9e49fb63d3
add copyrights everywhere start working on quadratic line segments (for quad intersection) git-svn-id: http://skia.googlecode.com/svn/trunk@5286 2bbb7eff-a529-9590-31e7-b0007b416f81
82 lines
1.9 KiB
C++
82 lines
1.9 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 "DataTypes.h"
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#include "Extrema.h"
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static int validUnitDivide(double numer, double denom, double* ratio)
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{
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if (numer < 0) {
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numer = -numer;
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denom = -denom;
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}
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if (denom == 0 || numer == 0 || numer >= denom)
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return 0;
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double r = numer / denom;
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if (r == 0) { // catch underflow if numer <<<< denom
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return 0;
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}
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*ratio = r;
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return 1;
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}
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/** From Numerical Recipes in C.
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Q = -1/2 (B + sign(B) sqrt[B*B - 4*A*C])
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x1 = Q / A
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x2 = C / Q
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*/
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static int findUnitQuadRoots(double A, double B, double C, double roots[2])
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{
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if (A == 0)
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return validUnitDivide(-C, B, roots);
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double* r = roots;
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double R = B*B - 4*A*C;
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if (R < 0) { // complex roots
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return 0;
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}
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R = sqrt(R);
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double Q = (B < 0) ? -(B-R)/2 : -(B+R)/2;
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r += validUnitDivide(Q, A, r);
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r += validUnitDivide(C, Q, r);
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if (r - roots == 2 && approximately_equal(roots[0], roots[1])) { // nearly-equal?
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r -= 1; // skip the double root
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}
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return (int)(r - roots);
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}
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/** Cubic'(t) = At^2 + Bt + C, where
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A = 3(-a + 3(b - c) + d)
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B = 6(a - 2b + c)
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C = 3(b - a)
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Solve for t, keeping only those that fit between 0 < t < 1
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*/
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int findExtrema(double a, double b, double c, double d, double tValues[2])
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{
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// we divide A,B,C by 3 to simplify
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double A = d - a + 3*(b - c);
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double B = 2*(a - b - b + c);
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double C = b - a;
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return findUnitQuadRoots(A, B, C, tValues);
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}
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/** Quad'(t) = At + B, where
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A = 2(a - 2b + c)
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B = 2(b - a)
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Solve for t, only if it fits between 0 < t < 1
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*/
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int findExtrema(double a, double b, double c, double tValue[1])
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{
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/* At + B == 0
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t = -B / A
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*/
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return validUnitDivide(a - b, a - b - b + c, tValue);
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}
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