[ODE] Maths Stuff

[Nate W]

On Fri, 25 Apr 2003, Ander Taylor wrote:

> I want to, given a vector and a plane that intersect, get the length of the 
> segments on either side of the plane.

If the line intersects the plane, this function will get you the point of
intersection:

VectorXYZ Generic::vecIntersectionOfLineAndPlane (
		const VectorXYZ &vecLineOrigin, 
		const VectorXYZ &vecLineDirection, 
		const VectorXYZ &vecPlaneNormal, 
		const VectorXYZ &vecPointOnPlane)
{
	real D = DotProduct (vecPlaneNormal, vecPointOnPlane);
	real t_Numerator = (DotProduct (vecPlaneNormal, vecLineOrigin) - D);
	real t_Denominator = DotProduct (vecPlaneNormal, vecLineDirection);
	real t = - (t_Numerator / t_Denominator);
	VectorXYZ vecResult = vecLineOrigin + (vecLineDirection * t);
	return vecResult;
}

Given the point of intersection, it's straightforward to find the distance
between that point and the line's endpoints.

-- 

Nate Waddoups
Redmond WA USA
http://www.natew.com