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#include "DataTypes.h"
#include "Extrema.h"
static int valid_unit_divide(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 SkFindUnitQuadRoots(double A, double B, double C, double roots[2])
{
if (A == 0)
return valid_unit_divide(-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 += valid_unit_divide(Q, A, r);
r += valid_unit_divide(C, Q, r);
if (r - roots == 2 && approximately_equal(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 betwee 0 < t < 1
*/
int SkFindCubicExtrema(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 SkFindUnitQuadRoots(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 SkFindQuadExtrema(double a, double b, double c, double tValue[1])
{
/* At + B == 0
t = -B / A
*/
return valid_unit_divide(a - b, a - b - b + c, tValue);
}
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