skia2/experimental/Intersection/QuadraticUtilities.cpp

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#include "QuadraticUtilities.h"
#include <math.h>
/*
Numeric Solutions (5.6) suggests to solve the quadratic by computing
Q = -1/2(B + sgn(B)Sqrt(B^2 - 4 A C))
and using the roots
t1 = Q / A
t2 = C / Q
*/
int quadraticRoots(double A, double B, double C, double t[2]) {
B *= 2;
double square = B * B - 4 * A * C;
if (square < 0) {
return 0;
}
double squareRt = sqrt(square);
double Q = (B + (B < 0 ? -squareRt : squareRt)) / -2;
int foundRoots = 0;
double ratio = Q / A;
if (ratio > -FLT_EPSILON && ratio < 1 + FLT_EPSILON) {
if (ratio < FLT_EPSILON) {
ratio = 0;
} else if (ratio > 1 - FLT_EPSILON) {
ratio = 1;
}
t[foundRoots++] = ratio;
}
ratio = C / Q;
if (ratio > -FLT_EPSILON && ratio < 1 + FLT_EPSILON) {
if (ratio < FLT_EPSILON) {
ratio = 0;
} else if (ratio > 1 - FLT_EPSILON) {
ratio = 1;
}
if (foundRoots == 0 || fabs(t[0] - ratio) >= FLT_EPSILON) {
t[foundRoots++] = ratio;
}
}
return foundRoots;
}
void dxdy_at_t(const Quadratic& quad, double t, double& x, double& y) {
double a = t - 1;
double b = 1 - 2 * t;
double c = t;
if (&x) {
x = a * quad[0].x + b * quad[1].x + c * quad[2].x;
}
if (&y) {
y = a * quad[0].y + b * quad[1].y + c * quad[2].y;
}
}
void xy_at_t(const Quadratic& quad, double t, double& x, double& y) {
double one_t = 1 - t;
double a = one_t * one_t;
double b = 2 * one_t * t;
double c = t * t;
if (&x) {
x = a * quad[0].x + b * quad[1].x + c * quad[2].x;
}
if (&y) {
y = a * quad[0].y + b * quad[1].y + c * quad[2].y;
}
}