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btMatrix3x3.h

/*
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 btMatrix3x3_H
#define btMatrix3x3_H

#include "btScalar.h"

#include "btVector3.h"
#include "btQuaternion.h"



///The btMatrix3x3 class implements a 3x3 rotation matrix, to perform linear algebra in combination with btQuaternion, btTransform and btVector3.
///Make sure to only include a pure orthogonal matrix without scaling.
00028 class btMatrix3x3 {
      public:
            btMatrix3x3 () {}
            
//          explicit btMatrix3x3(const btScalar *m) { setFromOpenGLSubMatrix(m); }
            
            explicit btMatrix3x3(const btQuaternion& q) { setRotation(q); }
            /*
            template <typename btScalar>
            Matrix3x3(const btScalar& yaw, const btScalar& pitch, const btScalar& roll)
            { 
                  setEulerYPR(yaw, pitch, roll);
            }
            */
            btMatrix3x3(const btScalar& xx, const btScalar& xy, const btScalar& xz,
                          const btScalar& yx, const btScalar& yy, const btScalar& yz,
                          const btScalar& zx, const btScalar& zy, const btScalar& zz)
            { 
                  setValue(xx, xy, xz, 
                               yx, yy, yz, 
                               zx, zy, zz);
            }
            
            SIMD_FORCE_INLINE btMatrix3x3 (const btMatrix3x3& other)
            {
                  m_el[0] = other.m_el[0];
                  m_el[1] = other.m_el[1];
                  m_el[2] = other.m_el[2];
            }

            SIMD_FORCE_INLINE btMatrix3x3& operator=(const btMatrix3x3& other)
            {
                  m_el[0] = other.m_el[0];
                  m_el[1] = other.m_el[1];
                  m_el[2] = other.m_el[2];
                  return *this;
            }

            SIMD_FORCE_INLINE btVector3 getColumn(int i) const
            {
                  return btVector3(m_el[0][i],m_el[1][i],m_el[2][i]);
            }
            


            SIMD_FORCE_INLINE const btVector3& getRow(int i) const
            {
                  return m_el[i];
            }


            SIMD_FORCE_INLINE btVector3&  operator[](int i)
            { 
                  btFullAssert(0 <= i && i < 3);
                  return m_el[i]; 
            }
            
            SIMD_FORCE_INLINE const btVector3& operator[](int i) const
            {
                  btFullAssert(0 <= i && i < 3);
                  return m_el[i]; 
            }
            
            btMatrix3x3& operator*=(const btMatrix3x3& m); 
            
      
      void setFromOpenGLSubMatrix(const btScalar *m)
            {
                  m_el[0].setValue(m[0],m[4],m[8]);
                  m_el[1].setValue(m[1],m[5],m[9]);
                  m_el[2].setValue(m[2],m[6],m[10]);

            }

            void setValue(const btScalar& xx, const btScalar& xy, const btScalar& xz, 
                                const btScalar& yx, const btScalar& yy, const btScalar& yz, 
                                const btScalar& zx, const btScalar& zy, const btScalar& zz)
            {
                  m_el[0].setValue(xx,xy,xz);
                  m_el[1].setValue(yx,yy,yz);
                  m_el[2].setValue(zx,zy,zz);
            }
  
            void setRotation(const btQuaternion& q) 
            {
                  btScalar d = q.length2();
                  btFullAssert(d != btScalar(0.0));
                  btScalar s = btScalar(2.0) / d;
                  btScalar xs = q.x() * s,   ys = q.y() * s,   zs = q.z() * s;
                  btScalar wx = q.w() * xs,  wy = q.w() * ys,  wz = q.w() * zs;
                  btScalar xx = q.x() * xs,  xy = q.x() * ys,  xz = q.x() * zs;
                  btScalar yy = q.y() * ys,  yz = q.y() * zs,  zz = q.z() * zs;
                  setValue(btScalar(1.0) - (yy + zz), xy - wz, xz + wy,
                               xy + wz, btScalar(1.0) - (xx + zz), yz - wx,
                               xz - wy, yz + wx, btScalar(1.0) - (xx + yy));
            }
            


            void setEulerYPR(const btScalar& yaw, const btScalar& pitch, const btScalar& roll) 
            {

                  btScalar cy(btCos(yaw)); 
                  btScalar  sy(btSin(yaw)); 
                  btScalar  cp(btCos(pitch)); 
                  btScalar  sp(btSin(pitch)); 
                  btScalar  cr(btCos(roll));
                  btScalar  sr(btSin(roll));
                  btScalar  cc = cy * cr; 
                  btScalar  cs = cy * sr; 
                  btScalar  sc = sy * cr; 
                  btScalar  ss = sy * sr;
                  setValue(cc - sp * ss, -cs - sp * sc, -sy * cp,
                     cp * sr,       cp * cr,      -sp,
                               sc + sp * cs, -ss + sp * cc,  cy * cp);
            
            }

      /**
       * setEulerZYX
       * @param euler a const reference to a btVector3 of euler angles
       * These angles are used to produce a rotation matrix. The euler
       * angles are applied in ZYX order. I.e a vector is first rotated 
       * about X then Y and then Z
       **/
      
00154       void setEulerZYX(btScalar eulerX,btScalar eulerY,btScalar eulerZ) {
            btScalar ci ( btCos(eulerX)); 
            btScalar cj ( btCos(eulerY)); 
            btScalar ch ( btCos(eulerZ)); 
            btScalar si ( btSin(eulerX)); 
            btScalar sj ( btSin(eulerY)); 
            btScalar sh ( btSin(eulerZ)); 
            btScalar cc = ci * ch; 
            btScalar cs = ci * sh; 
            btScalar sc = si * ch; 
            btScalar ss = si * sh;
            
            setValue(cj * ch, sj * sc - cs, sj * cc + ss,
                         cj * sh, sj * ss + cc, sj * cs - sc, 
                               -sj,      cj * si,      cj * ci);
      }

            void setIdentity()
            { 
                  setValue(btScalar(1.0), btScalar(0.0), btScalar(0.0), 
                               btScalar(0.0), btScalar(1.0), btScalar(0.0), 
                               btScalar(0.0), btScalar(0.0), btScalar(1.0)); 
            }
    
            void getOpenGLSubMatrix(btScalar *m) const 
            {
                  m[0]  = btScalar(m_el[0].x()); 
                  m[1]  = btScalar(m_el[1].x());
                  m[2]  = btScalar(m_el[2].x());
                  m[3]  = btScalar(0.0); 
                  m[4]  = btScalar(m_el[0].y());
                  m[5]  = btScalar(m_el[1].y());
                  m[6]  = btScalar(m_el[2].y());
                  m[7]  = btScalar(0.0); 
                  m[8]  = btScalar(m_el[0].z()); 
                  m[9]  = btScalar(m_el[1].z());
                  m[10] = btScalar(m_el[2].z());
                  m[11] = btScalar(0.0); 
            }

            void getRotation(btQuaternion& q) const
            {
                  btScalar trace = m_el[0].x() + m_el[1].y() + m_el[2].z();
                  btScalar temp[4];
                  
                  if (trace > btScalar(0.0)) 
                  {
                        btScalar s = btSqrt(trace + btScalar(1.0));
                        temp[3]=(s * btScalar(0.5));
                        s = btScalar(0.5) / s;
                        
                        temp[0]=((m_el[2].y() - m_el[1].z()) * s);
                        temp[1]=((m_el[0].z() - m_el[2].x()) * s);
                        temp[2]=((m_el[1].x() - m_el[0].y()) * s);
                  } 
                  else 
                  {
                        int i = m_el[0].x() < m_el[1].y() ? 
                              (m_el[1].y() < m_el[2].z() ? 2 : 1) :
                              (m_el[0].x() < m_el[2].z() ? 2 : 0); 
                        int j = (i + 1) % 3;  
                        int k = (i + 2) % 3;
                        
                        btScalar s = btSqrt(m_el[i][i] - m_el[j][j] - m_el[k][k] + btScalar(1.0));
                        temp[i] = s * btScalar(0.5);
                        s = btScalar(0.5) / s;
                        
                        temp[3] = (m_el[k][j] - m_el[j][k]) * s;
                        temp[j] = (m_el[j][i] + m_el[i][j]) * s;
                        temp[k] = (m_el[k][i] + m_el[i][k]) * s;
                  }
                  q.setValue(temp[0],temp[1],temp[2],temp[3]);
            }
      
            void getEuler(btScalar& yaw, btScalar& pitch, btScalar& roll) const
            {
                  
                  if (btScalar(m_el[1].z()) < btScalar(1))
                  {
                        if (btScalar(m_el[1].z()) > -btScalar(1))
                        {
                              yaw = btScalar(btAtan2(m_el[1].x(), m_el[0].x()));
                              pitch = btScalar(btAsin(-m_el[1].y()));
                              roll = btScalar(btAtan2(m_el[2].y(), m_el[2].z()));
                        }
                        else 
                        {
                              yaw = btScalar(-btAtan2(-m_el[0].y(), m_el[0].z()));
                              pitch = SIMD_HALF_PI;
                              roll = btScalar(0.0);
                        }
                  }
                  else
                  {
                        yaw = btScalar(btAtan2(-m_el[0].y(), m_el[0].z()));
                        pitch = -SIMD_HALF_PI;
                        roll = btScalar(0.0);
                  }
            }
            

      
            
            btMatrix3x3 scaled(const btVector3& s) const
            {
                  return btMatrix3x3(m_el[0].x() * s.x(), m_el[0].y() * s.y(), m_el[0].z() * s.z(),
                                                       m_el[1].x() * s.x(), m_el[1].y() * s.y(), m_el[1].z() * s.z(),
                                                       m_el[2].x() * s.x(), m_el[2].y() * s.y(), m_el[2].z() * s.z());
            }

            btScalar            determinant() const;
            btMatrix3x3 adjoint() const;
            btMatrix3x3 absolute() const;
            btMatrix3x3 transpose() const;
            btMatrix3x3 inverse() const; 
            
            btMatrix3x3 transposeTimes(const btMatrix3x3& m) const;
            btMatrix3x3 timesTranspose(const btMatrix3x3& m) const;
            
            SIMD_FORCE_INLINE btScalar tdotx(const btVector3& v) const 
            {
                  return m_el[0].x() * v.x() + m_el[1].x() * v.y() + m_el[2].x() * v.z();
            }
            SIMD_FORCE_INLINE btScalar tdoty(const btVector3& v) const 
            {
                  return m_el[0].y() * v.x() + m_el[1].y() * v.y() + m_el[2].y() * v.z();
            }
            SIMD_FORCE_INLINE btScalar tdotz(const btVector3& v) const 
            {
                  return m_el[0].z() * v.x() + m_el[1].z() * v.y() + m_el[2].z() * v.z();
            }
            

            ///diagonalizes this matrix by the Jacobi method. rot stores the rotation
            ///from the coordinate system in which the matrix is diagonal to the original
            ///coordinate system, i.e., old_this = rot * new_this * rot^T. The iteration
            ///stops when all off-diagonal elements are less than the threshold multiplied
            ///by the sum of the absolute values of the diagonal, or when maxSteps have
            ///been executed. Note that this matrix is assumed to be symmetric.
00293             void diagonalize(btMatrix3x3& rot, btScalar threshold, int maxSteps)
            {
             rot.setIdentity();
             for (int step = maxSteps; step > 0; step--)
             {
                  // find off-diagonal element [p][q] with largest magnitude
                  int p = 0;
                  int q = 1;
                  int r = 2;
                  btScalar max = btFabs(m_el[0][1]);
                  btScalar v = btFabs(m_el[0][2]);
                  if (v > max)
                  {
                     q = 2;
                     r = 1;
                     max = v;
                  }
                  v = btFabs(m_el[1][2]);
                  if (v > max)
                  {
                     p = 1;
                     q = 2;
                     r = 0;
                     max = v;
                  }

                  btScalar t = threshold * (btFabs(m_el[0][0]) + btFabs(m_el[1][1]) + btFabs(m_el[2][2]));
                  if (max <= t)
                  {
                     if (max <= SIMD_EPSILON * t)
                     {
                          return;
                     }
                     step = 1;
                  }

                  // compute Jacobi rotation J which leads to a zero for element [p][q] 
                  btScalar mpq = m_el[p][q];
                  btScalar theta = (m_el[q][q] - m_el[p][p]) / (2 * mpq);
                  btScalar theta2 = theta * theta;
                  btScalar cos;
                  btScalar sin;
                  if (theta2 * theta2 < btScalar(10 / SIMD_EPSILON))
                  {
                     t = (theta >= 0) ? 1 / (theta + btSqrt(1 + theta2))
                                                            : 1 / (theta - btSqrt(1 + theta2));
                     cos = 1 / btSqrt(1 + t * t);
                     sin = cos * t;
                  }
                  else
                  {
                     // approximation for large theta-value, i.e., a nearly diagonal matrix
                     t = 1 / (theta * (2 + btScalar(0.5) / theta2));
                     cos = 1 - btScalar(0.5) * t * t;
                     sin = cos * t;
                  }

                  // apply rotation to matrix (this = J^T * this * J)
                  m_el[p][q] = m_el[q][p] = 0;
                  m_el[p][p] -= t * mpq;
                  m_el[q][q] += t * mpq;
                  btScalar mrp = m_el[r][p];
                  btScalar mrq = m_el[r][q];
                  m_el[r][p] = m_el[p][r] = cos * mrp - sin * mrq;
                  m_el[r][q] = m_el[q][r] = cos * mrq + sin * mrp;

                  // apply rotation to rot (rot = rot * J)
                  for (int i = 0; i < 3; i++)
                  {
                     btVector3& row = rot[i];
                     mrp = row[p];
                     mrq = row[q];
                     row[p] = cos * mrp - sin * mrq;
                     row[q] = cos * mrq + sin * mrp;
                  }
             }
            }


            
      protected:
            btScalar cofac(int r1, int c1, int r2, int c2) const 
            {
                  return m_el[r1][c1] * m_el[r2][c2] - m_el[r1][c2] * m_el[r2][c1];
            }

            btVector3 m_el[3];
      };
      
      SIMD_FORCE_INLINE btMatrix3x3& 
      btMatrix3x3::operator*=(const btMatrix3x3& m)
      {
            setValue(m.tdotx(m_el[0]), m.tdoty(m_el[0]), m.tdotz(m_el[0]),
                         m.tdotx(m_el[1]), m.tdoty(m_el[1]), m.tdotz(m_el[1]),
                         m.tdotx(m_el[2]), m.tdoty(m_el[2]), m.tdotz(m_el[2]));
            return *this;
      }
      
      SIMD_FORCE_INLINE btScalar 
      btMatrix3x3::determinant() const
      { 
            return triple((*this)[0], (*this)[1], (*this)[2]);
      }
      

      SIMD_FORCE_INLINE btMatrix3x3 
      btMatrix3x3::absolute() const
      {
            return btMatrix3x3(
                  btFabs(m_el[0].x()), btFabs(m_el[0].y()), btFabs(m_el[0].z()),
                  btFabs(m_el[1].x()), btFabs(m_el[1].y()), btFabs(m_el[1].z()),
                  btFabs(m_el[2].x()), btFabs(m_el[2].y()), btFabs(m_el[2].z()));
      }

      SIMD_FORCE_INLINE btMatrix3x3 
      btMatrix3x3::transpose() const 
      {
            return btMatrix3x3(m_el[0].x(), m_el[1].x(), m_el[2].x(),
                                                 m_el[0].y(), m_el[1].y(), m_el[2].y(),
                                                 m_el[0].z(), m_el[1].z(), m_el[2].z());
      }
      
      SIMD_FORCE_INLINE btMatrix3x3 
      btMatrix3x3::adjoint() const 
      {
            return btMatrix3x3(cofac(1, 1, 2, 2), cofac(0, 2, 2, 1), cofac(0, 1, 1, 2),
                                                 cofac(1, 2, 2, 0), cofac(0, 0, 2, 2), cofac(0, 2, 1, 0),
                                                 cofac(1, 0, 2, 1), cofac(0, 1, 2, 0), cofac(0, 0, 1, 1));
      }
      
      SIMD_FORCE_INLINE btMatrix3x3 
      btMatrix3x3::inverse() const
      {
            btVector3 co(cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1));
            btScalar det = (*this)[0].dot(co);
            btFullAssert(det != btScalar(0.0));
            btScalar s = btScalar(1.0) / det;
            return btMatrix3x3(co.x() * s, cofac(0, 2, 2, 1) * s, cofac(0, 1, 1, 2) * s,
                                                 co.y() * s, cofac(0, 0, 2, 2) * s, cofac(0, 2, 1, 0) * s,
                                                 co.z() * s, cofac(0, 1, 2, 0) * s, cofac(0, 0, 1, 1) * s);
      }
      
      SIMD_FORCE_INLINE btMatrix3x3 
      btMatrix3x3::transposeTimes(const btMatrix3x3& m) const
      {
            return btMatrix3x3(
                  m_el[0].x() * m[0].x() + m_el[1].x() * m[1].x() + m_el[2].x() * m[2].x(),
                  m_el[0].x() * m[0].y() + m_el[1].x() * m[1].y() + m_el[2].x() * m[2].y(),
                  m_el[0].x() * m[0].z() + m_el[1].x() * m[1].z() + m_el[2].x() * m[2].z(),
                  m_el[0].y() * m[0].x() + m_el[1].y() * m[1].x() + m_el[2].y() * m[2].x(),
                  m_el[0].y() * m[0].y() + m_el[1].y() * m[1].y() + m_el[2].y() * m[2].y(),
                  m_el[0].y() * m[0].z() + m_el[1].y() * m[1].z() + m_el[2].y() * m[2].z(),
                  m_el[0].z() * m[0].x() + m_el[1].z() * m[1].x() + m_el[2].z() * m[2].x(),
                  m_el[0].z() * m[0].y() + m_el[1].z() * m[1].y() + m_el[2].z() * m[2].y(),
                  m_el[0].z() * m[0].z() + m_el[1].z() * m[1].z() + m_el[2].z() * m[2].z());
      }
      
      SIMD_FORCE_INLINE btMatrix3x3 
      btMatrix3x3::timesTranspose(const btMatrix3x3& m) const
      {
            return btMatrix3x3(
                  m_el[0].dot(m[0]), m_el[0].dot(m[1]), m_el[0].dot(m[2]),
                  m_el[1].dot(m[0]), m_el[1].dot(m[1]), m_el[1].dot(m[2]),
                  m_el[2].dot(m[0]), m_el[2].dot(m[1]), m_el[2].dot(m[2]));
            
      }

      SIMD_FORCE_INLINE btVector3 
      operator*(const btMatrix3x3& m, const btVector3& v) 
      {
            return btVector3(m[0].dot(v), m[1].dot(v), m[2].dot(v));
      }
      

      SIMD_FORCE_INLINE btVector3
      operator*(const btVector3& v, const btMatrix3x3& m)
      {
            return btVector3(m.tdotx(v), m.tdoty(v), m.tdotz(v));
      }

      SIMD_FORCE_INLINE btMatrix3x3 
      operator*(const btMatrix3x3& m1, const btMatrix3x3& m2)
      {
            return btMatrix3x3(
                  m2.tdotx( m1[0]), m2.tdoty( m1[0]), m2.tdotz( m1[0]),
                  m2.tdotx( m1[1]), m2.tdoty( m1[1]), m2.tdotz( m1[1]),
                  m2.tdotx( m1[2]), m2.tdoty( m1[2]), m2.tdotz( m1[2]));
      }

/*
      SIMD_FORCE_INLINE btMatrix3x3 btMultTransposeLeft(const btMatrix3x3& m1, const btMatrix3x3& m2) {
    return btMatrix3x3(
        m1[0][0] * m2[0][0] + m1[1][0] * m2[1][0] + m1[2][0] * m2[2][0],
        m1[0][0] * m2[0][1] + m1[1][0] * m2[1][1] + m1[2][0] * m2[2][1],
        m1[0][0] * m2[0][2] + m1[1][0] * m2[1][2] + m1[2][0] * m2[2][2],
        m1[0][1] * m2[0][0] + m1[1][1] * m2[1][0] + m1[2][1] * m2[2][0],
        m1[0][1] * m2[0][1] + m1[1][1] * m2[1][1] + m1[2][1] * m2[2][1],
        m1[0][1] * m2[0][2] + m1[1][1] * m2[1][2] + m1[2][1] * m2[2][2],
        m1[0][2] * m2[0][0] + m1[1][2] * m2[1][0] + m1[2][2] * m2[2][0],
        m1[0][2] * m2[0][1] + m1[1][2] * m2[1][1] + m1[2][2] * m2[2][1],
        m1[0][2] * m2[0][2] + m1[1][2] * m2[1][2] + m1[2][2] * m2[2][2]);
}
*/

SIMD_FORCE_INLINE bool operator==(const btMatrix3x3& m1, const btMatrix3x3& m2)
{
   return ( m1[0][0] == m2[0][0] && m1[1][0] == m2[1][0] && m1[2][0] == m2[2][0] &&
            m1[0][1] == m2[0][1] && m1[1][1] == m2[1][1] && m1[2][1] == m2[2][1] &&
            m1[0][2] == m2[0][2] && m1[1][2] == m2[1][2] && m1[2][2] == m2[2][2] );
}

#endif

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