/* Works out if there are 1 or 3 real roots of the equation, then
computes the values of the roots. */
void find_roots(float a1, float a2, float a3) {
float q, s;
q = (powf(a1, 2) - 3*a2)/9;
s = (2*powf(a1, 3) - 9*a1*a2 + 27*a3)/54;
// printf("Q = %.4f, S = %.4f\n", q, s);
if (powf(q, 3) - powf(s, 2) > 0){ // If there are three real roots
float theta, x1, x2, x3;
theta = acosf(s/sqrtf(powf(q, 3)));
x1 = -2 * sqrtf(q) * cosf(theta/3) - a1/3; //first root
x2 = -2 * sqrtf(q) * cosf((theta + 2*PI)/3) - a1/3; //second root
x3 = -2 * sqrtf(q) * cosf((theta + 4*PI)/3) - a1/3; //third root
printf("There are three real roots: %.3f, %.3f and %.3f.\n", x1, x2, x3);
test_cubic(a1, a2, a3, x1);
test_cubic(a1, a2, a3, x2);
test_cubic(a1, a2, a3, x3);
}
else if (powf(q, 3) - powf(s, 2) <= 0){ // Else if there is only one real root.
float a, sign, x1;
if (fabsf(s) < 0.000001) { // if S is equal to 0.
sign = 0;
}
else if (s > 0) {
sign = -1;
}
else if (s < 0) {
sign = 1;
}
a = sign * powf((sqrtf(powf(s, 2) - powf(q, 3)) + fabsf(s)), 1/3);
if (fabsf(a) > 0.000001) { // i.e if a does not equal 0
x1 = a + q/a - a1/3;
}
else {
x1 = a - a1/3;
}
printf("There is one real root: %.3f\n", x1);
test_cubic(a1, a2, a3, x1);
}
}
int main()
{
test_square();
test_triangular();
test_hexagonal();
test_cubic();
return 0;
}
void init() {
if (fOnce) {
return;
}
fOnce = true;
test_cubic();
test_cubic2();
fShowHairline = false;
fDStroke = 1;
fStroke = 10;
fMinStroke = 10;
fMaxStroke = 180;
const int V = 85;
fPath[0].moveTo(SkIntToScalar(40), SkIntToScalar(70));
fPath[0].lineTo(SkIntToScalar(70), SkIntToScalar(70) + SK_Scalar1/1);
fPath[0].lineTo(SkIntToScalar(110), SkIntToScalar(70));
fPath[1].moveTo(SkIntToScalar(40), SkIntToScalar(70));
fPath[1].lineTo(SkIntToScalar(70), SkIntToScalar(70) - SK_Scalar1/1);
fPath[1].lineTo(SkIntToScalar(110), SkIntToScalar(70));
fPath[2].moveTo(SkIntToScalar(V), SkIntToScalar(V));
fPath[2].lineTo(SkIntToScalar(50), SkIntToScalar(V));
fPath[2].lineTo(SkIntToScalar(50), SkIntToScalar(50));
fPath[3].moveTo(SkIntToScalar(50), SkIntToScalar(50));
fPath[3].lineTo(SkIntToScalar(50), SkIntToScalar(V));
fPath[3].lineTo(SkIntToScalar(V), SkIntToScalar(V));
fPath[4].moveTo(SkIntToScalar(50), SkIntToScalar(50));
fPath[4].lineTo(SkIntToScalar(50), SkIntToScalar(V));
fPath[4].lineTo(SkIntToScalar(52), SkIntToScalar(50));
fPath[5].moveTo(SkIntToScalar(52), SkIntToScalar(50));
fPath[5].lineTo(SkIntToScalar(50), SkIntToScalar(V));
fPath[5].lineTo(SkIntToScalar(50), SkIntToScalar(50));
this->setBGColor(0xFFDDDDDD);
}
void init() {
if (fOnce) {
return;
}
fOnce = true;
test_cubic();
test_cubic2();
fShowHairline = false;
fDStroke = 1;
fStroke = 10;
fMinStroke = 10;
fMaxStroke = 180;
const SkScalar V = 85;
fPath[0].moveTo(40, 70);
fPath[0].lineTo(70, 70 + SK_ScalarHalf);
fPath[0].lineTo(110, 70);
fPath[1].moveTo(40, 70);
fPath[1].lineTo(70, 70 - SK_ScalarHalf);
fPath[1].lineTo(110, 70);
fPath[2].moveTo(V, V);
fPath[2].lineTo(50, V);
fPath[2].lineTo(50, 50);
fPath[3].moveTo(50, 50);
fPath[3].lineTo(50, V);
fPath[3].lineTo(V, V);
fPath[4].moveTo(50, 50);
fPath[4].lineTo(50, V);
fPath[4].lineTo(52, 50);
fPath[5].moveTo(52, 50);
fPath[5].lineTo(50, V);
fPath[5].lineTo(50, 50);
this->setBGColor(0xFFDDDDDD);
}
PathView() {
test_cubic();
test_cubic2();
fShowHairline = false;
fDStroke = 1;
fStroke = 10;
fMinStroke = 10;
fMaxStroke = 180;
const int V = 85;
fPath[0].moveTo(SkIntToScalar(40), SkIntToScalar(70));
fPath[0].lineTo(SkIntToScalar(70), SkIntToScalar(70) + SK_Scalar1/1);
fPath[0].lineTo(SkIntToScalar(110), SkIntToScalar(70));
fPath[1].moveTo(SkIntToScalar(40), SkIntToScalar(70));
fPath[1].lineTo(SkIntToScalar(70), SkIntToScalar(70) - SK_Scalar1/1);
fPath[1].lineTo(SkIntToScalar(110), SkIntToScalar(70));
fPath[2].moveTo(SkIntToScalar(V), SkIntToScalar(V));
fPath[2].lineTo(SkIntToScalar(50), SkIntToScalar(V));
fPath[2].lineTo(SkIntToScalar(50), SkIntToScalar(50));
fPath[3].moveTo(SkIntToScalar(50), SkIntToScalar(50));
fPath[3].lineTo(SkIntToScalar(50), SkIntToScalar(V));
fPath[3].lineTo(SkIntToScalar(V), SkIntToScalar(V));
fPath[4].moveTo(SkIntToScalar(50), SkIntToScalar(50));
fPath[4].lineTo(SkIntToScalar(50), SkIntToScalar(V));
fPath[4].lineTo(SkIntToScalar(52), SkIntToScalar(50));
fPath[5].moveTo(SkIntToScalar(52), SkIntToScalar(50));
fPath[5].lineTo(SkIntToScalar(50), SkIntToScalar(V));
fPath[5].lineTo(SkIntToScalar(50), SkIntToScalar(50));
}
