--- /dev/null
+///////////////////////////////////////////////////////////////////////////
+//
+// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
+// Digital Ltd. LLC
+//
+// All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+// * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+// * Neither the name of Industrial Light & Magic nor the names of
+// its contributors may be used to endorse or promote products derived
+// from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
+///////////////////////////////////////////////////////////////////////////
+
+
+
+#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
projects / opencv / blobdiff