June 1995
Intermediate to advanced
438 pages
10h 53m
English
Content preview from Graphics Gems V (IBM Version)
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IV.9
Linear Form Curves
Shoemake Ken, University of Pennsylvania Philadelphia, Pennsylvania. E-mail address: shoemake@graphics.cis.upenn.edu
Introduction
Straight lines are simple curves: easy to understand, and easy to manipulate. A generalization, the multilinear form, underlies the common curves of computer graphics ( Ramshaw 1987, Barry and Goldman 1988). This gem uses multilinearity and symmetry to explain Lagrange polynomials, Bézier and B-spline curves, the de Casteljau and de Boor algorithms, and Catmull–Rom splines; and it unites all these in a single routine. Though space prevents it here, these methods can also be applied to other curves, to rectangular and triangular surface patches, and to geometric continuity.
Curves from ...
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