1 // Copyright (C) 2006 Mathias Froehlich - Mathias.Froehlich@web.de
3 // This library is free software; you can redistribute it and/or
4 // modify it under the terms of the GNU Library General Public
5 // License as published by the Free Software Foundation; either
6 // version 2 of the License, or (at your option) any later version.
8 // This library is distributed in the hope that it will be useful,
9 // but WITHOUT ANY WARRANTY; without even the implied warranty of
10 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
11 // Library General Public License for more details.
13 // You should have received a copy of the GNU General Public License
14 // along with this program; if not, write to the Free Software
15 // Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
25 struct SGVec3Storage {
26 /// Readonly raw storage interface
27 const T (&data(void) const)[3]
29 /// Readonly raw storage interface
41 struct SGVec3Storage<float> : public osg::Vec3f {
42 /// Access raw data by index, the index is unchecked
43 const float (&data(void) const)[3]
44 { return osg::Vec3f::_v; }
45 /// Access raw data by index, the index is unchecked
46 float (&data(void))[3]
47 { return osg::Vec3f::_v; }
49 const osg::Vec3f& osg() const
56 struct SGVec3Storage<double> : public osg::Vec3d {
57 /// Access raw data by index, the index is unchecked
58 const double (&data(void) const)[3]
59 { return osg::Vec3d::_v; }
60 /// Access raw data by index, the index is unchecked
61 double (&data(void))[3]
62 { return osg::Vec3d::_v; }
64 const osg::Vec3d& osg() const
72 class SGVec3 : protected SGVec3Storage<T> {
76 /// Default constructor. Does not initialize at all.
77 /// If you need them zero initialized, use SGVec3::zeros()
80 /// Initialize with nans in the debug build, that will guarantee to have
81 /// a fast uninitialized default constructor in the release but shows up
82 /// uninitialized values in the debug build very fast ...
84 for (unsigned i = 0; i < 3; ++i)
85 data()[i] = SGLimits<T>::quiet_NaN();
88 /// Constructor. Initialize by the given values
90 { data()[0] = x; data()[1] = y; data()[2] = z; }
91 /// Constructor. Initialize by the content of a plain array,
92 /// make sure it has at least 3 elements
93 explicit SGVec3(const T* d)
94 { data()[0] = d[0]; data()[1] = d[1]; data()[2] = d[2]; }
95 explicit SGVec3(const osg::Vec3f& d)
96 { data()[0] = d[0]; data()[1] = d[1]; data()[2] = d[2]; }
97 explicit SGVec3(const osg::Vec3d& d)
98 { data()[0] = d[0]; data()[1] = d[1]; data()[2] = d[2]; }
99 explicit SGVec3(const SGVec2<T>& v2, const T& v3 = 0)
100 { data()[0] = v2[0]; data()[1] = v2[1]; data()[2] = v3; }
102 /// Access by index, the index is unchecked
103 const T& operator()(unsigned i) const
104 { return data()[i]; }
105 /// Access by index, the index is unchecked
106 T& operator()(unsigned i)
107 { return data()[i]; }
109 /// Access raw data by index, the index is unchecked
110 const T& operator[](unsigned i) const
111 { return data()[i]; }
112 /// Access raw data by index, the index is unchecked
113 T& operator[](unsigned i)
114 { return data()[i]; }
116 /// Access the x component
117 const T& x(void) const
118 { return data()[0]; }
119 /// Access the x component
121 { return data()[0]; }
122 /// Access the y component
123 const T& y(void) const
124 { return data()[1]; }
125 /// Access the y component
127 { return data()[1]; }
128 /// Access the z component
129 const T& z(void) const
130 { return data()[2]; }
131 /// Access the z component
133 { return data()[2]; }
135 /// Get the data pointer
136 using SGVec3Storage<T>::data;
138 /// Readonly interface function to ssg's sgVec3/sgdVec3
139 const T (&sg(void) const)[3]
141 /// Interface function to ssg's sgVec3/sgdVec3
145 /// Interface function to osg's Vec3*
146 using SGVec3Storage<T>::osg;
149 SGVec3& operator+=(const SGVec3& v)
150 { data()[0] += v(0); data()[1] += v(1); data()[2] += v(2); return *this; }
151 /// Inplace subtraction
152 SGVec3& operator-=(const SGVec3& v)
153 { data()[0] -= v(0); data()[1] -= v(1); data()[2] -= v(2); return *this; }
154 /// Inplace scalar multiplication
156 SGVec3& operator*=(S s)
157 { data()[0] *= s; data()[1] *= s; data()[2] *= s; return *this; }
158 /// Inplace scalar multiplication by 1/s
160 SGVec3& operator/=(S s)
161 { return operator*=(1/T(s)); }
163 /// Return an all zero vector
164 static SGVec3 zeros(void)
165 { return SGVec3(0, 0, 0); }
166 /// Return unit vectors
167 static SGVec3 e1(void)
168 { return SGVec3(1, 0, 0); }
169 static SGVec3 e2(void)
170 { return SGVec3(0, 1, 0); }
171 static SGVec3 e3(void)
172 { return SGVec3(0, 0, 1); }
174 /// Constructor. Initialize by a geodetic coordinate
175 /// Note that this conversion is relatively expensive to compute
176 static SGVec3 fromGeod(const SGGeod& geod);
177 /// Constructor. Initialize by a geocentric coordinate
178 /// Note that this conversion is relatively expensive to compute
179 static SGVec3 fromGeoc(const SGGeoc& geoc);
185 SGVec3<double>::fromGeod(const SGGeod& geod)
188 SGGeodesy::SGGeodToCart(geod, cart);
195 SGVec3<float>::fromGeod(const SGGeod& geod)
198 SGGeodesy::SGGeodToCart(geod, cart);
199 return SGVec3<float>(cart(0), cart(1), cart(2));
205 SGVec3<double>::fromGeoc(const SGGeoc& geoc)
208 SGGeodesy::SGGeocToCart(geoc, cart);
215 SGVec3<float>::fromGeoc(const SGGeoc& geoc)
218 SGGeodesy::SGGeocToCart(geoc, cart);
219 return SGVec3<float>(cart(0), cart(1), cart(2));
222 /// Unary +, do nothing ...
226 operator+(const SGVec3<T>& v)
229 /// Unary -, do nearly nothing
233 operator-(const SGVec3<T>& v)
234 { return SGVec3<T>(-v(0), -v(1), -v(2)); }
240 operator+(const SGVec3<T>& v1, const SGVec3<T>& v2)
241 { return SGVec3<T>(v1(0)+v2(0), v1(1)+v2(1), v1(2)+v2(2)); }
247 operator-(const SGVec3<T>& v1, const SGVec3<T>& v2)
248 { return SGVec3<T>(v1(0)-v2(0), v1(1)-v2(1), v1(2)-v2(2)); }
250 /// Scalar multiplication
251 template<typename S, typename T>
254 operator*(S s, const SGVec3<T>& v)
255 { return SGVec3<T>(s*v(0), s*v(1), s*v(2)); }
257 /// Scalar multiplication
258 template<typename S, typename T>
261 operator*(const SGVec3<T>& v, S s)
262 { return SGVec3<T>(s*v(0), s*v(1), s*v(2)); }
264 /// multiplication as a multiplicator, that is assume that the first vector
265 /// represents a 3x3 diagonal matrix with the diagonal elements in the vector.
266 /// Then the result is the product of that matrix times the second vector.
270 mult(const SGVec3<T>& v1, const SGVec3<T>& v2)
271 { return SGVec3<T>(v1(0)*v2(0), v1(1)*v2(1), v1(2)*v2(2)); }
273 /// component wise min
277 min(const SGVec3<T>& v1, const SGVec3<T>& v2)
279 return SGVec3<T>(SGMisc<T>::min(v1(0), v2(0)),
280 SGMisc<T>::min(v1(1), v2(1)),
281 SGMisc<T>::min(v1(2), v2(2)));
283 template<typename S, typename T>
286 min(const SGVec3<T>& v, S s)
288 return SGVec3<T>(SGMisc<T>::min(s, v(0)),
289 SGMisc<T>::min(s, v(1)),
290 SGMisc<T>::min(s, v(2)));
292 template<typename S, typename T>
295 min(S s, const SGVec3<T>& v)
297 return SGVec3<T>(SGMisc<T>::min(s, v(0)),
298 SGMisc<T>::min(s, v(1)),
299 SGMisc<T>::min(s, v(2)));
302 /// component wise max
306 max(const SGVec3<T>& v1, const SGVec3<T>& v2)
308 return SGVec3<T>(SGMisc<T>::max(v1(0), v2(0)),
309 SGMisc<T>::max(v1(1), v2(1)),
310 SGMisc<T>::max(v1(2), v2(2)));
312 template<typename S, typename T>
315 max(const SGVec3<T>& v, S s)
317 return SGVec3<T>(SGMisc<T>::max(s, v(0)),
318 SGMisc<T>::max(s, v(1)),
319 SGMisc<T>::max(s, v(2)));
321 template<typename S, typename T>
324 max(S s, const SGVec3<T>& v)
326 return SGVec3<T>(SGMisc<T>::max(s, v(0)),
327 SGMisc<T>::max(s, v(1)),
328 SGMisc<T>::max(s, v(2)));
331 /// Scalar dot product
335 dot(const SGVec3<T>& v1, const SGVec3<T>& v2)
336 { return v1(0)*v2(0) + v1(1)*v2(1) + v1(2)*v2(2); }
338 /// The euclidean norm of the vector, that is what most people call length
342 norm(const SGVec3<T>& v)
343 { return sqrt(dot(v, v)); }
345 /// The euclidean norm of the vector, that is what most people call length
349 length(const SGVec3<T>& v)
350 { return sqrt(dot(v, v)); }
352 /// The 1-norm of the vector, this one is the fastest length function we
353 /// can implement on modern cpu's
357 norm1(const SGVec3<T>& v)
358 { return fabs(v(0)) + fabs(v(1)) + fabs(v(2)); }
360 /// The inf-norm of the vector
364 normI(const SGVec3<T>& v)
365 { return SGMisc<T>::max(fabs(v(0)), fabs(v(1)), fabs(v(2))); }
367 /// Vector cross product
371 cross(const SGVec3<T>& v1, const SGVec3<T>& v2)
373 return SGVec3<T>(v1(1)*v2(2) - v1(2)*v2(1),
374 v1(2)*v2(0) - v1(0)*v2(2),
375 v1(0)*v2(1) - v1(1)*v2(0));
378 /// return any normalized vector perpendicular to v
382 perpendicular(const SGVec3<T>& v)
384 T absv1 = fabs(v(0));
385 T absv2 = fabs(v(1));
386 T absv3 = fabs(v(2));
388 if (absv2 < absv1 && absv3 < absv1) {
390 return (1/sqrt(1+quot*quot))*SGVec3<T>(quot, -1, 0);
391 } else if (absv3 < absv2) {
393 return (1/sqrt(1+quot*quot))*SGVec3<T>(0, quot, -1);
394 } else if (SGLimits<T>::min() < absv3) {
396 return (1/sqrt(1+quot*quot))*SGVec3<T>(-1, 0, quot);
398 // the all zero case ...
399 return SGVec3<T>(0, 0, 0);
403 /// The euclidean norm of the vector, that is what most people call length
407 normalize(const SGVec3<T>& v)
408 { return (1/norm(v))*v; }
410 /// Return true if exactly the same
414 operator==(const SGVec3<T>& v1, const SGVec3<T>& v2)
415 { return v1(0) == v2(0) && v1(1) == v2(1) && v1(2) == v2(2); }
417 /// Return true if not exactly the same
421 operator!=(const SGVec3<T>& v1, const SGVec3<T>& v2)
422 { return ! (v1 == v2); }
424 /// Return true if smaller, good for putting that into a std::map
428 operator<(const SGVec3<T>& v1, const SGVec3<T>& v2)
430 if (v1(0) < v2(0)) return true;
431 else if (v2(0) < v1(0)) return false;
432 else if (v1(1) < v2(1)) return true;
433 else if (v2(1) < v1(1)) return false;
434 else return (v1(2) < v2(2));
440 operator<=(const SGVec3<T>& v1, const SGVec3<T>& v2)
442 if (v1(0) < v2(0)) return true;
443 else if (v2(0) < v1(0)) return false;
444 else if (v1(1) < v2(1)) return true;
445 else if (v2(1) < v1(1)) return false;
446 else return (v1(2) <= v2(2));
452 operator>(const SGVec3<T>& v1, const SGVec3<T>& v2)
453 { return operator<(v2, v1); }
458 operator>=(const SGVec3<T>& v1, const SGVec3<T>& v2)
459 { return operator<=(v2, v1); }
461 /// Return true if equal to the relative tolerance tol
465 equivalent(const SGVec3<T>& v1, const SGVec3<T>& v2, T rtol, T atol)
466 { return norm1(v1 - v2) < rtol*(norm1(v1) + norm1(v2)) + atol; }
468 /// Return true if equal to the relative tolerance tol
472 equivalent(const SGVec3<T>& v1, const SGVec3<T>& v2, T rtol)
473 { return norm1(v1 - v2) < rtol*(norm1(v1) + norm1(v2)); }
475 /// Return true if about equal to roundoff of the underlying type
479 equivalent(const SGVec3<T>& v1, const SGVec3<T>& v2)
481 T tol = 100*SGLimits<T>::epsilon();
482 return equivalent(v1, v2, tol, tol);
485 /// The euclidean distance of the two vectors
489 dist(const SGVec3<T>& v1, const SGVec3<T>& v2)
490 { return norm(v1 - v2); }
492 /// The squared euclidean distance of the two vectors
496 distSqr(const SGVec3<T>& v1, const SGVec3<T>& v2)
497 { SGVec3<T> tmp = v1 - v2; return dot(tmp, tmp); }
503 isNaN(const SGVec3<T>& v)
505 return SGMisc<T>::isNaN(v(0)) ||
506 SGMisc<T>::isNaN(v(1)) || SGMisc<T>::isNaN(v(2));
510 /// Output to an ostream
511 template<typename char_type, typename traits_type, typename T>
513 std::basic_ostream<char_type, traits_type>&
514 operator<<(std::basic_ostream<char_type, traits_type>& s, const SGVec3<T>& v)
515 { return s << "[ " << v(0) << ", " << v(1) << ", " << v(2) << " ]"; }
519 toVec3f(const SGVec3d& v)
520 { return SGVec3f((float)v(0), (float)v(1), (float)v(2)); }
524 toVec3d(const SGVec3f& v)
525 { return SGVec3d(v(0), v(1), v(2)); }