some brute-force method for creating vertices from a convex defined by plane equations, and creating plane equations from a point cloud

src/LinearMath/btGeometryUtil.cpp

@@ -0,0 +1,168 @@
+/*
+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 "btGeometryUtil.h"
+
+bool	btGeometryUtil::isPointInsidePlanes(const std::vector<btVector3>& planeEquations, const btVector3& point, float	margin)
+{
+	int numbrushes = planeEquations.size();
+	for (int i=0;i<numbrushes;i++)
+	{
+		const btVector3& N1 = planeEquations[i];
+		float dist = float(N1.dot(point))+float(N1[3])-margin;
+		if (dist>0.f)
+		{
+			return false;
+		}
+	}
+	return true;
+		
+}
+
+
+bool	btGeometryUtil::areVerticesBehindPlane(const btVector3& planeNormal, const std::vector<btVector3>& vertices, float	margin)
+{
+	int numvertices = vertices.size();
+	for (int i=0;i<numvertices;i++)
+	{
+		const btVector3& N1 = vertices[i];
+		float dist = float(planeNormal.dot(N1))+float(planeNormal[3])-margin;
+		if (dist>0.f)
+		{
+			return false;
+		}
+	}
+	return true;
+}
+
+bool notExist(const btVector3& planeEquation,const std::vector<btVector3>& planeEquations)
+{
+	int numbrushes = planeEquations.size();
+	for (int i=0;i<numbrushes;i++)
+	{
+		const btVector3& N1 = planeEquations[i];
+		if (planeEquation.dot(N1) > 0.999f)
+		{
+			return false;
+		} 
+	}
+	return true;
+}
+
+void	btGeometryUtil::getPlaneEquationsFromVertices(std::vector<btVector3>& vertices, std::vector<btVector3>& planeEquationsOut )
+{
+		const int numvertices = vertices.size();
+	// brute force:
+	for (int i=0;i<numvertices;i++)
+	{
+		const btVector3& N1 = vertices[i];
+		
+
+		for (int j=i+1;j<numvertices;j++)
+		{
+			const btVector3& N2 = vertices[j];
+				
+			for (int k=j+1;k<numvertices;k++)
+			{
+
+				const btVector3& N3 = vertices[k];
+
+				btVector3 planeEquation,edge0,edge1;
+				edge0 = N2-N1;
+				edge1 = N3-N1;
+				float normalSign = 1.f;
+				for (int ww=0;ww<2;ww++)
+				{
+					planeEquation = normalSign * edge0.cross(edge1);
+					if (planeEquation.length2() > 0.0001f)
+					{
+						planeEquation.normalize();
+						if (notExist(planeEquation,planeEquationsOut))
+						{
+							planeEquation[3] = -planeEquation.dot(N1);
+							
+								//check if inside, and replace supportingVertexOut if needed
+								if (areVerticesBehindPlane(planeEquation,vertices,0.01f))
+								{
+									planeEquationsOut.push_back(planeEquation);
+								}
+						}
+					}
+					normalSign = -1.f;
+				}
+			
+			}
+		}
+	}
+
+}
+
+void	btGeometryUtil::getVerticesFromPlaneEquations(const std::vector<btVector3>& planeEquations , std::vector<btVector3>& verticesOut )
+{
+	const int numbrushes = planeEquations.size();
+	// brute force:
+	for (int i=0;i<numbrushes;i++)
+	{
+		const btVector3& N1 = planeEquations[i];
+		
+
+		for (int j=i+1;j<numbrushes;j++)
+		{
+			const btVector3& N2 = planeEquations[j];
+				
+			for (int k=j+1;k<numbrushes;k++)
+			{
+
+				const btVector3& N3 = planeEquations[k];
+
+				btVector3 n2n3; n2n3 = N2.cross(N3);
+				btVector3 n3n1; n3n1 = N3.cross(N1);
+				btVector3 n1n2; n1n2 = N1.cross(N2);
+				
+				if ( ( n2n3.length2() > 0.0001f ) &&
+					 ( n3n1.length2() > 0.0001f ) &&
+					 ( n1n2.length2() > 0.0001f ) )
+				{
+					//point P out of 3 plane equations:
+
+					//	d1 ( N2 * N3 ) + d2 ( N3 * N1 ) + d3 ( N1 * N2 )  
+					//P =  -------------------------------------------------------------------------  
+					//   N1 . ( N2 * N3 )  
+
+
+					float quotient = (N1.dot(n2n3));
+					if (btFabs(quotient) > 0.000001f)
+					{
+						quotient = -1.f / quotient;
+						n2n3 *= N1[3];
+						n3n1 *= N2[3];
+						n1n2 *= N3[3];
+						btVector3 potentialVertex = n2n3;
+						potentialVertex += n3n1;
+						potentialVertex += n1n2;
+						potentialVertex *= quotient;
+
+						//check if inside, and replace supportingVertexOut if needed
+						if (isPointInsidePlanes(planeEquations,potentialVertex,0.01f))
+						{
+							verticesOut.push_back(potentialVertex);
+						}
+					}
+				}
+			}
+		}
+	}
+}

src/LinearMath/btGeometryUtil.h

@@ -0,0 +1,39 @@
+/*
+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.
+*/
+
+
+#ifndef BT_GEOMETRY_UTIL_H
+#define BT_GEOMETRY_UTIL_H
+#include <vector>
+#include "btVector3.h"
+
+class btGeometryUtil
+{
+	public:
+	
+	
+		static void	getPlaneEquationsFromVertices(std::vector<btVector3>& vertices, std::vector<btVector3>& planeEquationsOut );
+
+		static void	getVerticesFromPlaneEquations(const std::vector<btVector3>& planeEquations , std::vector<btVector3>& verticesOut );
+	
+		static bool	isInside(const std::vector<btVector3>& vertices, const btVector3& planeNormal, float	margin);
+		
+		static bool	isPointInsidePlanes(const std::vector<btVector3>& planeEquations, const btVector3& point, float	margin);
+
+		static bool	areVerticesBehindPlane(const btVector3& planeNormal, const std::vector<btVector3>& vertices, float	margin);
+
+};
+
+
+#endif //BT_GEOMETRY_UTIL_H