/// <summary>
/// Returns the intersection point of the three planes: `b`, `c`,
/// and this plane. If no intersection is found, `null` is returned.
/// </summary>
/// <param name="b">One of the three planes to use in the calculation.</param>
/// <param name="c">One of the three planes to use in the calculation.</param>
/// <returns>The intersection, or `null` if none is found.</returns>
public Vector3d?Intersect3(Planed b, Planed c)
{
double denom = _normal.Cross(b._normal).Dot(c._normal);
if (Mathd.IsZeroApprox(denom))
{
return(null);
}
Vector3d result = b._normal.Cross(c._normal) * D +
c._normal.Cross(_normal) * b.D +
_normal.Cross(b._normal) * c.D;
return(result / denom);
}
/// <summary>
/// Returns the intersection point of a ray consisting of the
/// position `from` and the direction normal `dir` with this plane.
/// If no intersection is found, `null` is returned.
/// </summary>
/// <param name="from">The start of the ray.</param>
/// <param name="dir">The direction of the ray, normalized.</param>
/// <returns>The intersection, or `null` if none is found.</returns>
public Vector3d?IntersectRay(Vector3d from, Vector3d dir)
{
double den = _normal.Dot(dir);
if (Mathd.IsZeroApprox(den))
{
return(null);
}
double dist = (_normal.Dot(from) - D) / den;
// This is a ray, before the emitting pos (from) does not exist
if (dist > Mathd.Epsilon)
{
return(null);
}
return(from + dir * -dist);
}
/// <summary>
/// Returns the intersection point of a line segment from
/// position `begin` to position `end` with this plane.
/// If no intersection is found, `null` is returned.
/// </summary>
/// <param name="begin">The start of the line segment.</param>
/// <param name="end">The end of the line segment.</param>
/// <returns>The intersection, or `null` if none is found.</returns>
public Vector3d?IntersectSegment(Vector3d begin, Vector3d end)
{
Vector3d segment = begin - end;
double den = _normal.Dot(segment);
if (Mathd.IsZeroApprox(den))
{
return(null);
}
double dist = (_normal.Dot(begin) - D) / den;
// Only allow dist to be in the range of 0 to 1, with tolerance.
if (dist < -Mathd.Epsilon || dist > 1.0f + Mathd.Epsilon)
{
return(null);
}
return(begin + segment * -dist);
}
