| /////////////////////////////////////////////////////////////////////////// |
| // |
| // 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: |
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| // notice, this list of conditions and the following disclaimer. |
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| // 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 |
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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 |
