Blame Imath/ImathFrame.h

Packit 8dc392
///////////////////////////////////////////////////////////////////////////
Packit 8dc392
//
Packit 8dc392
// Copyright (c) 2002-2012, Industrial Light & Magic, a division of Lucas
Packit 8dc392
// Digital Ltd. LLC
Packit 8dc392
// 
Packit 8dc392
// All rights reserved.
Packit 8dc392
// 
Packit 8dc392
// Redistribution and use in source and binary forms, with or without
Packit 8dc392
// modification, are permitted provided that the following conditions are
Packit 8dc392
// met:
Packit 8dc392
// *       Redistributions of source code must retain the above copyright
Packit 8dc392
// notice, this list of conditions and the following disclaimer.
Packit 8dc392
// *       Redistributions in binary form must reproduce the above
Packit 8dc392
// copyright notice, this list of conditions and the following disclaimer
Packit 8dc392
// in the documentation and/or other materials provided with the
Packit 8dc392
// distribution.
Packit 8dc392
// *       Neither the name of Industrial Light & Magic nor the names of
Packit 8dc392
// its contributors may be used to endorse or promote products derived
Packit 8dc392
// from this software without specific prior written permission. 
Packit 8dc392
// 
Packit 8dc392
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
Packit 8dc392
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
Packit 8dc392
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
Packit 8dc392
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
Packit 8dc392
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
Packit 8dc392
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
Packit 8dc392
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
Packit 8dc392
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
Packit 8dc392
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
Packit 8dc392
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
Packit 8dc392
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
Packit 8dc392
//
Packit 8dc392
///////////////////////////////////////////////////////////////////////////
Packit 8dc392
Packit 8dc392
Packit 8dc392
Packit 8dc392
#ifndef INCLUDED_IMATHFRAME_H
Packit 8dc392
#define INCLUDED_IMATHFRAME_H
Packit 8dc392
Packit 8dc392
#include "ImathNamespace.h"
Packit 8dc392
Packit 8dc392
IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
Packit 8dc392
Packit 8dc392
template<class T> class Vec3;
Packit 8dc392
template<class T> class Matrix44;
Packit 8dc392
Packit 8dc392
//
Packit 8dc392
//  These methods compute a set of reference frames, defined by their
Packit 8dc392
//  transformation matrix, along a curve. It is designed so that the 
Packit 8dc392
//  array of points and the array of matrices used to fetch these routines 
Packit 8dc392
//  don't need to be ordered as the curve.
Packit 8dc392
//  
Packit 8dc392
//  A typical usage would be :
Packit 8dc392
//
Packit 8dc392
//      m[0] = IMATH_INTERNAL_NAMESPACE::firstFrame( p[0], p[1], p[2] );
Packit 8dc392
//      for( int i = 1; i < n - 1; i++ )
Packit 8dc392
//      {
Packit 8dc392
//          m[i] = IMATH_INTERNAL_NAMESPACE::nextFrame( m[i-1], p[i-1], p[i], t[i-1], t[i] );
Packit 8dc392
//      }
Packit 8dc392
//      m[n-1] = IMATH_INTERNAL_NAMESPACE::lastFrame( m[n-2], p[n-2], p[n-1] );
Packit 8dc392
//
Packit 8dc392
//  See Graphics Gems I for the underlying algorithm.
Packit 8dc392
// 
Packit 8dc392
Packit 8dc392
template<class T> Matrix44<T> firstFrame( const Vec3<T>&,    // First point
Packit 8dc392
                                          const Vec3<T>&,    // Second point 
Packit 8dc392
                                          const Vec3<T>& );  // Third point
Packit 8dc392
Packit 8dc392
template<class T> Matrix44<T> nextFrame( const Matrix44<T>&, // Previous matrix
Packit 8dc392
                                         const Vec3<T>&,     // Previous point
Packit 8dc392
                                         const Vec3<T>&,     // Current point
Packit 8dc392
                                         Vec3<T>&,           // Previous tangent
Packit 8dc392
                                         Vec3<T>& );         // Current tangent
Packit 8dc392
Packit 8dc392
template<class T> Matrix44<T> lastFrame( const Matrix44<T>&, // Previous matrix
Packit 8dc392
                                         const Vec3<T>&,     // Previous point
Packit 8dc392
                                         const Vec3<T>& );   // Last point
Packit 8dc392
Packit 8dc392
//
Packit 8dc392
//  firstFrame - Compute the first reference frame along a curve.
Packit 8dc392
//
Packit 8dc392
//  This function returns the transformation matrix to the reference frame
Packit 8dc392
//  defined by the three points 'pi', 'pj' and 'pk'. Note that if the two
Packit 8dc392
//  vectors <pi,pj> and <pi,pk> are colinears, an arbitrary twist value will
Packit 8dc392
//  be choosen.
Packit 8dc392
//
Packit 8dc392
//  Throw 'NullVecExc' if 'pi' and 'pj' are equals.
Packit 8dc392
//
Packit 8dc392
Packit 8dc392
template<class T> Matrix44<T> firstFrame
Packit 8dc392
( 
Packit 8dc392
    const Vec3<T>& pi,             // First point
Packit 8dc392
    const Vec3<T>& pj,             // Second point
Packit 8dc392
    const Vec3<T>& pk )            // Third point
Packit 8dc392
{
Packit 8dc392
    Vec3<T> t = pj - pi; t.normalizeExc();
Packit 8dc392
Packit 8dc392
    Vec3<T> n = t.cross( pk - pi ); n.normalize();
Packit 8dc392
    if( n.length() == 0.0f )
Packit 8dc392
    {
Packit 8dc392
        int i = fabs( t[0] ) < fabs( t[1] ) ? 0 : 1;
Packit 8dc392
        if( fabs( t[2] ) < fabs( t[i] )) i = 2;
Packit 8dc392
Packit 8dc392
        Vec3<T> v( 0.0, 0.0, 0.0 ); v[i] = 1.0;
Packit 8dc392
        n = t.cross( v ); n.normalize();
Packit 8dc392
    }
Packit 8dc392
Packit 8dc392
    Vec3<T> b = t.cross( n );
Packit 8dc392
Packit 8dc392
    Matrix44<T> M;
Packit 8dc392
Packit 8dc392
    M[0][0] =  t[0]; M[0][1] =  t[1]; M[0][2] =  t[2]; M[0][3] = 0.0,
Packit 8dc392
    M[1][0] =  n[0]; M[1][1] =  n[1]; M[1][2] =  n[2]; M[1][3] = 0.0,
Packit 8dc392
    M[2][0] =  b[0]; M[2][1] =  b[1]; M[2][2] =  b[2]; M[2][3] = 0.0,
Packit 8dc392
    M[3][0] = pi[0]; M[3][1] = pi[1]; M[3][2] = pi[2]; M[3][3] = 1.0;
Packit 8dc392
Packit 8dc392
    return M;
Packit 8dc392
}
Packit 8dc392
Packit 8dc392
//
Packit 8dc392
//  nextFrame - Compute the next reference frame along a curve.
Packit 8dc392
//
Packit 8dc392
//  This function returns the transformation matrix to the next reference 
Packit 8dc392
//  frame defined by the previously computed transformation matrix and the
Packit 8dc392
//  new point and tangent vector along the curve.
Packit 8dc392
//
Packit 8dc392
Packit 8dc392
template<class T> Matrix44<T> nextFrame
Packit 8dc392
( 
Packit 8dc392
    const Matrix44<T>&  Mi,             // Previous matrix
Packit 8dc392
    const Vec3<T>&      pi,             // Previous point
Packit 8dc392
    const Vec3<T>&      pj,             // Current point
Packit 8dc392
    Vec3<T>&            ti,             // Previous tangent vector
Packit 8dc392
    Vec3<T>&            tj )            // Current tangent vector
Packit 8dc392
{
Packit 8dc392
    Vec3<T> a(0.0, 0.0, 0.0);		// Rotation axis.
Packit 8dc392
    T r = 0.0;				// Rotation angle.
Packit 8dc392
Packit 8dc392
    if( ti.length() != 0.0 && tj.length() != 0.0 )
Packit 8dc392
    {
Packit 8dc392
        ti.normalize(); tj.normalize();
Packit 8dc392
        T dot = ti.dot( tj ); 
Packit 8dc392
Packit 8dc392
        //
Packit 8dc392
        //  This is *really* necessary :
Packit 8dc392
        //
Packit 8dc392
Packit 8dc392
        if( dot > 1.0 ) dot = 1.0; 
Packit 8dc392
        else if( dot < -1.0 ) dot = -1.0;
Packit 8dc392
Packit 8dc392
        r = acosf( dot );
Packit 8dc392
        a = ti.cross( tj );
Packit 8dc392
    }
Packit 8dc392
Packit 8dc392
    if( a.length() != 0.0 && r != 0.0 )
Packit 8dc392
    {
Packit 8dc392
        Matrix44<T> R; R.setAxisAngle( a, r );
Packit 8dc392
        Matrix44<T> Tj; Tj.translate(  pj );
Packit 8dc392
        Matrix44<T> Ti; Ti.translate( -pi );
Packit 8dc392
Packit 8dc392
        return Mi * Ti * R * Tj;
Packit 8dc392
    }
Packit 8dc392
    else
Packit 8dc392
    {
Packit 8dc392
        Matrix44<T> Tr; Tr.translate( pj - pi );
Packit 8dc392
Packit 8dc392
        return Mi * Tr;
Packit 8dc392
    }
Packit 8dc392
}
Packit 8dc392
Packit 8dc392
//
Packit 8dc392
//  lastFrame - Compute the last reference frame along a curve.
Packit 8dc392
//
Packit 8dc392
//  This function returns the transformation matrix to the last reference 
Packit 8dc392
//  frame defined by the previously computed transformation matrix and the
Packit 8dc392
//  last point along the curve.
Packit 8dc392
//
Packit 8dc392
Packit 8dc392
template<class T> Matrix44<T> lastFrame
Packit 8dc392
( 
Packit 8dc392
    const Matrix44<T>&  Mi,             // Previous matrix
Packit 8dc392
    const Vec3<T>&      pi,             // Previous point
Packit 8dc392
    const Vec3<T>&      pj )            // Last point
Packit 8dc392
{
Packit 8dc392
    Matrix44<T> Tr; Tr.translate( pj - pi );
Packit 8dc392
Packit 8dc392
    return Mi * Tr;
Packit 8dc392
}
Packit 8dc392
Packit 8dc392
IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
Packit 8dc392
Packit 8dc392
#endif // INCLUDED_IMATHFRAME_H