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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 "DataTypes.h" // Sources // computer-aided design - volume 22 number 9 november 1990 pp 538 - 549 // online at http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf // This turns a line segment into a parameterized line, of the form // ax + by + c = 0 // When a^2 + b^2 == 1, the line is normalized. // The distance to the line for (x, y) is d(x,y) = ax + by + c // // Note that the distances below are not necessarily normalized. To get the true // distance, it's necessary to either call normalize() after xxxEndPoints(), or // divide the result of xxxDistance() by sqrt(normalSquared()) class LineParameters { public: void cubicEndPoints(const Cubic& pts) { cubicEndPoints(pts, 0, 3); } void cubicEndPoints(const Cubic& pts, int s, int e) { a = approximately_pin(pts[s].y - pts[e].y); b = approximately_pin(pts[e].x - pts[s].x); c = pts[s].x * pts[e].y - pts[e].x * pts[s].y; } void lineEndPoints(const _Line& pts) { a = approximately_pin(pts[0].y - pts[1].y); b = approximately_pin(pts[1].x - pts[0].x); c = pts[0].x * pts[1].y - pts[1].x * pts[0].y; } void quadEndPoints(const Quadratic& pts) { quadEndPoints(pts, 0, 2); } void quadEndPoints(const Quadratic& pts, int s, int e) { a = approximately_pin(pts[s].y - pts[e].y); b = approximately_pin(pts[e].x - pts[s].x); c = pts[s].x * pts[e].y - pts[e].x * pts[s].y; } double normalSquared() const { return a * a + b * b; } bool normalize() { double normal = sqrt(normalSquared()); if (approximately_zero(normal)) { a = b = c = 0; return false; } double reciprocal = 1 / normal; a *= reciprocal; b *= reciprocal; c *= reciprocal; return true; } void cubicDistanceY(const Cubic& pts, Cubic& distance) const { double oneThird = 1 / 3.0; for (int index = 0; index < 4; ++index) { distance[index].x = index * oneThird; distance[index].y = a * pts[index].x + b * pts[index].y + c; } } void quadDistanceY(const Quadratic& pts, Quadratic& distance) const { double oneHalf = 1 / 2.0; for (int index = 0; index < 3; ++index) { distance[index].x = index * oneHalf; distance[index].y = a * pts[index].x + b * pts[index].y + c; } } double controlPtDistance(const Cubic& pts, int index) const { SkASSERT(index == 1 || index == 2); return a * pts[index].x + b * pts[index].y + c; } double controlPtDistance(const Quadratic& pts) const { return a * pts[1].x + b * pts[1].y + c; } double pointDistance(const _Point& pt) const { return a * pt.x + b * pt.y + c; } double dx() const { return b; } double dy() const { return -a; } private: double a; double b; double c; };