/*************************************************************************
 *                                                                       *
 * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith.       *
 * All rights reserved.  Email: russ@q12.org   Web: www.q12.org          *
 *                                                                       *
 * This library is free software; you can redistribute it and/or         *
 * modify it under the terms of EITHER:                                  *
 *   (1) The GNU Lesser General Public License as published by the Free  *
 *       Software Foundation; either version 2.1 of the License, or (at  *
 *       your option) any later version. The text of the GNU Lesser      *
 *       General Public License is included with this library in the     *
 *       file LICENSE.TXT.                                               *
 *   (2) The BSD-style license that is included with this library in     *
 *       the file LICENSE-BSD.TXT.                                       *
 *                                                                       *
 * This library is distributed in the hope that it will be useful,       *
 * but WITHOUT ANY WARRANTY; without even the implied warranty of        *
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files    *
 * LICENSE.TXT and LICENSE-BSD.TXT for more details.                     *
 *                                                                       *
 *************************************************************************/

#include <ode/odeconfig.h>
#include "ode_mass.hpp"
#include "ode_math.hpp"
#include "matrix.h"
#include "odemath.h"

#define dDEBUGMSG(e)

// Local dependencies
#include "collision_kernel.h"

#if dTRIMESH_ENABLED
#include "collision_trimesh_internal.h"
#endif // dTRIMESH_ENABLED

#define	SQR(x)			((x)*(x))						//!< Returns x square
#define	CUBE(x)			((x)*(x)*(x))					//!< Returns x cube

#define _I(i,j) I[(i)*4+(j)]


// return 1 if ok, 0 if bad

int dMassCheck (const dMass *m)
{
    int i;

    if (m->mass <= 0) {
        dDEBUGMSG ("mass must be > 0");
        return 0;
    }
    if (!dIsPositiveDefinite (m->I,3,NULL)) {
        dDEBUGMSG ("inertia must be positive definite");
        return 0;
    }

    // verify that the center of mass position is consistent with the mass
    // and inertia matrix. this is done by checking that the inertia around
    // the center of mass is also positive definite. from the comment in
    // dMassTranslate(), if the body is translated so that its center of mass
    // is at the point of reference, then the new inertia is:
    //   I + mass*crossmat(c)^2
    // note that requiring this to be positive definite is exactly equivalent
    // to requiring that the spatial inertia matrix
    //   [ mass*eye(3,3)   M*crossmat(c)^T ]
    //   [ M*crossmat(c)   I               ]
    // is positive definite, given that I is PD and mass>0. see the theorem
    // about partitioned PD matrices for proof.

    dMatrix3 I2,chat;
    dSetZero (chat,12);
    dSetCrossMatrixPlus (chat,m->c,4);
    dMultiply0_333 (I2,chat,chat);
    for (i=0; i<3; i++) I2[i] = m->I[i] + m->mass*I2[i];
    for (i=4; i<7; i++) I2[i] = m->I[i] + m->mass*I2[i];
    for (i=8; i<11; i++) I2[i] = m->I[i] + m->mass*I2[i];
    if (!dIsPositiveDefinite (I2,3,NULL)) {
        dDEBUGMSG ("center of mass inconsistent with mass parameters");
        return 0;
    }
    return 1;
}


void dMassSetZero (dMass *m)
{
    dAASSERT (m);
    m->mass = REAL(0.0);
    dSetZero (m->c,sizeof(m->c) / sizeof(dReal));
    dSetZero (m->I,sizeof(m->I) / sizeof(dReal));
}


void dMassSetParameters (dMass *m, dReal themass,
                         dReal cgx, dReal cgy, dReal cgz,
                         dReal I11, dReal I22, dReal I33,
                         dReal I12, dReal I13, dReal I23)
{
    dAASSERT (m);
    dMassSetZero (m);
    m->mass = themass;
    m->c[0] = cgx;
    m->c[1] = cgy;
    m->c[2] = cgz;
    m->_I(0,0) = I11;
    m->_I(1,1) = I22;
    m->_I(2,2) = I33;
    m->_I(0,1) = I12;
    m->_I(0,2) = I13;
    m->_I(1,2) = I23;
    m->_I(1,0) = I12;
    m->_I(2,0) = I13;
    m->_I(2,1) = I23;
    dMassCheck (m);
}


void dMassSetSphere (dMass *m, dReal density, dReal radius)
{
    dMassSetSphereTotal (m, (dReal) ((REAL(4.0)/REAL(3.0)) * M_PI *
        radius*radius*radius * density), radius);
}


void dMassSetSphereTotal (dMass *m, dReal total_mass, dReal radius)
{
    dAASSERT (m);
    dMassSetZero (m);
    m->mass = total_mass;
    dReal II = REAL(0.4) * total_mass * radius*radius;
    m->_I(0,0) = II;
    m->_I(1,1) = II;
    m->_I(2,2) = II;

# ifndef dNODEBUG
    dMassCheck (m);
# endif
}


void dMassSetCapsule (dMass *m, dReal density, int direction,
                      dReal radius, dReal length)
{
    dReal M1,M2,Ia,Ib;
    dAASSERT (m);
    dUASSERT (direction >= 1 && direction <= 3,"bad direction number");
    dMassSetZero (m);
    M1 = (dReal) (M_PI*radius*radius*length*density);			  // cylinder mass
    M2 = (dReal) ((REAL(4.0)/REAL(3.0))*M_PI*radius*radius*radius*density); // total cap mass
    m->mass = M1+M2;
    Ia = M1*(REAL(0.25)*radius*radius + (REAL(1.0)/REAL(12.0))*length*length) +
        M2*(REAL(0.4)*radius*radius + REAL(0.375)*radius*length + REAL(0.25)*length*length);
    Ib = (M1*REAL(0.5) + M2*REAL(0.4))*radius*radius;
    m->_I(0,0) = Ia;
    m->_I(1,1) = Ia;
    m->_I(2,2) = Ia;
    m->_I(direction-1,direction-1) = Ib;

# ifndef dNODEBUG
    dMassCheck (m);
# endif
}


void dMassSetCapsuleTotal (dMass *m, dReal total_mass, int direction,
                           dReal a, dReal b)
{
    dMassSetCapsule (m, 1.0, direction, a, b);
    dMassAdjust (m, total_mass);
}


void dMassSetCylinder (dMass *m, dReal density, int direction,
                       dReal radius, dReal length)
{
    dMassSetCylinderTotal (m, (dReal) (M_PI*radius*radius*length*density),
        direction, radius, length);
}

void dMassSetCylinderTotal (dMass *m, dReal total_mass, int direction,
                            dReal radius, dReal length)
{
    dReal r2,I;
    dAASSERT (m);
    dUASSERT (direction >= 1 && direction <= 3,"bad direction number");
    dMassSetZero (m);
    r2 = radius*radius;
    m->mass = total_mass;
    I = total_mass*(REAL(0.25)*r2 + (REAL(1.0)/REAL(12.0))*length*length);
    m->_I(0,0) = I;
    m->_I(1,1) = I;
    m->_I(2,2) = I;
    m->_I(direction-1,direction-1) = total_mass*REAL(0.5)*r2;

# ifndef dNODEBUG
    dMassCheck (m);
# endif
}


void dMassSetBox (dMass *m, dReal density,
                  dReal lx, dReal ly, dReal lz)
{
    dMassSetBoxTotal (m, lx*ly*lz*density, lx, ly, lz);
}


void dMassSetBoxTotal (dMass *m, dReal total_mass,
                       dReal lx, dReal ly, dReal lz)
{
    dAASSERT (m);
    dMassSetZero (m);
    m->mass = total_mass;
    m->_I(0,0) = total_mass/REAL(12.0) * (ly*ly + lz*lz);
    m->_I(1,1) = total_mass/REAL(12.0) * (lx*lx + lz*lz);
    m->_I(2,2) = total_mass/REAL(12.0) * (lx*lx + ly*ly);

# ifndef dNODEBUG
    dMassCheck (m);
# endif
}






/*
* dMassSetTrimesh, implementation by Gero Mueller.
* Based on Brian Mirtich, "Fast and Accurate Computation of
* Polyhedral Mass Properties," journal of graphics tools, volume 1,
* number 2, 1996.
*/
void dMassSetTrimesh( dMass *m, dReal density, dGeomID g )
{
    dAASSERT (m);
    dUASSERT(g && g->type == dTriMeshClass, "argument not a trimesh");

    dMassSetZero (m);

#if dTRIMESH_ENABLED

    dxTriMesh *TriMesh = static_cast<dxTriMesh *>(g);
    unsigned int triangles = TriMesh->getMeshTriangleCount();

    dReal nx, ny, nz;
    unsigned int i, A, B, C;
    // face integrals
    dReal Fa, Fb, Fc, Faa, Fbb, Fcc, Faaa, Fbbb, Fccc, Faab, Fbbc, Fcca;

    // projection integrals
    dReal P1, Pa, Pb, Paa, Pab, Pbb, Paaa, Paab, Pabb, Pbbb;

    dReal T0 = 0;
    dReal T1[3] = {0., 0., 0.};
    dReal T2[3] = {0., 0., 0.};
    dReal TP[3] = {0., 0., 0.};

    for( i = 0; i < triangles; i++ )	 	
    {
        dVector3 v[3];
        TriMesh->fetchMeshTransformedTriangle(v, i);

        dVector3 n, a, b;
        dSubtractVectors3( a, v[1], v[0] ); 
        dSubtractVectors3( b, v[2], v[0] ); 
        dCalcVectorCross3( n, b, a );
        nx = fabs(n[0]);
        ny = fabs(n[1]);
        nz = fabs(n[2]);

        if( nx > ny && nx > nz )
            C = 0;
        else
            C = (ny > nz) ? 1 : 2;

        // Even though all triangles might be initially valid, 
        // a triangle may degenerate into a segment after applying 
        // space transformation.
        if (n[C] != REAL(0.0))
        {
            A = (C + 1) % 3;
            B = (A + 1) % 3;

            // calculate face integrals
            {
                dReal w;
                dReal k1, k2, k3, k4;

                //compProjectionIntegrals(f);
                {
                    dReal a0=0, a1=0, da;
                    dReal b0=0, b1=0, db;
                    dReal a0_2, a0_3, a0_4, b0_2, b0_3, b0_4;
                    dReal a1_2, a1_3, b1_2, b1_3;
                    dReal C1, Ca, Caa, Caaa, Cb, Cbb, Cbbb;
                    dReal Cab, Kab, Caab, Kaab, Cabb, Kabb;

                    P1 = Pa = Pb = Paa = Pab = Pbb = Paaa = Paab = Pabb = Pbbb = 0.0;

                    for( int j = 0; j < 3; j++)
                    {
                        switch(j)
                        {
                        case 0:
                            a0 = v[0][A];
                            b0 = v[0][B];
                            a1 = v[1][A];
                            b1 = v[1][B];
                            break;
                        case 1:
                            a0 = v[1][A];
                            b0 = v[1][B];
                            a1 = v[2][A];
                            b1 = v[2][B];
                            break;
                        case 2:
                            a0 = v[2][A];
                            b0 = v[2][B];
                            a1 = v[0][A];
                            b1 = v[0][B];
                            break;
                        }
                        da = a1 - a0;
                        db = b1 - b0;
                        a0_2 = a0 * a0; a0_3 = a0_2 * a0; a0_4 = a0_3 * a0;
                        b0_2 = b0 * b0; b0_3 = b0_2 * b0; b0_4 = b0_3 * b0;
                        a1_2 = a1 * a1; a1_3 = a1_2 * a1; 
                        b1_2 = b1 * b1; b1_3 = b1_2 * b1;

                        C1 = a1 + a0;
                        Ca = a1*C1 + a0_2; Caa = a1*Ca + a0_3; Caaa = a1*Caa + a0_4;
                        Cb = b1*(b1 + b0) + b0_2; Cbb = b1*Cb + b0_3; Cbbb = b1*Cbb + b0_4;
                        Cab = 3*a1_2 + 2*a1*a0 + a0_2; Kab = a1_2 + 2*a1*a0 + 3*a0_2;
                        Caab = a0*Cab + 4*a1_3; Kaab = a1*Kab + 4*a0_3;
                        Cabb = 4*b1_3 + 3*b1_2*b0 + 2*b1*b0_2 + b0_3;
                        Kabb = b1_3 + 2*b1_2*b0 + 3*b1*b0_2 + 4*b0_3;

                        P1 += db*C1;
                        Pa += db*Ca;
                        Paa += db*Caa;
                        Paaa += db*Caaa;
                        Pb += da*Cb;
                        Pbb += da*Cbb;
                        Pbbb += da*Cbbb;
                        Pab += db*(b1*Cab + b0*Kab);
                        Paab += db*(b1*Caab + b0*Kaab);
                        Pabb += da*(a1*Cabb + a0*Kabb);
                    }

                    P1 /= 2.0;
                    Pa /= 6.0;
                    Paa /= 12.0;
                    Paaa /= 20.0;
                    Pb /= -6.0;
                    Pbb /= -12.0;
                    Pbbb /= -20.0;
                    Pab /= 24.0;
                    Paab /= 60.0;
                    Pabb /= -60.0;
                }

                w = - dCalcVectorDot3(n, v[0]);

                k1 = 1 / n[C]; k2 = k1 * k1; k3 = k2 * k1; k4 = k3 * k1;

                Fa = k1 * Pa;
                Fb = k1 * Pb;
                Fc = -k2 * (n[A]*Pa + n[B]*Pb + w*P1);

                Faa = k1 * Paa;
                Fbb = k1 * Pbb;
                Fcc = k3 * (SQR(n[A])*Paa + 2*n[A]*n[B]*Pab + SQR(n[B])*Pbb +
                    w*(2*(n[A]*Pa + n[B]*Pb) + w*P1));

                Faaa = k1 * Paaa;
                Fbbb = k1 * Pbbb;
                Fccc = -k4 * (CUBE(n[A])*Paaa + 3*SQR(n[A])*n[B]*Paab 
                    + 3*n[A]*SQR(n[B])*Pabb + CUBE(n[B])*Pbbb
                    + 3*w*(SQR(n[A])*Paa + 2*n[A]*n[B]*Pab + SQR(n[B])*Pbb)
                    + w*w*(3*(n[A]*Pa + n[B]*Pb) + w*P1));

                Faab = k1 * Paab;
                Fbbc = -k2 * (n[A]*Pabb + n[B]*Pbbb + w*Pbb);
                Fcca = k3 * (SQR(n[A])*Paaa + 2*n[A]*n[B]*Paab + SQR(n[B])*Pabb
                    + w*(2*(n[A]*Paa + n[B]*Pab) + w*Pa));
            }


            T0 += n[0] * ((A == 0) ? Fa : ((B == 0) ? Fb : Fc));

            T1[A] += n[A] * Faa;
            T1[B] += n[B] * Fbb;
            T1[C] += n[C] * Fcc;
            T2[A] += n[A] * Faaa;
            T2[B] += n[B] * Fbbb;
            T2[C] += n[C] * Fccc;
            TP[A] += n[A] * Faab;
            TP[B] += n[B] * Fbbc;
            TP[C] += n[C] * Fcca;
        }
    }

    T1[0] /= 2; T1[1] /= 2; T1[2] /= 2;
    T2[0] /= 3; T2[1] /= 3; T2[2] /= 3;
    TP[0] /= 2; TP[1] /= 2; TP[2] /= 2;

    m->mass = density * T0;
    m->_I(0,0) = density * (T2[1] + T2[2]);
    m->_I(1,1) = density * (T2[2] + T2[0]);
    m->_I(2,2) = density * (T2[0] + T2[1]);
    m->_I(0,1) = - density * TP[0];
    m->_I(1,0) = - density * TP[0];
    m->_I(2,1) = - density * TP[1];
    m->_I(1,2) = - density * TP[1];
    m->_I(2,0) = - density * TP[2];
    m->_I(0,2) = - density * TP[2];

    // Added to address SF bug 1729095
    dMassTranslate( m, T1[0] / T0,  T1[1] / T0,  T1[2] / T0 );

# ifndef dNODEBUG
    dMassCheck (m);
# endif

#endif // dTRIMESH_ENABLED
}


void dMassSetTrimeshTotal( dMass *m, dReal total_mass, dGeomID g)
{
    dAASSERT( m );
    dUASSERT( g && g->type == dTriMeshClass, "argument not a trimesh" );
    dMassSetTrimesh( m, 1.0, g );
    dMassAdjust( m, total_mass );
}




void dMassAdjust (dMass *m, dReal newmass)
{
    dAASSERT (m);
    dReal scale = newmass / m->mass;
    m->mass = newmass;
    for (int i=0; i<3; i++) for (int j=0; j<3; j++) m->_I(i,j) *= scale;

# ifndef dNODEBUG
    dMassCheck (m);
# endif
}


void dMassTranslate (dMass *m, dReal x, dReal y, dReal z)
{
    // if the body is translated by `a' relative to its point of reference,
    // the new inertia about the point of reference is:
    //
    //   I + mass*(crossmat(c)^2 - crossmat(c+a)^2)
    //
    // where c is the existing center of mass and I is the old inertia.

    int i,j;
    dMatrix3 ahat,chat,t1,t2;
    dReal a[3];

    dAASSERT (m);

    // adjust inertia matrix
    dSetZero (chat,12);
    dSetCrossMatrixPlus (chat,m->c,4);
    a[0] = x + m->c[0];
    a[1] = y + m->c[1];
    a[2] = z + m->c[2];
    dSetZero (ahat,12);
    dSetCrossMatrixPlus (ahat,a,4);
    dMultiply0_333 (t1,ahat,ahat);
    dMultiply0_333 (t2,chat,chat);
    for (i=0; i<3; i++) for (j=0; j<3; j++)
        m->_I(i,j) += m->mass * (t2[i*4+j]-t1[i*4+j]);

    // ensure perfect symmetry
    m->_I(1,0) = m->_I(0,1);
    m->_I(2,0) = m->_I(0,2);
    m->_I(2,1) = m->_I(1,2);

    // adjust center of mass
    m->c[0] += x;
    m->c[1] += y;
    m->c[2] += z;

# ifndef dNODEBUG
    dMassCheck (m);
# endif
}


void dMassRotate (dMass *m, const dMatrix3 R)
{
    // if the body is rotated by `R' relative to its point of reference,
    // the new inertia about the point of reference is:
    //
    //   R * I * R'
    //
    // where I is the old inertia.

    dMatrix3 t1;
    dReal t2[3];

    dAASSERT (m);

    // rotate inertia matrix
    dMultiply2_333 (t1,m->I,R);
    dMultiply0_333 (m->I,R,t1);

    // ensure perfect symmetry
    m->_I(1,0) = m->_I(0,1);
    m->_I(2,0) = m->_I(0,2);
    m->_I(2,1) = m->_I(1,2);

    // rotate center of mass
    dMultiply0_331 (t2,R,m->c);
    m->c[0] = t2[0];
    m->c[1] = t2[1];
    m->c[2] = t2[2];

# ifndef dNODEBUG
    dMassCheck (m);
# endif
}


void dMassAdd (dMass *a, const dMass *b)
{
    int i;
    dAASSERT (a && b);
    dReal denom = dRecip (a->mass + b->mass);
    for (i=0; i<3; i++) a->c[i] = (a->c[i]*a->mass + b->c[i]*b->mass)*denom;
    a->mass += b->mass;
    for (i=0; i<12; i++) a->I[i] += b->I[i];
}


// Backwards compatible API
void dMassSetCappedCylinder(dMass *a, dReal b, int c, dReal d, dReal e)
{
    return dMassSetCapsule(a,b,c,d,e);
}

void dMassSetCappedCylinderTotal(dMass *a, dReal b, int c, dReal d, dReal e)
{
    return dMassSetCapsuleTotal(a,b,c,d,e);
}