CSE 167 Lecture 9: L9 2/5/19
5 Feb 2019
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F(u) = (1-u)p0 + up1 decasteljau: quadratic bezier curve. F(u) = (1-u)2 p0 + u2 p2 + 2u(1-u) p1. Affine combination (1-u)2 + u2 + 2u(1-u) = [(1-u)2 + u]2 = 1. Each step can be done with a linear interpolation of the points! P0, p1, p2, p3 - degree 3, order 4 dc diagram: F(u) = p0(1-u)3 + p3 u2 + p1 3u(1-u)2 + p2 3u2(1-u) Input: control points ci w/ 0 <= i <= n where n is the degree. Output: f(u) where u is the parameter for evaluation. For (level = n; level >= 0; level--) { For (i = 0; i <= level; i++) { level = (1-u) * pi. // final value at the lowest level f(u) = p0. Can be optimized to do w/o auxiliary storage: remove the level! Once you compute the combination, you can effectively remove the point and overwrite it! Bk n(u) are bernstein-bezier polynomials n(u) = [n!/k!(n-k)!] (1-u)n-kuk n(u)
