source: NonGTP/OpenEXR/include/Imath/ImathFrame.h @ 855

Revision 855, 6.5 KB checked in by igarcia, 19 years ago (diff)
Line 
1///////////////////////////////////////////////////////////////////////////
2//
3// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
4// Digital Ltd. LLC
5//
6// All rights reserved.
7//
8// Redistribution and use in source and binary forms, with or without
9// modification, are permitted provided that the following conditions are
10// met:
11// *       Redistributions of source code must retain the above copyright
12// notice, this list of conditions and the following disclaimer.
13// *       Redistributions in binary form must reproduce the above
14// copyright notice, this list of conditions and the following disclaimer
15// in the documentation and/or other materials provided with the
16// distribution.
17// *       Neither the name of Industrial Light & Magic nor the names of
18// its contributors may be used to endorse or promote products derived
19// from this software without specific prior written permission.
20//
21// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
22// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
23// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
24// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
25// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
26// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
27// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
28// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
29// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
30// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
31// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
32//
33///////////////////////////////////////////////////////////////////////////
34
35
36
37#ifndef INCLUDED_IMATHFRAME_H
38#define INCLUDED_IMATHFRAME_H
39
40namespace Imath {
41
42template<class T> class Vec3;
43template<class T> class Matrix44;
44
45//
46//  These methods compute a set of reference frames, defined by their
47//  transformation matrix, along a curve. It is designed so that the
48//  array of points and the array of matrices used to fetch these routines
49//  don't need to be ordered as the curve.
50// 
51//  A typical usage would be :
52//
53//      m[0] = Imath::firstFrame( p[0], p[1], p[2] );
54//      for( int i = 1; i < n - 1; i++ )
55//      {
56//          m[i] = Imath::nextFrame( m[i-1], p[i-1], p[i], t[i-1], t[i] );
57//      }
58//      m[n-1] = Imath::lastFrame( m[n-2], p[n-2], p[n-1] );
59//
60//  See Graphics Gems I for the underlying algorithm.
61//
62
63template<class T> Matrix44<T> firstFrame( const Vec3<T>&,    // First point
64                                          const Vec3<T>&,    // Second point
65                                          const Vec3<T>& );  // Third point
66
67template<class T> Matrix44<T> nextFrame( const Matrix44<T>&, // Previous matrix
68                                         const Vec3<T>&,     // Previous point
69                                         const Vec3<T>&,     // Current point
70                                         Vec3<T>&,           // Previous tangent
71                                         Vec3<T>& );         // Current tangent
72
73template<class T> Matrix44<T> lastFrame( const Matrix44<T>&, // Previous matrix
74                                         const Vec3<T>&,     // Previous point
75                                         const Vec3<T>& );   // Last point
76
77//
78//  firstFrame - Compute the first reference frame along a curve.
79//
80//  This function returns the transformation matrix to the reference frame
81//  defined by the three points 'pi', 'pj' and 'pk'. Note that if the two
82//  vectors <pi,pj> and <pi,pk> are colinears, an arbitrary twist value will
83//  be choosen.
84//
85//  Throw 'NullVecExc' if 'pi' and 'pj' are equals.
86//
87
88template<class T> Matrix44<T> firstFrame
89(
90    const Vec3<T>& pi,             // First point
91    const Vec3<T>& pj,             // Second point
92    const Vec3<T>& pk )            // Third point
93{
94    Vec3<T> t = pj - pi; t.normalizeExc();
95
96    Vec3<T> n = t.cross( pk - pi ); n.normalize();
97    if( n.length() == 0.0f )
98    {
99        int i = fabs( t[0] ) < fabs( t[1] ) ? 0 : 1;
100        if( fabs( t[2] ) < fabs( t[i] )) i = 2;
101
102        Vec3<T> v( 0.0, 0.0, 0.0 ); v[i] = 1.0;
103        n = t.cross( v ); n.normalize();
104    }
105
106    Vec3<T> b = t.cross( n );
107
108    Matrix44<T> M;
109
110    M[0][0] =  t[0]; M[0][1] =  t[1]; M[0][2] =  t[2]; M[0][3] = 0.0,
111    M[1][0] =  n[0]; M[1][1] =  n[1]; M[1][2] =  n[2]; M[1][3] = 0.0,
112    M[2][0] =  b[0]; M[2][1] =  b[1]; M[2][2] =  b[2]; M[2][3] = 0.0,
113    M[3][0] = pi[0]; M[3][1] = pi[1]; M[3][2] = pi[2]; M[3][3] = 1.0;
114
115    return M;
116}
117
118//
119//  nextFrame - Compute the next reference frame along a curve.
120//
121//  This function returns the transformation matrix to the next reference
122//  frame defined by the previously computed transformation matrix and the
123//  new point and tangent vector along the curve.
124//
125
126template<class T> Matrix44<T> nextFrame
127(
128    const Matrix44<T>&  Mi,             // Previous matrix
129    const Vec3<T>&      pi,             // Previous point
130    const Vec3<T>&      pj,             // Current point
131    Vec3<T>&            ti,             // Previous tangent vector
132    Vec3<T>&            tj )            // Current tangent vector
133{
134    Vec3<T> a(0.0, 0.0, 0.0);           // Rotation axis.
135    T r = 0.0;                          // Rotation angle.
136
137    if( ti.length() != 0.0 && tj.length() != 0.0 )
138    {
139        ti.normalize(); tj.normalize();
140        T dot = ti.dot( tj );
141
142        //
143        //  This is *really* necessary :
144        //
145
146        if( dot > 1.0 ) dot = 1.0;
147        else if( dot < -1.0 ) dot = -1.0;
148
149        r = acosf( dot );
150        a = ti.cross( tj );
151    }
152
153    if( a.length() != 0.0 && r != 0.0 )
154    {
155        Matrix44<T> R; R.setAxisAngle( a, r );
156        Matrix44<T> Tj; Tj.translate(  pj );
157        Matrix44<T> Ti; Ti.translate( -pi );
158
159        return Mi * Ti * R * Tj;
160    }
161    else
162    {
163        Matrix44<T> Tr; Tr.translate( pj - pi );
164
165        return Mi * Tr;
166    }
167}
168
169//
170//  lastFrame - Compute the last reference frame along a curve.
171//
172//  This function returns the transformation matrix to the last reference
173//  frame defined by the previously computed transformation matrix and the
174//  last point along the curve.
175//
176
177template<class T> Matrix44<T> lastFrame
178(
179    const Matrix44<T>&  Mi,             // Previous matrix
180    const Vec3<T>&      pi,             // Previous point
181    const Vec3<T>&      pj )            // Last point
182{
183    Matrix44<T> Tr; Tr.translate( pj - pi );
184
185    return Mi * Tr;
186}
187
188} // namespace Imath
189
190#endif
Note: See TracBrowser for help on using the repository browser.