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ImathFrame.h
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/////////////////////////////////////////////////////////////////////////// // // Copyright (c) 2002-2012, 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 #include "ImathNamespace.h" IMATH_INTERNAL_NAMESPACE_HEADER_ENTER 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_INTERNAL_NAMESPACE::firstFrame( p[0], p[1], p[2] ); // for( int i = 1; i < n - 1; i++ ) // { // m[i] = IMATH_INTERNAL_NAMESPACE::nextFrame( m[i-1], p[i-1], p[i], t[i-1], t[i] ); // } // m[n-1] = IMATH_INTERNAL_NAMESPACE::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; } IMATH_INTERNAL_NAMESPACE_HEADER_EXIT #endif // INCLUDED_IMATHFRAME_H