05c4bad470
git-svn-id: http://skia.googlecode.com/svn/trunk@7294 2bbb7eff-a529-9590-31e7-b0007b416f81
102 lines
2.8 KiB
C++
102 lines
2.8 KiB
C++
/*
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* Copyright 2012 Google Inc.
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*
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* Use of this source code is governed by a BSD-style license that can be
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* found in the LICENSE file.
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*/
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#include "QuadraticUtilities.h"
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#include <math.h>
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/*
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Numeric Solutions (5.6) suggests to solve the quadratic by computing
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Q = -1/2(B + sgn(B)Sqrt(B^2 - 4 A C))
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and using the roots
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t1 = Q / A
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t2 = C / Q
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*/
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// note: caller expects multiple results to be sorted smaller first
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// note: http://en.wikipedia.org/wiki/Loss_of_significance has an interesting
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// analysis of the quadratic equation, suggesting why the following looks at
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// the sign of B -- and further suggesting that the greatest loss of precision
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// is in b squared less two a c
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int quadraticRoots(double A, double B, double C, double t[2]) {
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B *= 2;
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double square = B * B - 4 * A * C;
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if (approximately_negative(square)) {
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if (!approximately_positive(square)) {
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return 0;
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}
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square = 0;
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}
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double squareRt = sqrt(square);
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double Q = (B + (B < 0 ? -squareRt : squareRt)) / -2;
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int foundRoots = 0;
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double ratio = Q / A;
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if (approximately_zero_or_more(ratio) && approximately_one_or_less(ratio)) {
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if (approximately_less_than_zero(ratio)) {
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ratio = 0;
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} else if (approximately_greater_than_one(ratio)) {
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ratio = 1;
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}
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t[0] = ratio;
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++foundRoots;
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}
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ratio = C / Q;
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if (approximately_zero_or_more(ratio) && approximately_one_or_less(ratio)) {
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if (approximately_less_than_zero(ratio)) {
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ratio = 0;
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} else if (approximately_greater_than_one(ratio)) {
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ratio = 1;
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}
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if (foundRoots == 0 || !approximately_negative(ratio - t[0])) {
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t[foundRoots++] = ratio;
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} else if (!approximately_negative(t[0] - ratio)) {
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t[foundRoots++] = t[0];
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t[0] = ratio;
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}
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}
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return foundRoots;
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}
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static double derivativeAtT(const double* quad, double t) {
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double a = t - 1;
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double b = 1 - 2 * t;
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double c = t;
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return a * quad[0] + b * quad[2] + c * quad[4];
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}
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double dx_at_t(const Quadratic& quad, double t) {
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return derivativeAtT(&quad[0].x, t);
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}
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double dy_at_t(const Quadratic& quad, double t) {
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return derivativeAtT(&quad[0].y, t);
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}
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void dxdy_at_t(const Quadratic& quad, double t, _Point& dxy) {
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double a = t - 1;
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double b = 1 - 2 * t;
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double c = t;
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dxy.x = a * quad[0].x + b * quad[1].x + c * quad[2].x;
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dxy.y = a * quad[0].y + b * quad[1].y + c * quad[2].y;
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}
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void xy_at_t(const Quadratic& quad, double t, double& x, double& y) {
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double one_t = 1 - t;
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double a = one_t * one_t;
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double b = 2 * one_t * t;
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double c = t * t;
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if (&x) {
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x = a * quad[0].x + b * quad[1].x + c * quad[2].x;
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}
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if (&y) {
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y = a * quad[0].y + b * quad[1].y + c * quad[2].y;
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}
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}
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