By David F. Rogers
For one week after receiving this ebook I agreed with an previous very serious evaluation. I replaced my brain. the topic isn't effortless yet written through a person who is familiar with his enterprise. Having acquired used to his notation i locate this booklet increasingly more necessary and refer again to it every time an issue arises and customarily uncover the answer or a few pointer to the reply.
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Additional info for An Introduction to NURBS: With Historical Perspective (The Morgan Kaufmann Series in Computer Graphics)
5 R e s u l t s for Bdzier c u r v e s e g m e n t for Ex. 1. J,~,i(t)- where (n) and (n) ti(1 - t)~-i i! (~ - i)! Here, n = 3, b e c a u s e t h e r e are four vertices. (3-~)! 1 T h e p o i n t s on t h e c u r v e are t h e n P ( 0 ) = B0 = [1 1] P ( 0 . 765] P(1) = Ba = [3 1] Notice that the basis functions, Jn, i, determine how much of each polygon vertex is used to construct a point on the curve. The results are shown in Fig. 5. B~zier Curve Algorithm U s i n g Eqs. ( 2 . 1 ) - ( 2 . 3 ) a n d E x .
4 shows t h e b l e n d i n g f u n c t i o n s for several values of n. N o t i c e t h e s y m m e t r y of t h e functions. E a c h of t h e b l e n d i n g f u n c t i o n s is of d e g r e e t This notation and control polygon numbering scheme is chosen to be consistent with the vast body of existing literature on B@zier curves and Bernstein basis functions. e. (Y-I)! The control polygon vertices are numbered from 1 to N. The transformations n -- N and i - I - 1 convert between the two notations.
Riesenfeld, by then at Utah, was responsible for unification in terms of the nonuniform rational B-spline or NURBS curves and surfaces. My final contribution to the history was to act as host for Jeff Lane from Utah in 1975, following my move to the University of East Anglia. Lane's thesis on B-spline methods appeared in 1976. R. (Robin) Forrest Norwich, January 2000 15 Cambridge University Computer Aided Design Group's Mark II foam cutter (circa 1973). (Courtesy of Robin Forrest). Robin Forrest was responsible for the mechanical design and construction of the Cambridge CAD Group's Mark II foam-cutting machine, with Charles Lang and David Wheeler responsible for the electrical and electronic design.
An Introduction to NURBS: With Historical Perspective (The Morgan Kaufmann Series in Computer Graphics) by David F. Rogers