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portada Mathematical Aspects of Geometric Modelling
Type
Physical Book
Collection
CBMS-NSF Regional Conference Series in Applied Mathematics
Year
1994
Language
English
Pages
265
Format
Paperback
Dimensions
22.8x15.1x1.6 cm
ISBN13
9780898713312

Mathematical Aspects of Geometric Modelling

Charles A. Micchelli (Author) · SIAM - Society for Industrial and Applied Mathematics · Paperback

Mathematical Aspects of Geometric Modelling - Charles A. Micchelli

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129,39 €

Synopsis "Mathematical Aspects of Geometric Modelling"

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 (this theme appears in one form or another in every chapter), and iterative refinement, also called subdivision.

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 (this theme appears in one form or another in every chapter), and iterative refinement, also called subdivision. Here, simple iterative geometric algorithms produce, in the limit, curves with complex analytic structure.

In the first two chapters, the de Casteljau subdivision for Bernstein-Bézier 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. Chapters three and four deal with concepts of ""visual smoothness"" of curves, and the intriguing idea of generating smooth multivariate piecewise polynomials as volumes of ""slices"" of polyhedra. The final chapter discusses recursive algorithms for the evaluation of polynomials. Each chapter contains introductory material as well as more advanced results.

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