Computer-graphics algorithms {de Casteljau's algorithm} {Farin-Boehm algorithm} can evaluate parametric curves {Bézier curve} or surfaces {Bézier surface}. Linear, quadratic, and cubic Bézier-curve {Bézier polygon} splines can draw any shape.
history
Paul de Casteljau invented de Casteljau's algorithm [1959]. Pierre Bézier of France designed automobiles [1962].
equations
Lines can use two points P0 and P1 {control points} and have equation f(t) = (1 - t) * P0 + t * P1, where 0 <= t <= 1. Quadratics can start at P0, go toward P1, and end at P3: f(t) = (1 - t)^2 * P0 + 2 * t * (1 - t) * P1 + t^2 * P2, where 0 <= t <= 1. Cubics can start at P0, go toward first P1 then P2, and end at P3. f(t) = (1 - t)^3 * P0 + 3 * t * (1 - t)^2 * P1 + 3 * t^2 * (1 - t) * P2 + t^3 * P3, where 0 <= t <= 1.
interface
Drawing programs display control points, which control lines.
Mathematical Sciences>Computer Science>Software>Graphics
3-Computer Science-Software-Graphics
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Date Modified: 2022.0224