private double IntersectRayDisk(Disk disk, Vector O, Vector D)
{
O = new Vector(O.D1 - disk.Position.D1, O.D2 - disk.Position.D2, O.D3 - disk.Position.D3);
if (disk.Rotation != null)
{
D = D.MultiplyMatrix(disk.Rotation.Rotation);
O = O.MultiplyMatrix(disk.Rotation.Rotation);
}
var t = -O.D3 / D.D3;
var x = D.D1 * t + O.D1;
var y = D.D2 * t + O.D2;
if (x * x / disk.A + y * y / disk.B < disk.R2)
{
return(t);
}
return(double.PositiveInfinity);
}
private double IntersectRayTorus(Torus torus, Vector O, Vector D)
{
var o = O;
var d = D;
var r = torus.TubeRadius;
var R = torus.SweptRadius;
o = new Vector(o.D1 - torus.Position.D1, o.D2 - torus.Position.D2, o.D3 - torus.Position.D3);
if (torus.Rotation != null)
{
d = d.MultiplyMatrix(torus.Rotation.Rotation);
o = o.MultiplyMatrix(torus.Rotation.Rotation);
}
var intersectBox = IntersectRayBox(o, d.Invert(), torus.AroundBox);
if (double.IsNaN(intersectBox) || double.IsPositiveInfinity(intersectBox))
{
return(double.NaN);
}
var ox = o.D1;
var oy = o.D2;
var oz = o.D3;
var dx = d.D1;
var dy = d.D2;
var dz = d.D3;
var rPow2 = r * r;
var RPow2 = R * R;
var dyPow2 = dy * dy;
var oyPow2 = oy * oy;
// define the coefficients of the quartic equation
var sum_d_sqrd = dx * dx + dyPow2 + dz * dz;
var e = ox * ox + oyPow2 + oz * oz -
RPow2 - rPow2;
var f = ox * dx + oy * dy + oz * dz;
var four_a_sqrd = 4.0 * RPow2;
var coeffs = new[]
{
sum_d_sqrd *sum_d_sqrd,
4.0 *sum_d_sqrd *f,
2.0 *sum_d_sqrd *e + 4.0 *f *f + four_a_sqrd *dyPow2,
4.0 *f *e + 2.0 *four_a_sqrd *oy *dy,
e *e - four_a_sqrd *(rPow2 - oyPow2)
};
var solve = RealPolynomialRootFinder.FindRoots(coeffs);
if (solve == null)
{
return(double.PositiveInfinity);
}
var min = double.PositiveInfinity;
for (var i = 0; i < solve.Count; i++)
{
if (solve[i].IsReal() && solve[i].Real > 0.0001 && solve[i].Real < min)
{
min = solve[i].Real;
}
}
return(min);
}
private double IntersectRaySurface(Surface surface, Vector O, Vector D)
{
var origO = new Vector(O);
var origD = new Vector(D);
var a = surface.A;
var b = surface.B;
var c = surface.C;
var d = surface.D;
var e = surface.E;
var f = surface.F;
O = new Vector(O.D1 - surface.Position.D1, O.D2 - surface.Position.D2, O.D3 - surface.Position.D3);
if (surface.Rotation != null)
{
D = D.MultiplyMatrix(surface.Rotation.Rotation);
O = O.MultiplyMatrix(surface.Rotation.Rotation);
}
var d1 = D.D1;
var d2 = D.D2;
var d3 = D.D3;
var o1 = O.D1;
var o2 = O.D2;
var o3 = O.D3;
var p1 = 2 * a * d1 * o1 + 2 * b * d2 * o2 + 2 * c * d3 * o3 + d * d3 + d2 * e;
var p2 = a * d1.Pow2() + b * d2.Pow2() + c * d3.Pow2();
var p3 = a * o1.Pow2() + b * o2.Pow2() + c * o3.Pow2() + d * o3 + e * o2 + f;
var p4 = Math.Sqrt(p1.Pow2() - 4 * p2 * p3);
//division by zero
if (Math.Abs(p2) < 1e-20)
{
var t = -p3 / p1;
return(t);
}
var min = double.PositiveInfinity;
var max = double.PositiveInfinity;
var t1 = (-p1 - p4) / (2 * p2);
var t2 = (-p1 + p4) / (2 * p2);
var epsilon = 1e-4;
if (t1 > epsilon && t1 < min)
{
min = t1;
max = t2;
}
if (t2 > epsilon && t2 < min)
{
min = t2;
max = t1;
}
var vMin = new Vector(surface.XMin, surface.YMin, surface.ZMin);
var vMax = new Vector(surface.XMax, surface.YMax, surface.ZMax);
if (!CheckSurfaceEdges(origD, origO, ref min, ref max, vMin, vMax, epsilon))
{
return(double.PositiveInfinity);
}
return(min);
}