DistancePointToRectangle Struct Template Reference
[XEngineMath Library]

List of all members.

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Detailed Description

template<unsigned int Dimension>
struct XEngine::Math::DistanceAlgorithms::DistancePointToRectangle< Dimension >

Returns the distance between the given rectangle and point.

	Given a rectangle X = B + s * E0 + t * E1 and a point P we determine
	the projection P' of P onto the plane of the rectangle
		P' = B + s * E0 + t * E1
	with
		s = (P - B) * E0 / E0^2
		t = (P - B) * E1 / E1^2
	Determining the correct region and closest point is a simple matter
	of analysing s and t.
	If both s and t are in [0, 1] then the closest point to P lies inside
	the recangle and the distance is
		|P - B - s * E0 - t * E0| with s and t as above.
	If one of the two, either s or t, are in [0, 1] and the other one is
	either < 0 or > 1, then the closest point to P is the projection of
	P to the corresponding edge of the rectangle. For example, for s < 0
	and t in [0, 1] we would get as distance
		|P - B - t * E0|, again with t as above.
	If both s and t are outside the interval [0, 1] then the corresponding
	corner point of the rectangle is the closest point.
	

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The documentation for this struct was generated from the following files:

• XDistanceAlgorithms.h
• XDistanceAlgorithms.cpp

 

Created with doxygen on: Thu Jan 6 14:12:15 2005 Copyright © by Martin Ecker