PxMassProperties.h

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#ifndef PX_PHYSICS_EXTENSIONS_MASS_PROPERTIES_H
#define PX_PHYSICS_EXTENSIONS_MASS_PROPERTIES_H

#include "PxPhysXConfig.h"
#include "foundation/PxMath.h"
#include "foundation/PxMathUtils.h"
#include "foundation/PxVec3.h"
#include "foundation/PxMat33.h"
#include "foundation/PxQuat.h"
#include "foundation/PxTransform.h"
#include "geometry/PxGeometry.h"
#include "geometry/PxBoxGeometry.h"
#include "geometry/PxSphereGeometry.h"
#include "geometry/PxCapsuleGeometry.h"
#include "geometry/PxConvexMeshGeometry.h"
#include "geometry/PxConvexMesh.h"

#if !PX_DOXYGEN
namespace physx
{
#endif

class PxMassProperties
{
public:
    PX_FORCE_INLINE PxMassProperties() : inertiaTensor(PxIdentity), centerOfMass(0.0f), mass(1.0f) {}

    PX_FORCE_INLINE PxMassProperties(const PxReal m, const PxMat33& inertiaT, const PxVec3& com) : inertiaTensor(inertiaT), centerOfMass(com), mass(m) {}

    PxMassProperties(const PxGeometry& geometry)
    {
        switch (geometry.getType())
        {
            case PxGeometryType::eSPHERE:
            {
                const PxSphereGeometry& s = static_cast<const PxSphereGeometry&>(geometry);
                mass = (4.0f / 3.0f) * PxPi * s.radius * s.radius * s.radius;
                inertiaTensor = PxMat33::createDiagonal(PxVec3(2.0f / 5.0f * mass * s.radius * s.radius));
                centerOfMass = PxVec3(0.0f);
            }
            break;

            case PxGeometryType::eBOX:
            {
                const PxBoxGeometry& b = static_cast<const PxBoxGeometry&>(geometry);
                mass = b.halfExtents.x * b.halfExtents.y * b.halfExtents.z * 8.0f;
                PxVec3 d2 = b.halfExtents.multiply(b.halfExtents);
                inertiaTensor = PxMat33::createDiagonal(PxVec3(d2.y + d2.z, d2.x + d2.z, d2.x + d2.y)) * (mass * 1.0f / 3.0f);
                centerOfMass = PxVec3(0.0f);
            }
            break;

            case PxGeometryType::eCAPSULE:
            {
                const PxCapsuleGeometry& c = static_cast<const PxCapsuleGeometry&>(geometry);
                PxReal r = c.radius, h = c.halfHeight;
                mass = ((4.0f / 3.0f) * r + 2 * c.halfHeight) * PxPi * r * r;

                PxReal a = r*r*r * (8.0f / 15.0f) + h*r*r * (3.0f / 2.0f) + h*h*r * (4.0f / 3.0f) + h*h*h * (2.0f / 3.0f);
                PxReal b = r*r*r * (8.0f / 15.0f) + h*r*r;
                inertiaTensor = PxMat33::createDiagonal(PxVec3(b, a, a) * PxPi * r * r);
                centerOfMass = PxVec3(0.0f);
            }
            break;

            case PxGeometryType::eCONVEXMESH:
            {
                const PxConvexMeshGeometry& c = static_cast<const PxConvexMeshGeometry&>(geometry);
                PxVec3 unscaledCoM;
                PxMat33 unscaledInertiaTensorNonCOM; // inertia tensor of convex mesh in mesh local space
                PxMat33 unscaledInertiaTensorCOM;
                PxReal unscaledMass;
                c.convexMesh->getMassInformation(unscaledMass, unscaledInertiaTensorNonCOM, unscaledCoM);               

                // inertia tensor relative to center of mass
                unscaledInertiaTensorCOM[0][0] = unscaledInertiaTensorNonCOM[0][0] - unscaledMass*PxReal((unscaledCoM.y*unscaledCoM.y+unscaledCoM.z*unscaledCoM.z));
                unscaledInertiaTensorCOM[1][1] = unscaledInertiaTensorNonCOM[1][1] - unscaledMass*PxReal((unscaledCoM.z*unscaledCoM.z+unscaledCoM.x*unscaledCoM.x));
                unscaledInertiaTensorCOM[2][2] = unscaledInertiaTensorNonCOM[2][2] - unscaledMass*PxReal((unscaledCoM.x*unscaledCoM.x+unscaledCoM.y*unscaledCoM.y));
                unscaledInertiaTensorCOM[0][1] = unscaledInertiaTensorCOM[1][0] = (unscaledInertiaTensorNonCOM[0][1] + unscaledMass*PxReal(unscaledCoM.x*unscaledCoM.y));
                unscaledInertiaTensorCOM[1][2] = unscaledInertiaTensorCOM[2][1] = (unscaledInertiaTensorNonCOM[1][2] + unscaledMass*PxReal(unscaledCoM.y*unscaledCoM.z));
                unscaledInertiaTensorCOM[0][2] = unscaledInertiaTensorCOM[2][0] = (unscaledInertiaTensorNonCOM[0][2] + unscaledMass*PxReal(unscaledCoM.z*unscaledCoM.x));

                const PxMeshScale& s = c.scale;
                mass = unscaledMass * s.scale.x * s.scale.y * s.scale.z;
                centerOfMass = s.rotation.rotate(s.scale.multiply(s.rotation.rotateInv(unscaledCoM)));
                inertiaTensor = scaleInertia(unscaledInertiaTensorCOM, s.rotation, s.scale);
            }
            break;

            case PxGeometryType::eHEIGHTFIELD:
            case PxGeometryType::ePLANE:
            case PxGeometryType::eTRIANGLEMESH:
            case PxGeometryType::eINVALID:
            case PxGeometryType::eGEOMETRY_COUNT:
            {
                *this = PxMassProperties();
            }
            break;
        }

        PX_ASSERT(inertiaTensor.column0.isFinite() && inertiaTensor.column1.isFinite() && inertiaTensor.column2.isFinite());
        PX_ASSERT(centerOfMass.isFinite());
        PX_ASSERT(PxIsFinite(mass));
    }

    PX_FORCE_INLINE PxMassProperties operator*(const PxReal scale) const
    {
        PX_ASSERT(PxIsFinite(scale));

        return PxMassProperties(mass * scale, inertiaTensor * scale, centerOfMass);
    }

    PX_FORCE_INLINE void translate(const PxVec3& t)
    {
        PX_ASSERT(t.isFinite());

        inertiaTensor = translateInertia(inertiaTensor, mass, t);
        centerOfMass += t;

        PX_ASSERT(inertiaTensor.column0.isFinite() && inertiaTensor.column1.isFinite() && inertiaTensor.column2.isFinite());
        PX_ASSERT(centerOfMass.isFinite());
    }

    PX_FORCE_INLINE static PxVec3 getMassSpaceInertia(const PxMat33& inertia, PxQuat& massFrame)
    {
        PX_ASSERT(inertia.column0.isFinite() && inertia.column1.isFinite() && inertia.column2.isFinite());

        PxVec3 diagT = PxDiagonalize(inertia, massFrame);
        PX_ASSERT(diagT.isFinite());
        PX_ASSERT(massFrame.isFinite());
        return diagT;
    }

    PX_FORCE_INLINE static PxMat33 translateInertia(const PxMat33& inertia, const PxReal mass, const PxVec3& t)
    {
        PX_ASSERT(inertia.column0.isFinite() && inertia.column1.isFinite() && inertia.column2.isFinite());
        PX_ASSERT(PxIsFinite(mass));
        PX_ASSERT(t.isFinite());

        PxMat33 s(  PxVec3(0,t.z,-t.y),
                    PxVec3(-t.z,0,t.x),
                    PxVec3(t.y,-t.x,0) );

        PxMat33 translatedIT = s.getTranspose() * s * mass + inertia;
        PX_ASSERT(translatedIT.column0.isFinite() && translatedIT.column1.isFinite() && translatedIT.column2.isFinite());
        return translatedIT;
    }

    PX_FORCE_INLINE static PxMat33 rotateInertia(const PxMat33& inertia, const PxQuat& q)
    {
        PX_ASSERT(inertia.column0.isFinite() && inertia.column1.isFinite() && inertia.column2.isFinite());
        PX_ASSERT(q.isUnit());

        PxMat33 m(q);
        PxMat33 rotatedIT = m * inertia * m.getTranspose();
        PX_ASSERT(rotatedIT.column0.isFinite() && rotatedIT.column1.isFinite() && rotatedIT.column2.isFinite());
        return rotatedIT;
    }

    static PxMat33 scaleInertia(const PxMat33& inertia, const PxQuat& scaleRotation, const PxVec3& scale)
    {
        PX_ASSERT(inertia.column0.isFinite() && inertia.column1.isFinite() && inertia.column2.isFinite());
        PX_ASSERT(scaleRotation.isUnit());
        PX_ASSERT(scale.isFinite());

        PxMat33 localInertiaT = rotateInertia(inertia, scaleRotation); // rotate inertia into scaling frame
        PxVec3 diagonal(localInertiaT[0][0], localInertiaT[1][1], localInertiaT[2][2]);

        PxVec3 xyz2 = PxVec3(diagonal.dot(PxVec3(0.5f))) - diagonal; // original x^2, y^2, z^2
        PxVec3 scaledxyz2 = xyz2.multiply(scale).multiply(scale);

        PxReal  xx = scaledxyz2.y + scaledxyz2.z,
                yy = scaledxyz2.z + scaledxyz2.x,
                zz = scaledxyz2.x + scaledxyz2.y;

        PxReal  xy = localInertiaT[0][1] * scale.x * scale.y,
                xz = localInertiaT[0][2] * scale.x * scale.z,
                yz = localInertiaT[1][2] * scale.y * scale.z;

        PxMat33 scaledInertia(  PxVec3(xx, xy, xz),
                                PxVec3(xy, yy, yz),
                                PxVec3(xz, yz, zz));

        PxMat33 scaledIT = rotateInertia(scaledInertia * (scale.x * scale.y * scale.z), scaleRotation.getConjugate());
        PX_ASSERT(scaledIT.column0.isFinite() && scaledIT.column1.isFinite() && scaledIT.column2.isFinite());
        return scaledIT;
    }

    static PxMassProperties sum(const PxMassProperties* props, const PxTransform* transforms, const PxU32 count)
    {
        PxReal combinedMass = 0.0f;
        PxVec3 combinedCoM(0.0f);
        PxMat33 combinedInertiaT = PxMat33(PxZero);

        for(PxU32 i = 0; i < count; i++)
        {
            PX_ASSERT(props[i].inertiaTensor.column0.isFinite() && props[i].inertiaTensor.column1.isFinite() && props[i].inertiaTensor.column2.isFinite());
            PX_ASSERT(props[i].centerOfMass.isFinite());
            PX_ASSERT(PxIsFinite(props[i].mass));

            combinedMass += props[i].mass;
            const PxVec3 comTm = transforms[i].transform(props[i].centerOfMass);
            combinedCoM += comTm * props[i].mass;
        }

        combinedCoM /= combinedMass;

        for(PxU32 i = 0; i < count; i++)
        {
            const PxVec3 comTm = transforms[i].transform(props[i].centerOfMass);
            combinedInertiaT += translateInertia(rotateInertia(props[i].inertiaTensor, transforms[i].q), props[i].mass, combinedCoM - comTm);
        }

        PX_ASSERT(combinedInertiaT.column0.isFinite() && combinedInertiaT.column1.isFinite() && combinedInertiaT.column2.isFinite());
        PX_ASSERT(combinedCoM.isFinite());
        PX_ASSERT(PxIsFinite(combinedMass));

        return PxMassProperties(combinedMass, combinedInertiaT, combinedCoM);
    }


    PxMat33 inertiaTensor;          
    PxVec3  centerOfMass;           
    PxReal  mass;                   
};

#if !PX_DOXYGEN
} // namespace physx
#endif

#endif