Torque3D/Engine/lib/bullet/src/Bullet3Geometry/b3GeometryUtil.cpp

/*
Copyright (c) 2003-2006 Gino van den Bergen / Erwin Coumans  http://continuousphysics.com/Bullet/

This software is provided 'as-is', without any express or implied warranty.
In no event will the authors be held liable for any damages arising from the use of this software.
Permission is granted to anyone to use this software for any purpose, 
including commercial applications, and to alter it and redistribute it freely, 
subject to the following restrictions:

1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
*/

#include "b3GeometryUtil.h"

/*
  Make sure this dummy function never changes so that it
  can be used by probes that are checking whether the
  library is actually installed.
*/
extern "C"
{
	void b3BulletMathProbe();

	void b3BulletMathProbe() {}
}

bool b3GeometryUtil::isPointInsidePlanes(const b3AlignedObjectArray<b3Vector3>& planeEquations, const b3Vector3& point, b3Scalar margin)
{
	int numbrushes = planeEquations.size();
	for (int i = 0; i < numbrushes; i++)
	{
		const b3Vector3& N1 = planeEquations[i];
		b3Scalar dist = b3Scalar(N1.dot(point)) + b3Scalar(N1[3]) - margin;
		if (dist > b3Scalar(0.))
		{
			return false;
		}
	}
	return true;
}

bool b3GeometryUtil::areVerticesBehindPlane(const b3Vector3& planeNormal, const b3AlignedObjectArray<b3Vector3>& vertices, b3Scalar margin)
{
	int numvertices = vertices.size();
	for (int i = 0; i < numvertices; i++)
	{
		const b3Vector3& N1 = vertices[i];
		b3Scalar dist = b3Scalar(planeNormal.dot(N1)) + b3Scalar(planeNormal[3]) - margin;
		if (dist > b3Scalar(0.))
		{
			return false;
		}
	}
	return true;
}

bool notExist(const b3Vector3& planeEquation, const b3AlignedObjectArray<b3Vector3>& planeEquations);

bool notExist(const b3Vector3& planeEquation, const b3AlignedObjectArray<b3Vector3>& planeEquations)
{
	int numbrushes = planeEquations.size();
	for (int i = 0; i < numbrushes; i++)
	{
		const b3Vector3& N1 = planeEquations[i];
		if (planeEquation.dot(N1) > b3Scalar(0.999))
		{
			return false;
		}
	}
	return true;
}

void b3GeometryUtil::getPlaneEquationsFromVertices(b3AlignedObjectArray<b3Vector3>& vertices, b3AlignedObjectArray<b3Vector3>& planeEquationsOut)
{
	const int numvertices = vertices.size();
	// brute force:
	for (int i = 0; i < numvertices; i++)
	{
		const b3Vector3& N1 = vertices[i];

		for (int j = i + 1; j < numvertices; j++)
		{
			const b3Vector3& N2 = vertices[j];

			for (int k = j + 1; k < numvertices; k++)
			{
				const b3Vector3& N3 = vertices[k];

				b3Vector3 planeEquation, edge0, edge1;
				edge0 = N2 - N1;
				edge1 = N3 - N1;
				b3Scalar normalSign = b3Scalar(1.);
				for (int ww = 0; ww < 2; ww++)
				{
					planeEquation = normalSign * edge0.cross(edge1);
					if (planeEquation.length2() > b3Scalar(0.0001))
					{
						planeEquation.normalize();
						if (notExist(planeEquation, planeEquationsOut))
						{
							planeEquation[3] = -planeEquation.dot(N1);

							//check if inside, and replace supportingVertexOut if needed
							if (areVerticesBehindPlane(planeEquation, vertices, b3Scalar(0.01)))
							{
								planeEquationsOut.push_back(planeEquation);
							}
						}
					}
					normalSign = b3Scalar(-1.);
				}
			}
		}
	}
}

void b3GeometryUtil::getVerticesFromPlaneEquations(const b3AlignedObjectArray<b3Vector3>& planeEquations, b3AlignedObjectArray<b3Vector3>& verticesOut)
{
	const int numbrushes = planeEquations.size();
	// brute force:
	for (int i = 0; i < numbrushes; i++)
	{
		const b3Vector3& N1 = planeEquations[i];

		for (int j = i + 1; j < numbrushes; j++)
		{
			const b3Vector3& N2 = planeEquations[j];

			for (int k = j + 1; k < numbrushes; k++)
			{
				const b3Vector3& N3 = planeEquations[k];

				b3Vector3 n2n3;
				n2n3 = N2.cross(N3);
				b3Vector3 n3n1;
				n3n1 = N3.cross(N1);
				b3Vector3 n1n2;
				n1n2 = N1.cross(N2);

				if ((n2n3.length2() > b3Scalar(0.0001)) &&
					(n3n1.length2() > b3Scalar(0.0001)) &&
					(n1n2.length2() > b3Scalar(0.0001)))
				{
					//point P out of 3 plane equations:

					//	d1 ( N2 * N3 ) + d2 ( N3 * N1 ) + d3 ( N1 * N2 )
					//P =  -------------------------------------------------------------------------
					//   N1 . ( N2 * N3 )

					b3Scalar quotient = (N1.dot(n2n3));
					if (b3Fabs(quotient) > b3Scalar(0.000001))
					{
						quotient = b3Scalar(-1.) / quotient;
						n2n3 *= N1[3];
						n3n1 *= N2[3];
						n1n2 *= N3[3];
						b3Vector3 potentialVertex = n2n3;
						potentialVertex += n3n1;
						potentialVertex += n1n2;
						potentialVertex *= quotient;

						//check if inside, and replace supportingVertexOut if needed
						if (isPointInsidePlanes(planeEquations, potentialVertex, b3Scalar(0.01)))
						{
							verticesOut.push_back(potentialVertex);
						}
					}
				}
			}
		}
	}
}