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 /* * Copyright 2012 Google Inc. * * Use of this source code is governed by a BSD-style license that can be * found in the LICENSE file. */ #include "CubicLineSegments.h" #include "QuadraticLineSegments.h" // http://cagd.cs.byu.edu/~557/text/cagd.pdf 2.7 // A hodograph is the first derivative curve void hodograph(const Cubic& cubic, Quadratic& hodo) { hodo[0].x = 3 * (cubic[1].x - cubic[0].x); hodo[0].y = 3 * (cubic[1].y - cubic[0].y); hodo[1].x = 3 * (cubic[2].x - cubic[1].x); hodo[1].y = 3 * (cubic[2].y - cubic[1].y); hodo[2].x = 3 * (cubic[3].x - cubic[2].x); hodo[2].y = 3 * (cubic[3].y - cubic[2].y); } // A 2nd hodograph is the second derivative curve void secondHodograph(const Cubic& cubic, _Line& hodo2) { Quadratic hodo; hodograph(cubic, hodo); hodograph(hodo, hodo2); } // The number of line segments required to approximate the cubic // see http://cagd.cs.byu.edu/~557/text/cagd.pdf 10.6 double subDivisions(const Cubic& cubic) { _Line hodo2; secondHodograph(cubic, hodo2); double maxX = SkTMax(hodo2[1].x, hodo2[1].x); double maxY = SkTMax(hodo2[1].y, hodo2[1].y); double dist = sqrt(maxX * maxX + maxY * maxY); double segments = sqrt(dist / (8 * FLT_EPSILON)); return segments; }