include/cinder/Matrix.h
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00001 /*
00002  Copyright (c) 2011, The Cinder Project: http://libcinder.org All rights reserved.
00003  This code is intended for use with the Cinder C++ library: http://libcinder.org
00004 
00005  Redistribution and use in source and binary forms, with or without modification, are permitted provided that
00006  the following conditions are met:
00007 
00008     * Redistributions of source code must retain the above copyright notice, this list of conditions and
00009     the following disclaimer.
00010     * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and
00011     the following disclaimer in the documentation and/or other materials provided with the distribution.
00012 
00013  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED
00014  WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
00015  PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
00016  ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
00017  TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
00018  HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
00019  NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
00020  POSSIBILITY OF SUCH DAMAGE.
00021 */
00022 
00023 
00024 #pragma once
00025 
00026 #include "cinder/Cinder.h"
00027 #include "cinder/CinderMath.h"
00028 #include "cinder/Matrix22.h"
00029 #include "cinder/MatrixAffine2.h"
00030 #include "cinder/Matrix33.h"
00031 #include "cinder/Matrix44.h"
00032 #include "cinder/MatrixAlgo.h"
00033 
00034 namespace cinder { 
00035 
00037 // Parallel Transport Frames
00038 //
00039 //  These methods compute a set of reference frames, defined by their
00040 //  transformation matrix, along a curve. It is designed so that the 
00041 //  array of points and the array of matrices used to fetch these routines 
00042 //  don't need to be ordered as the curve.
00043 //  
00044 //  A typical usage would be :
00045 //
00046 //      m[0] = Imath::firstFrame( p[0], p[1], p[2] );
00047 //      for( int i = 1; i < n - 1; i++ )
00048 //      {
00049 //          m[i] = Imath::nextFrame( m[i-1], p[i-1], p[i], t[i-1], t[i] );
00050 //      }
00051 //      m[n-1] = Imath::lastFrame( m[n-2], p[n-2], p[n-1] );
00052 //
00053 //  See Graphics Gems I for the underlying algorithm.
00054 //  These are also called Parallel Transport Frames
00055 //    see Game Programming Gems 2, Section 2.5
00056 
00057 // Vec3
00058 template< typename T >
00059 Matrix44<T> firstFrame( 
00060     const Vec3<T> &firstPoint,
00061     const Vec3<T> &secondPoint, 
00062     const Vec3<T> &thirdPoint
00063 );
00064 
00065 template< typename T >
00066 Matrix44<T> nextFrame( 
00067     const Matrix44<T> &prevMatrix, 
00068     const Vec3<T> &prevPoint,
00069     const Vec3<T> &curPoint,
00070     Vec3<T> &prevTangent, 
00071     Vec3<T> &curTangent 
00072 );
00073             
00074 template< typename T >
00075 Matrix44<T> lastFrame( 
00076     const Matrix44<T> &prevMatrix, 
00077     const Vec3<T> &prevPoint, 
00078     const Vec3<T> &lastPoint 
00079 );
00080 
00081 // Vec4
00082 template< typename T >
00083 Matrix44<T> firstFrame( 
00084     const Vec4<T> &firstPoint,
00085     const Vec4<T> &secondPoint, 
00086     const Vec4<T> &thirdPoint
00087 )
00088 {
00089     return firstFrame( firstPoint.xyz(), secondPoint.xyz(), thirdPoint.xyz() );
00090 }
00091 
00092 template< typename T >
00093 Matrix44<T> nextFrame( 
00094     const Matrix44<T> &prevMatrix, 
00095     const Vec4<T> &prevPoint,
00096     const Vec4<T> &curPoint,
00097     Vec4<T> &prevTangent, 
00098     Vec4<T> &curTangent 
00099 )
00100 {
00101     Vec3<T> aPrevTangent = prevTangent.xyz();
00102     Vec3<T> aCurTangent = curTangent.xyz();
00103     return nextFrame( prevMatrix, prevPoint.xyz(), curPoint.xyz(), aPrevTangent, aCurTangent );
00104 }
00105             
00106 template< typename T >
00107 Matrix44<T> lastFrame( 
00108     const Matrix44<T> &prevMatrix, 
00109     const Vec4<T> &prevPoint, 
00110     const Vec4<T> &lastPoint 
00111 )
00112 {
00113     return lastFrame( prevMatrix, prevPoint.xyz(), lastPoint.xyz() );
00114 }
00115 
00116 } // namespace cinder