72 lines
1.8 KiB
C++
72 lines
1.8 KiB
C++
|
|
#include "equation-solver.h"
|
|
|
|
#define _USE_MATH_DEFINES
|
|
#include <cmath>
|
|
|
|
namespace msdfgen {
|
|
|
|
int solveQuadratic(double x[2], double a, double b, double c) {
|
|
// a == 0 -> linear equation
|
|
if (a == 0 || fabs(b) > 1e12*fabs(a)) {
|
|
// a == 0, b == 0 -> no solution
|
|
if (b == 0) {
|
|
if (c == 0)
|
|
return -1; // 0 == 0
|
|
return 0;
|
|
}
|
|
x[0] = -c/b;
|
|
return 1;
|
|
}
|
|
double dscr = b*b-4*a*c;
|
|
if (dscr > 0) {
|
|
dscr = sqrt(dscr);
|
|
x[0] = (-b+dscr)/(2*a);
|
|
x[1] = (-b-dscr)/(2*a);
|
|
return 2;
|
|
} else if (dscr == 0) {
|
|
x[0] = -b/(2*a);
|
|
return 1;
|
|
} else
|
|
return 0;
|
|
}
|
|
|
|
static int solveCubicNormed(double x[3], double a, double b, double c) {
|
|
double a2 = a*a;
|
|
double q = 1/9.*(a2-3*b);
|
|
double r = 1/54.*(a*(2*a2-9*b)+27*c);
|
|
double r2 = r*r;
|
|
double q3 = q*q*q;
|
|
a *= 1/3.;
|
|
if (r2 < q3) {
|
|
double t = r/sqrt(q3);
|
|
if (t < -1) t = -1;
|
|
if (t > 1) t = 1;
|
|
t = acos(t);
|
|
q = -2*sqrt(q);
|
|
x[0] = q*cos(1/3.*t)-a;
|
|
x[1] = q*cos(1/3.*(t+2*M_PI))-a;
|
|
x[2] = q*cos(1/3.*(t-2*M_PI))-a;
|
|
return 3;
|
|
} else {
|
|
double u = (r < 0 ? 1 : -1)*pow(fabs(r)+sqrt(r2-q3), 1/3.);
|
|
double v = u == 0 ? 0 : q/u;
|
|
x[0] = (u+v)-a;
|
|
if (u == v || fabs(u-v) < 1e-12*fabs(u+v)) {
|
|
x[1] = -.5*(u+v)-a;
|
|
return 2;
|
|
}
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
int solveCubic(double x[3], double a, double b, double c, double d) {
|
|
if (a != 0) {
|
|
double bn = b/a;
|
|
if (fabs(bn) < 1e6) // Above this ratio, the numerical error gets larger than if we treated a as zero
|
|
return solveCubicNormed(x, bn, c/a, d/a);
|
|
}
|
|
return solveQuadratic(x, b, c, d);
|
|
}
|
|
|
|
}
|