in Back Matter
- Calcul formel by James H. Davenport in Back Matter
- Algebraic Topology: A First Course (Mathematics Lecture Note Series) by Marvin J. Greenberg in Back Matter
- Curves and Surfaces by Pierre-Jean Laurent in Back Matter
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