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