Added btCapsuleShape. This could already be simulated by simply adding 2 spheres to the btMultiSphereShape, but this was bad documented/unknown.

For tapered capsules, you can still use btMultiSphereShape, just pass 2 spheres with different radius.

src/BulletCollision/CollisionShapes/btCapsuleShape.cpp

@@ -0,0 +1,146 @@
+/*
+Bullet Continuous Collision Detection and Physics Library
+Copyright (c) 2003-2006 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 "btCapsuleShape.h"
+
+#include "BulletCollision/CollisionShapes/btCollisionMargin.h"
+#include "LinearMath/btQuaternion.h"
+
+btCapsuleShape::btCapsuleShape(float radius, float height)
+{
+	m_implicitShapeDimensions.setValue(radius,0.5f*height,radius);
+}
+
+ 
+ btVector3	btCapsuleShape::localGetSupportingVertexWithoutMargin(const btVector3& vec0)const
+{
+
+	btVector3 supVec(0,0,0);
+
+	btScalar maxDot(btScalar(-1e30));
+
+	btVector3 vec = vec0;
+	btScalar lenSqr = vec.length2();
+	if (lenSqr < btScalar(0.0001))
+	{
+		vec.setValue(1,0,0);
+	} else
+	{
+		btScalar rlen = btScalar(1.) / btSqrt(lenSqr );
+		vec *= rlen;
+	}
+
+	btVector3 vtx;
+	btScalar newDot;
+	
+	float radius = getRadius();
+
+
+	{
+		btVector3 pos(0,getHalfHeight(),0);
+		vtx = pos +vec*m_localScaling*(radius) - vec * getMargin();
+		newDot = vec.dot(vtx);
+		if (newDot > maxDot)
+		{
+			maxDot = newDot;
+			supVec = vtx;
+		}
+	}
+	{
+		btVector3 pos(0,-getHalfHeight(),0);
+		vtx = pos +vec*m_localScaling*(radius) - vec * getMargin();
+		newDot = vec.dot(vtx);
+		if (newDot > maxDot)
+		{
+			maxDot = newDot;
+			supVec = vtx;
+		}
+	}
+
+	return supVec;
+
+}
+
+ void	btCapsuleShape::batchedUnitVectorGetSupportingVertexWithoutMargin(const btVector3* vectors,btVector3* supportVerticesOut,int numVectors) const
+{
+
+	
+	float radius = getRadius();
+
+	for (int j=0;j<numVectors;j++)
+	{
+		btScalar maxDot(btScalar(-1e30));
+		const btVector3& vec = vectors[j];
+
+		btVector3 vtx;
+		btScalar newDot;
+		{
+			btVector3 pos(0,getHalfHeight(),0);
+			vtx = pos +vec*m_localScaling*(radius) - vec * getMargin();
+			newDot = vec.dot(vtx);
+			if (newDot > maxDot)
+			{
+				maxDot = newDot;
+				supportVerticesOut[j] = vtx;
+			}
+		}
+		{
+			btVector3 pos(0,-getHalfHeight(),0);
+			vtx = pos +vec*m_localScaling*(radius) - vec * getMargin();
+			newDot = vec.dot(vtx);
+			if (newDot > maxDot)
+			{
+				maxDot = newDot;
+				supportVerticesOut[j] = vtx;
+			}
+		}
+		
+	}
+}
+
+
+void	btCapsuleShape::calculateLocalInertia(btScalar mass,btVector3& inertia)
+{
+	//as an approximation, take the inertia of the box that bounds the spheres
+
+	btTransform ident;
+	ident.setIdentity();
+
+	
+	float radius = getRadius();
+
+	btVector3 halfExtents(radius,radius+getHalfHeight(),radius);
+
+	btScalar margin = CONVEX_DISTANCE_MARGIN;
+
+	btScalar lx=btScalar(2.)*(halfExtents[0]+margin);
+	btScalar ly=btScalar(2.)*(halfExtents[1]+margin);
+	btScalar lz=btScalar(2.)*(halfExtents[2]+margin);
+	const btScalar x2 = lx*lx;
+	const btScalar y2 = ly*ly;
+	const btScalar z2 = lz*lz;
+	const btScalar scaledmass = mass * btScalar(.08333333);
+
+	inertia[0] = scaledmass * (y2+z2);
+	inertia[1] = scaledmass * (x2+z2);
+	inertia[2] = scaledmass * (x2+y2);
+
+}
+
+
+
+
+