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Mathematical Aspects of Geometric Modeling

Charles A. Micchelli

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This monograph examines in detail certain concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies these ideas. The two principal themes of the text are the use of piecewise polynomial representation , and iterative refinement, also called subdivision. Here, simple iterative geometric algorithms produce, in the limit, curves with complex analytic structure. In the first three chapters, the de Casteljau subdivision for Bernstein-Bezier curves is used to introduce matrix subdivision, and the Lane-Riesenfield algorithm for computing cardinal splines is tied into stationary subdivision. This ultimately leads to the construction of prewavelets of compact support. The remainder of the book deals with concepts of "visual smoothness" of curves, along with the intriguing idea of generating smooth multivariate piecewise polynomials as volumes of "slices" of polyhedra.

Language: English

Pages: 266

Format: Paperback

Publisher: Society for Industrial and Applied Mathematics (SIAM)

Release: January 01, 1987

ISBN: 0898713315

ISBN 13: 9780898713312

Mathematical Aspects of Geometric Modeling

Charles A. Micchelli

0/5 ( ratings)

This monograph examines in detail certain concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies these ideas. The two principal themes of the text are the use of piecewise polynomial representation , and iterative refinement, also called subdivision. Here, simple iterative geometric algorithms produce, in the limit, curves with complex analytic structure. In the first three chapters, the de Casteljau subdivision for Bernstein-Bezier curves is used to introduce matrix subdivision, and the Lane-Riesenfield algorithm for computing cardinal splines is tied into stationary subdivision. This ultimately leads to the construction of prewavelets of compact support. The remainder of the book deals with concepts of "visual smoothness" of curves, along with the intriguing idea of generating smooth multivariate piecewise polynomials as volumes of "slices" of polyhedra.

Language: English

Pages: 266

Format: Paperback

Publisher: Society for Industrial and Applied Mathematics (SIAM)

Release: January 01, 1987

ISBN: 0898713315

ISBN 13: 9780898713312

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Total Positivity and Its Applications

Selected Papers of Alan J Hoffman (with Commentary)

Stationary Subdivision

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