6d0032a8ec
git-svn-id: http://skia.googlecode.com/svn/trunk@7031 2bbb7eff-a529-9590-31e7-b0007b416f81
82 lines
1.9 KiB
C++
82 lines
1.9 KiB
C++
/*
|
|
* 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"
|
|
#include "Extrema.h"
|
|
|
|
static int validUnitDivide(double numer, double denom, double* ratio)
|
|
{
|
|
if (numer < 0) {
|
|
numer = -numer;
|
|
denom = -denom;
|
|
}
|
|
if (denom == 0 || numer == 0 || numer >= denom)
|
|
return 0;
|
|
double r = numer / denom;
|
|
if (r == 0) { // catch underflow if numer <<<< denom
|
|
return 0;
|
|
}
|
|
*ratio = r;
|
|
return 1;
|
|
}
|
|
|
|
/** From Numerical Recipes in C.
|
|
|
|
Q = -1/2 (B + sign(B) sqrt[B*B - 4*A*C])
|
|
x1 = Q / A
|
|
x2 = C / Q
|
|
*/
|
|
static int findUnitQuadRoots(double A, double B, double C, double roots[2])
|
|
{
|
|
if (A == 0)
|
|
return validUnitDivide(-C, B, roots);
|
|
|
|
double* r = roots;
|
|
|
|
double R = B*B - 4*A*C;
|
|
if (R < 0) { // complex roots
|
|
return 0;
|
|
}
|
|
R = sqrt(R);
|
|
|
|
double Q = (B < 0) ? -(B-R)/2 : -(B+R)/2;
|
|
r += validUnitDivide(Q, A, r);
|
|
r += validUnitDivide(C, Q, r);
|
|
if (r - roots == 2 && AlmostEqualUlps(roots[0], roots[1])) { // nearly-equal?
|
|
r -= 1; // skip the double root
|
|
}
|
|
return (int)(r - roots);
|
|
}
|
|
|
|
/** Cubic'(t) = At^2 + Bt + C, where
|
|
A = 3(-a + 3(b - c) + d)
|
|
B = 6(a - 2b + c)
|
|
C = 3(b - a)
|
|
Solve for t, keeping only those that fit between 0 < t < 1
|
|
*/
|
|
int findExtrema(double a, double b, double c, double d, double tValues[2])
|
|
{
|
|
// we divide A,B,C by 3 to simplify
|
|
double A = d - a + 3*(b - c);
|
|
double B = 2*(a - b - b + c);
|
|
double C = b - a;
|
|
|
|
return findUnitQuadRoots(A, B, C, tValues);
|
|
}
|
|
|
|
/** Quad'(t) = At + B, where
|
|
A = 2(a - 2b + c)
|
|
B = 2(b - a)
|
|
Solve for t, only if it fits between 0 < t < 1
|
|
*/
|
|
int findExtrema(double a, double b, double c, double tValue[1])
|
|
{
|
|
/* At + B == 0
|
|
t = -B / A
|
|
*/
|
|
return validUnitDivide(a - b, a - b - b + c, tValue);
|
|
}
|