Computer Graphics and Geometric Modeling Using Beta-splines by Brian A. Barsky

By Brian A. Barsky

Special effects and Geometric Modeling utilizing Beta-splines (Computer technology Workbench) [Hardcover] [May 03, 1988]

Show description

Read Online or Download Computer Graphics and Geometric Modeling Using Beta-splines PDF

Best desktop publishing books

Pagemaker 7 from A to Z: A Quick Reference of More Than 300 PageMaker Tasks, Terms and Tricks

Excellent for fashion designer who desires a short reference, this e-book covers the latest model of the preferred computing device publishing application Adobe PageMaker 7. Packing greater than three hundred activity descriptions, time period definitions, and advice, clients can simply find a job by using the original alphabetical association of knowledge.

Macromedia Fireworks MX 2004 Fast & Easy Web Development

Do not spend it slow wading via manuals to benefit Macromedia Fireworks MX 2004. Spend it doing what you do top - growing web content! The hands-on method of "Macromedia Fireworks MX 2004 quickly & effortless internet improvement" could have you up and working very quickly. reveal through monitor, use this finished advisor to customise Fireworks MX 2004, use layers to regulate photos, optimize and export images, upload animation for your pics, create and increase pop-up menus, and use instruments and filters to create refined pictures.

How to Do Everything Adobe Acrobat X

Adobe Acrobat X показывает вам, как создавать, защищать, оптимизировать и распределять PDF-файлы. Получите советы для добавления мультимедийных функций, возможности сотрудничества с другими пользователями, упорядочение документов, а также сбора различных типов файлов в портфолио PDF. На основании Acrobat seasoned X, который включает в себя все особенности Acrobat X, это практическое руководство поможет Вам освоить возможности этого мощного программного обеспечения в кратчайшие сроки.


Quotation details: Mimesis: Desarticulations (Paris: Flammarion, 1975), pp. 166-275.

Additional info for Computer Graphics and Geometric Modeling Using Beta-splines

Example text

This notion can be formalized quite elegantly by drawing on graph theory. The set of control vertices can be considered as a graph {V, E} whose vertices form the set V= {Vuli = 0, 1, ... , m; j = 0, 1, ... , n} and with the set of edges E = {(Vii' Vi,j+dli = 0, 1, ... , m; j = 0, 1, ... , n- 1} u {(Vu, Vi+t)li = 0, 1, ... , m- 1; j = 0, 1, ... , n} The interior vertices are the vertices Vu where 1~ i ~ m - 1 and and the boundary vertices are 1~j ~ n- 1 7 Derivation of the Beta-spline Curve Representation 30 'end control - - - - - - - - - vertices Fig.

7 Derivation of the Beta-spline Curve Representation 32 The Beta-spline formulation exploits the piecewise representation, in order to achieve local control, by defining each piece in terms of only a few nearby vertices. F or Beta-spline curves, each curve segment is controlled by only four of the control vertices and is completely unaffected by all the other control vertices. Equivalently, a given control vertex only influences four curve segments and has no effect whatsoever on the remaining segments.

Moreover, the combination coefficients of this linear combination are unique since the basis functions are linearly independent. Therefore, every Beta-spline curve segment with ß1 > 0 and ß2 ~ 0 has a unique representation as a linear combination of these basis functions, where the combination coefficients are the associated control vertices. The Beta-spline basis functions are derived in the following section. The Beta-spline curve segment Qi(u) is controlled by the control vertices Vi+" r = -2, -1, 0, 1.

Download PDF sample

Rated 4.36 of 5 – based on 25 votes

Published by admin