///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
//
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///////////////////////////////////////////////////////////////////////////
#ifndef INCLUDED_IMATHFRAME_H
#define INCLUDED_IMATHFRAME_H
namespace Imath {
template<class T> class Vec3;
template<class T> class Matrix44;
//
// These methods compute a set of reference frames, defined by their
// transformation matrix, along a curve. It is designed so that the
// array of points and the array of matrices used to fetch these routines
// don't need to be ordered as the curve.
//
// A typical usage would be :
//
// m[0] = Imath::firstFrame( p[0], p[1], p[2] );
// for( int i = 1; i < n - 1; i++ )
// {
// m[i] = Imath::nextFrame( m[i-1], p[i-1], p[i], t[i-1], t[i] );
// }
// m[n-1] = Imath::lastFrame( m[n-2], p[n-2], p[n-1] );
//
// See Graphics Gems I for the underlying algorithm.
//
template<class T> Matrix44<T> firstFrame( const Vec3<T>&, // First point
const Vec3<T>&, // Second point
const Vec3<T>& ); // Third point
template<class T> Matrix44<T> nextFrame( const Matrix44<T>&, // Previous matrix
const Vec3<T>&, // Previous point
const Vec3<T>&, // Current point
Vec3<T>&, // Previous tangent
Vec3<T>& ); // Current tangent
template<class T> Matrix44<T> lastFrame( const Matrix44<T>&, // Previous matrix
const Vec3<T>&, // Previous point
const Vec3<T>& ); // Last point
//
// firstFrame - Compute the first reference frame along a curve.
//
// This function returns the transformation matrix to the reference frame
// defined by the three points 'pi', 'pj' and 'pk'. Note that if the two
// vectors <pi,pj> and <pi,pk> are colinears, an arbitrary twist value will
// be choosen.
//
// Throw 'NullVecExc' if 'pi' and 'pj' are equals.
//
template<class T> Matrix44<T> firstFrame
(
const Vec3<T>& pi, // First point
const Vec3<T>& pj, // Second point
const Vec3<T>& pk ) // Third point
{
Vec3<T> t = pj - pi; t.normalizeExc();
Vec3<T> n = t.cross( pk - pi ); n.normalize();
if( n.length() == 0.0f )
{
int i = fabs( t[0] ) < fabs( t[1] ) ? 0 : 1;
if( fabs( t[2] ) < fabs( t[i] )) i = 2;
Vec3<T> v( 0.0, 0.0, 0.0 ); v[i] = 1.0;
n = t.cross( v ); n.normalize();
}
Vec3<T> b = t.cross( n );
Matrix44<T> M;
M[0][0] = t[0]; M[0][1] = t[1]; M[0][2] = t[2]; M[0][3] = 0.0,
M[1][0] = n[0]; M[1][1] = n[1]; M[1][2] = n[2]; M[1][3] = 0.0,
M[2][0] = b[0]; M[2][1] = b[1]; M[2][2] = b[2]; M[2][3] = 0.0,
M[3][0] = pi[0]; M[3][1] = pi[1]; M[3][2] = pi[2]; M[3][3] = 1.0;
return M;
}
//
// nextFrame - Compute the next reference frame along a curve.
//
// This function returns the transformation matrix to the next reference
// frame defined by the previously computed transformation matrix and the
// new point and tangent vector along the curve.
//
template<class T> Matrix44<T> nextFrame
(
const Matrix44<T>& Mi, // Previous matrix
const Vec3<T>& pi, // Previous point
const Vec3<T>& pj, // Current point
Vec3<T>& ti, // Previous tangent vector
Vec3<T>& tj ) // Current tangent vector
{
Vec3<T> a(0.0, 0.0, 0.0); // Rotation axis.
T r = 0.0; // Rotation angle.
if( ti.length() != 0.0 && tj.length() != 0.0 )
{
ti.normalize(); tj.normalize();
T dot = ti.dot( tj );
//
// This is *really* necessary :
//
if( dot > 1.0 ) dot = 1.0;
else if( dot < -1.0 ) dot = -1.0;
r = acosf( dot );
a = ti.cross( tj );
}
if( a.length() != 0.0 && r != 0.0 )
{
Matrix44<T> R; R.setAxisAngle( a, r );
Matrix44<T> Tj; Tj.translate( pj );
Matrix44<T> Ti; Ti.translate( -pi );
return Mi * Ti * R * Tj;
}
else
{
Matrix44<T> Tr; Tr.translate( pj - pi );
return Mi * Tr;
}
}
//
// lastFrame - Compute the last reference frame along a curve.
//
// This function returns the transformation matrix to the last reference
// frame defined by the previously computed transformation matrix and the
// last point along the curve.
//
template<class T> Matrix44<T> lastFrame
(
const Matrix44<T>& Mi, // Previous matrix
const Vec3<T>& pi, // Previous point
const Vec3<T>& pj ) // Last point
{
Matrix44<T> Tr; Tr.translate( pj - pi );
return Mi * Tr;
}
} // namespace Imath
#endif