public override bool HitTest(Ray3 ray, out double t)
{
ray = ray.Transform(InvPosition);
double dx = ray.Direction.X;
double dy = ray.Direction.Y;
double dz = ray.Direction.Z;
double x0 = ray.Position.X;
double y0 = ray.Position.Y;
double z0 = ray.Position.Z;
double a = dx * dx * dx * dx + dy * dy * dy * dy + dz * dz * dz * dz;
double b = 4.0 * dx * dx * dx * x0 + 4.0 * dy * dy * dy * y0 + 4.0 * dz * dz * dz;
double c = 6.0 * dx * dx * x0 * x0 - 5.0 * dx * dx + 6.0 * dy * dy * y0 * y0 - 5.0 * dy * dy + 6.0 * dz * dz * z0 * z0 - 5.0 * dz * dz;
double d = 4.0 * dx * x0 * x0 * x0 - 10.0 * dx * x0 + 4.0 * dy * y0 * y0 * y0 - 10.0 * dy * y0 + 4.0 * dz * z0 * z0 * z0;
double e = x0 * x0 * x0 * x0 - 5.0 * x0 * x0 + y0 * y0 * y0 * y0 - 5.0 * y0 * y0 + z0 * z0 * z0 * z0 - 5.0 * z0 * z0 + 11.8;
RealPolynomial poly = new RealPolynomial(a, b, c, d, e);
//poly /= new RealPolynomial(100000);
//poly.Normalize();
double ev = poly.Eval(1.0);
double[] cof = poly.FindRoots(MathUtil.Epsilon, false);
//double[] cof=RealPolynomial.SolveQuartic(a, b, c, d, e);
bool found = false;
t = double.MaxValue;
foreach (var tt in RealPolynomial.SolveQuadric(a, b, c))
{
if (tt > 1e-4 && tt < t)
{
t = tt;
found = true;
}
}
return(found);
}
private static double[] GetRealRoots(double c3, double c2, double c1, double c0)
{
RealPolynomial rp = new RealPolynomial(c3, c2, c1, c0);
return(rp.FindRoots(true));
}
public static Point2d[] EllipseCircle(Ellipse2d el, Circle2d ci)
{
Transform2d tr = el.ToStandardPosition;
ci = new Circle2d(ci); //dont modify original circle, but this copy
ci.Transform(tr);
double b = el.Ratio, b2 = b * b, b4 = b2 * b2;
double i = ci.Center.X, i2 = i * i, i4 = i2 * i2;
double j = ci.Center.Y, j2 = j * j, j4 = j2 * j2;
double r = ci.Radius, r2 = r * r, r4 = r2 * r2;
double x4 = b4 - 2 * b2 + 1;
double x3 = 4 * b2 * i - 4 * i;
double x2 = b2 * (2 * r2 + 2 * j2 - 2 * i2 + 2) - 2 * r2 + 2 * j2 + 6 * i2 - 2 * b4;
double x1 = 4 * i * r2 - 4 * i * j2 - 4 * i * i * i - 4 * b2 * i;
double x0 = r4 + (-2 * j2 - 2 * i2) * r2 + b2 * (-2 * r2 - 2 * j2 + 2 * i2) + j4 + 2 * i2 * j2 + i4 + b4;
//double[] xs = RealPolynomial.SolveQuartic2(x4, x3, x2, x1, x0, 1e-30);
RealPolynomial rp = new RealPolynomial(x4, x3, x2, x1, x0);
double[] xs = rp.FindRoots(true);
if (xs == null)
{
return(null); //no intersections
}
Point2dSet resultset = new Point2dSet();
foreach (double x in xs)
{
//test the two possible y:s to be solutions for this x
double y = (1 - x * x) * b2;
if (y < 0.0)
{
continue;
}
y = Math.Sqrt(y);
for (int t = 0; t < 2; t++) //test booth y solutions...
{
double err = x * x + y * y / b2 - 1.0; //on ellipse
double err2 = MathUtil.Square(x - i) + MathUtil.Square(y - j) - r2; //on circle
if (MathUtil.IsZero(err, 1e-7) && MathUtil.IsZero(err2, MathUtil.Epsilon))
{
resultset.Add(new Point2d(x, y));
}
y = -y; // ...by inverting y in second turn
}
}
if (resultset.Count == 0)
{
return(null);
}
resultset.Transform(tr.Inversed); //back to original position
return(resultset.ToArray());
}
public override bool HitTest(Ray3 ray, out double t)
{
ray = ray.Transform(InvPosition);
double x0 = ray.Position.X;
double y0 = ray.Position.Y;
double z0 = ray.Position.Z;
double dx = ray.Direction.X;
double dy = ray.Direction.Y;
double dz = ray.Direction.Z;
double A = x0 * x0 + y0 * y0 + z0 * z0;
double B = 2 * (x0 * dx + y0 * dy + z0 * dz);
double R2 = R * R;
double r2 = r * r;
double t4 = A * A;
double t3 = 2 * A * B;
double t2 = 2 * A * R2 + B * B + 2 * A * A - 2 * r2 * A;
double t1 = 2 * B * (R2 + A - r2);
double t0 = (2 * A - 2 * r2) * R2 + A * A - 2 * r2 * A + r2 * r2;
t2 -= 4 * R2 * (dx * dx + dy * dy);
t1 -= 8 * R2 * (dx * x0 + dy * y0);
t0 -= 4 * R2 * (x0 * x0 + y0 * y0);
RealPolynomial rp = new RealPolynomial(t4, t3, 2, t1, t0);
//rp.Normalize();
double[] roots = rp.FindRoots();
/*
*
* Vector3 p = ray.Position.ToVector();
* Vector3 d = ray.Direction;
*
* double alpha = d.Dot(d);
* double beta = 2.0 * p.Dot(d);
* double gamma = p.Dot(p) - tubeRadius*tubeRadius - centralRadius*centralRadius;
*
* // quatric coefficients
* double a4 = alpha*alpha;
* double a3 = 2.0 * alpha * beta;
* double a2 = beta*beta + (2.0 * alpha * gamma) + (4.0 * centralRadius*centralRadius * d.Z*d.Z);
* double a1 = (2.0 * beta * gamma) + (8 * centralRadius*centralRadius * p.Z * d.Z);
* double a0 = gamma*gamma + (4.0 * centralRadius*centralRadius * p.Z*p.Z) - (4.0 * centralRadius*centralRadius * tubeRadius*tubeRadius);
*
* // solve polynomial
* double[] roots = RealPolynomial.SolveQuartic(a4, a3, a2, a1, a0);
*/
bool found = false;
t = double.MaxValue;
foreach (var tt in roots)
{
if (tt > 1e-4 && tt < t)
{
t = tt;
found = true;
}
}
return(found);
}