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