By Charles A. Micchelli
This monograph examines intimately yes options which are beneficial for the modeling of curves and surfaces and emphasizes the mathematical thought that underlies those principles. the 2 central topics of the textual content are using piecewise polynomial illustration (this subject matter seems to be in a single shape or one other in each chapter), and iterative refinement, also referred to as subdivision. the following, easy 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 eventually results in the development of prewavelets of compact help. the rest of the booklet offers with thoughts of "visual smoothness" of curves, in addition to the interesting notion of producing gentle multivariate piecewise polynomials as volumes of "slices" of polyhedra.
Read Online or Download Mathematical Aspects of Geometric Modeling (CBMS-NSF Regional Conference Series in Applied Mathematics) PDF
Similar Algebraic Geometry books
Algebraic topology is a simple a part of sleek arithmetic, and a few wisdom of this quarter is vital for any complicated paintings when it comes to geometry, together with topology itself, differential geometry, algebraic geometry, and Lie teams. This booklet offers a close therapy of algebraic topology either for lecturers of the topic and for complicated graduate scholars in arithmetic both focusing on this sector or carrying on with directly to different fields.
First textbook-level account of uncomplicated examples and strategies during this region. appropriate for self-study through a reader who is aware a bit commutative algebra and algebraic geometry already. David Eisenbud is a well known mathematician and present president of the yank Mathematical Society, in addition to a profitable Springer writer.
Grothendieck’s appealing idea of schemes permeates smooth algebraic geometry and underlies its functions to quantity thought, physics, and utilized arithmetic. this straightforward account of that concept emphasizes and explains the common geometric recommendations at the back of the definitions. within the ebook, thoughts are illustrated with primary examples, and specific calculations convey how the buildings of scheme concept are conducted in perform.
This vintage textual content, written by means of one of many best mathematicians of the 20 th century, is now to be had in a inexpensive paperback variation. Exposition is headquartered at the foundations of affine geometry, the geometry of quadratic types, and the constitution of the overall linear team. Context is broadened via the inclusion of projective and symplectic geometry and the constitution of symplectic and orthogonal teams.
Additional info for Mathematical Aspects of Geometric Modeling (CBMS-NSF Regional Conference Series in Applied Mathematics)