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

By Brian A. Barsky

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

Similar desktop publishing books

Get 3D AutoCAD 2004/2005: One Step at a Time PDF

This thorough textual content will educate you ways to exploit AutoCAD's startup wizards to open a brand new drawing, realize a number of the components of the AutoCAD consumer interface, use colour, use linetypes, create dimensions, and lots more and plenty extra.

Get Teach Yourself VISUALLY HTML and CSS PDF

Are you a visible learner? Do you wish directions that assist you to do whatever - and bypass the long-winded reasons? if this is the case, then this e-book is for you. Open it up and you will find transparent, step by step display photographs that assist you take on greater than a hundred seventy five projects concerning HTML and CSS. every one task-based unfold covers a unmarried process, certain to assist you wake up and operating with HTML and CSS very quickly.

Dig deep down into the hot positive aspects of SONAR four and how to overcome every one via step by step examples and workouts which are designed to make your composing and recording periods run extra easily. From at the start customizing SONAR four to making and generating a encompass sound combine, prepare to discover all that SONAR four has to provide!

Zhigang Xiang's Schaum’s Outline of Computer Graphics PDF

Ratings of examples and difficulties let scholars to hone their abilities. transparent factors of basic initiatives facilitate scholars’ knowing of significant options. New! Chapters on shading types, shadow, and texture―including the Phong illumination model―explain the newest concepts and instruments for reaching photorealism in special effects.

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

Sample text

1), and rearranging, these computational requirements become m(23 + 4d)(p + 1) multiplications, m(2 + 3(9 + d) x (p + 1)) additions/subtractions, and dm(p + 1) divisions. It should be noted that this algorithm naturally computes the general curve evaluated at a different set of values of the domain parameter on each segment, with no loss of efficiency. 3) where S;g(ß1(u), ß2(u)) is given by S;g(ß1(u), ß2(u)) = 1 I dgr(ß1(u), ß2(u))Vi+r r=-2 for g = 0, 1, 2, 3 . 4) Using these equations, the following algorithm computes a general curve composed of m segments where the i 1h segment is evaluated at P; + 1 values of the domain parameter: for i := 1 to m do begin jump1 := alpha1;- alpha1;_ 1 ; jump2 := alpha2; - alpha2;_ 1 ; for each u in {u;klk = 0, 1, ...

This assumption can be exploited to efficiently evaluate a Beta-spline curve. Observe that all the coefficient functions have a constant denominator of ~- Thus, all the divisions can be performed prior to the actual computation of the Beta-spline basis functions. The following algorithm evaluates the basis functions at p + 1 given values of the domain parameter u, for a given value of each uniform shape parameter, ß1 and ß2, and requires 7 + 9(p + 1) multiplications, 12 + 2 + 9(p + 1) additionsjsubtractions, and 8 divisions.

Since a single control vertex influences only four curve segments and has no effect on the other segments, the consequences of moving one vertex are limited to four segments. Computationally, this implies that the movement of a control vertex requires the re-evaluation of only four segments. Moreover, even the four affected segments need not be completely recomputed. Although each of these segments is controlled by four vertices, only one of these vertices has changed position. Therefore, the change in each of these segments is due only to the modification of the position of one control vertex.