Read e-book online An Introduction to NURBS: With Historical Perspective (The PDF

By David F. Rogers

ISBN-10: 1558606696

ISBN-13: 9781558606692

For one week after receiving this booklet I agreed with an past very serious overview. I replaced my brain. the topic isn't really effortless yet written through anyone who understands his enterprise. Having received used to his notation i locate this booklet an increasing number of precious and refer again to it every time an issue arises and typically 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)

Example text

The parameter t varies from train tO tm~x along the curve P ( t ) ) The convention % - 0 is adopted. Formally, a B-spline curve is defined as a polynomial spline function of order k (degree k - 1), because it satisfies the following two conditions: P(t) is a polynomial of degree k - 1 on each interval xi <_ t < xi+l. P(t) and its derivatives of order 1, 2 , - . , k - 2 are all continuous over the entire curve. Thus, for example, a fourth-order B-spline curve is a piecewise cubic curve. 3) i=1 Each basis function is positive or zero for all p a r a m e t e r values, t h a t is, N~,k _> O.

1 Convex hull properties of B-spline curves.

The transformations n -- N and i - I - 1 convert between the two notations. 1 / 1 J20 0 . 4 J5,4 // t (d) B~zier/Bernstein blending functions. (a) Three polygon points, n = 2; (b) four polygon points, n = 3; (c) five polygon points, n -- 4; (d) six polygon points, n - 5. n. For example, each of the four blending functions shown in Fig. 4b for n = 3 is a cubic. 4) for example, for a cubic n = 3. 4b illustrates this result. and J3,2(2/3) = 4/9 Chapter E x a m i n i n g Eqs. , at t - 0, shows t h a t n !

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An Introduction to NURBS: With Historical Perspective (The Morgan Kaufmann Series in Computer Graphics) by David F. Rogers

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