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- W145834140 abstract "This chapter focuses on linear form curves. Straight lines are simple curves—easy to understand, and easy to manipulate. A generalization, the multilinear form, underlies the common curves of computer graphics. Through every pair of distinct points there is a unique line; this is an axiom of Euclidean geometry. But use of points and lines in computer graphics is impossible without a numerical representation. Points are commonly represented using (x, y, z) coordinates. Lines, however, may be represented in a variety of ways—Pliicker coordinates, implicit equations, parametric equations—depending on the task. This chapter uses the concept of 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. The code presented in the chapter generates curves of many different flavors. Specific possibilities include Lagrange interpolants, Bézier curves, B-spline curves, and Cn Catmull–Rom splines." @default.
- W145834140 created "2016-06-24" @default.
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- W145834140 date "1995-01-01" @default.
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- W145834140 title "Linear Form Curves" @default.
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- W145834140 doi "https://doi.org/10.1016/b978-0-12-543457-7.50037-1" @default.
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