By Charles A. Micchelli
This monograph examines intimately definite thoughts which are worthwhile for the modeling of curves and surfaces and emphasizes the mathematical concept that underlies those rules. the 2 central topics of the textual content are using piecewise polynomial illustration (this subject appears to be like in a single shape or one other in each chapter), and iterative refinement, often known as subdivision. the following, uncomplicated iterative geometric algorithms produce, within the restrict, curves with advanced analytic constitution. within the first 3 chapters, the de Casteljau subdivision for Bernstein-Bezier curves is used to introduce matrix subdivision, and the Lane-Riesenfield set of rules for computing cardinal splines is tied into desk bound subdivision. This finally ends up in the development of prewavelets of compact aid. the rest of the ebook offers with suggestions of "visual smoothness" of curves, in addition to the exciting thought of producing delicate multivariate piecewise polynomials as volumes of "slices" of polyhedra.
Read or Download Mathematical Aspects of Geometric Modeling (CBMS-NSF Regional Conference Series in Applied Mathematics) PDF
Similar Algebraic Geometry books
This paintings attracts jointly principles from algebraic topology, sensible research and geometry. it's a instrument - a method of conveying details between those 3 matters - and it's been used with good fortune to find theorems throughout a large span of arithmetic. the aim of this e-book is to acquaint the reader with the fundamental rules of analytic K-homology and strengthen a few of its purposes.
First textbook-level account of uncomplicated examples and strategies during this sector. compatible for self-study by means of a reader who is aware a bit commutative algebra and algebraic geometry already. David Eisenbud is a widely known mathematician and present president of the yankee Mathematical Society, in addition to a profitable Springer writer.
"It provides a delicate portrait of an outstanding man or woman. It describes safely and intelligibly on a nontechnical point the area of mathematical principles during which Hilbert created his masterpieces. And it illuminates the heritage of German social historical past opposed to which the drama of Hilberts lifestyles was once performed.
From the preface of the writer: ". .. i've got divided this paintings into books; within the first of those i've got restrained myself to these issues touching on natural research. within the moment e-book i've got defined these factor which has to be recognized from geometry, for the reason that research is usually constructed in the sort of manner that its software to geometry is proven.
Additional info for Mathematical Aspects of Geometric Modeling (CBMS-NSF Regional Conference Series in Applied Mathematics)