/*************************************************************************
 *                                                                       *
 * 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/config.h>
#include <ode/mass.h>
#include <ode/odemath.h>
#include <ode/matrix.h>

// Local dependencies
#include "collision_kernel.h"

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

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


// return 1 if ok, 0 if bad

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

  if (m->mass <= 0) {
    return 0;
  }
  if (!dIsPositiveDefinite (m->I,3)) {
    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);
  dCROSSMAT (chat,m->c,4,+,-);
  dMULTIPLY0_333 (I2,chat,chat);
  for (i=0; i<3; i++) I2[i] = m->I[i] + dMUL(m->mass,I2[i]);
  for (i=4; i<7; i++) I2[i] = m->I[i] + dMUL(m->mass,I2[i]);
  for (i=8; i<11; i++) I2[i] = m->I[i] + dMUL(m->mass,I2[i]);
  if (!dIsPositiveDefinite (I2,3)) {
    return 0;
  }
  return 1;
}


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


EXPORT_C void dMassSetParameters (dMass *m, dReal themass,
			 dReal cgx, dReal cgy, dReal cgz,
			 dReal I11, dReal I22, dReal I33,
			 dReal I12, dReal I13, dReal I23)
{
  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);
}


EXPORT_C void dMassSetSphere (dMass *m, dReal density, dReal radius)
{
  dMassSetSphereTotal (m, dMUL(dDIV(REAL(4.0),REAL(3.0)), dMUL(dPI,dMUL(CUBE(radius),density))), radius);
}


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

# ifndef dNODEBUG
  dMassCheck (m);
# endif
}


EXPORT_C void dMassSetCapsule (dMass *m, dReal density, int direction,
		      dReal radius, dReal length)
{
  dReal M1,M2,Ia,Ib;
  dMassSetZero (m);
  M1 = dMUL(dPI,dMUL(SQR(radius),dMUL(length,density)));			// cylinder mass
  M2 = dMUL(dDIV(REAL(4.0),REAL(3.0)),dMUL(dPI,dMUL(CUBE(radius),density)));	// total cap mass
  m->mass = M1+M2;
  Ia = dMUL(M1,(dMUL(REAL(0.25),SQR(radius)) + dMUL(dDIV(REAL(1.0),REAL(12.0)),SQR(length)))) +
    dMUL(M2,(dMUL(REAL(0.4),SQR(radius)) + dMUL(REAL(0.375),dMUL(radius,length)) + dMUL(REAL(0.25),SQR(length))));
  Ib = dMUL((dMUL(M1,REAL(0.5)) + dMUL(M2,REAL(0.4))),SQR(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
}


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


EXPORT_C void dMassSetCylinder (dMass *m, dReal density, int direction,
		       dReal radius, dReal length)
{
  dMassSetCylinderTotal (m, dMUL(dPI,dMUL(SQR(radius),dMUL(length,density))),
			    direction, radius, length);
}

EXPORT_C void dMassSetCylinderTotal (dMass *m, dReal total_mass, int direction,
			    dReal radius, dReal length)
{
  dReal r2,I;
  dMassSetZero (m);
  r2 = SQR(radius);
  m->mass = total_mass;
  I = dMUL(total_mass,(dMUL(REAL(0.25),r2) + dMUL(dDIV(REAL(1.0),REAL(12.0)),SQR(length))));
  m->_I(0,0) = I;
  m->_I(1,1) = I;
  m->_I(2,2) = I;
  m->_I(direction-1,direction-1) = dMUL(total_mass,dMUL(REAL(0.5),r2));

# ifndef dNODEBUG
  dMassCheck (m);
# endif
}


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


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

# ifndef dNODEBUG
  dMassCheck (m);
# endif
}

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

# ifndef dNODEBUG
  dMassCheck (m);
# endif
}


EXPORT_C 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];

  // adjust inertia matrix
  dSetZero (chat,12);
  dCROSSMAT (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);
  dCROSSMAT (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) += dMUL(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
}


EXPORT_C 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];

  // 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
}


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