MATH_BEGIN_NAMESPACE
/// Computes the closest point pair on two lines.
/** The first line is specified by two points start0 and end0. The second line is specified by
two points start1 and end1.
The implementation of this function follows http://paulbourke.net/geometry/lineline3d/ .
@param v0 The starting point of the first line.
@param v10 The direction vector of the first line. This can be unnormalized.
@param v2 The starting point of the second line.
@param v32 The direction vector of the second line. This can be unnormalized.
@param d [out] Receives the normalized distance of the closest point along the first line.
@param d2 [out] Receives the normalized distance of the closest point along the second line.
@return Returns the closest point on line start0<->end0 to the second line.
@note This is a low-level utility function. You probably want to use ClosestPoint() or Distance() instead.
@see ClosestPoint(), Distance(). */
void Line::ClosestPointLineLine(const vec &v0, const vec &v10, const vec &v2, const vec &v32, float &d, float &d2)
{
assume(!v10.IsZero());
assume(!v32.IsZero());
vec v02 = v0 - v2;
float d0232 = v02.Dot(v32);
float d3210 = v32.Dot(v10);
float d3232 = v32.Dot(v32);
assume(d3232 != 0.f); // Don't call with a zero direction vector.
float d0210 = v02.Dot(v10);
float d1010 = v10.Dot(v10);
float denom = d1010*d3232 - d3210*d3210;
if (denom != 0.f)
d = (d0232*d3210 - d0210*d3232) / denom;
else
d = 0.f;
d2 = (d0232 + d * d3210) / d3232;
}
