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]; }
100 /// Access by index, the index is unchecked
101 const T& operator()(unsigned i) const
102 { return data()[i]; }
103 /// Access by index, the index is unchecked
104 T& operator()(unsigned i)
105 { return data()[i]; }
107 /// Access raw data by index, the index is unchecked
108 const T& operator[](unsigned i) const
109 { return data()[i]; }
110 /// Access raw data by index, the index is unchecked
111 T& operator[](unsigned i)
112 { return data()[i]; }
114 /// Access the x component
115 const T& x(void) const
116 { return data()[0]; }
117 /// Access the x component
119 { return data()[0]; }
120 /// Access the y component
121 const T& y(void) const
122 { return data()[1]; }
123 /// Access the y component
125 { return data()[1]; }
126 /// Access the z component
127 const T& z(void) const
128 { return data()[2]; }
129 /// Access the z component
131 { return data()[2]; }
133 /// Get the data pointer
134 using SGVec3Storage<T>::data;
136 /// Readonly interface function to ssg's sgVec3/sgdVec3
137 const T (&sg(void) const)[3]
139 /// Interface function to ssg's sgVec3/sgdVec3
143 /// Interface function to osg's Vec3*
144 using SGVec3Storage<T>::osg;
147 SGVec3& operator+=(const SGVec3& v)
148 { data()[0] += v(0); data()[1] += v(1); data()[2] += v(2); return *this; }
149 /// Inplace subtraction
150 SGVec3& operator-=(const SGVec3& v)
151 { data()[0] -= v(0); data()[1] -= v(1); data()[2] -= v(2); return *this; }
152 /// Inplace scalar multiplication
154 SGVec3& operator*=(S s)
155 { data()[0] *= s; data()[1] *= s; data()[2] *= s; return *this; }
156 /// Inplace scalar multiplication by 1/s
158 SGVec3& operator/=(S s)
159 { return operator*=(1/T(s)); }
161 /// Return an all zero vector
162 static SGVec3 zeros(void)
163 { return SGVec3(0, 0, 0); }
164 /// Return unit vectors
165 static SGVec3 e1(void)
166 { return SGVec3(1, 0, 0); }
167 static SGVec3 e2(void)
168 { return SGVec3(0, 1, 0); }
169 static SGVec3 e3(void)
170 { return SGVec3(0, 0, 1); }
172 /// Constructor. Initialize by a geodetic coordinate
173 /// Note that this conversion is relatively expensive to compute
174 static SGVec3 fromGeod(const SGGeod& geod);
175 /// Constructor. Initialize by a geocentric coordinate
176 /// Note that this conversion is relatively expensive to compute
177 static SGVec3 fromGeoc(const SGGeoc& geoc);
183 SGVec3<double>::fromGeod(const SGGeod& geod)
186 SGGeodesy::SGGeodToCart(geod, cart);
193 SGVec3<float>::fromGeod(const SGGeod& geod)
196 SGGeodesy::SGGeodToCart(geod, cart);
197 return SGVec3<float>(cart(0), cart(1), cart(2));
203 SGVec3<double>::fromGeoc(const SGGeoc& geoc)
206 SGGeodesy::SGGeocToCart(geoc, cart);
213 SGVec3<float>::fromGeoc(const SGGeoc& geoc)
216 SGGeodesy::SGGeocToCart(geoc, cart);
217 return SGVec3<float>(cart(0), cart(1), cart(2));
220 /// Unary +, do nothing ...
224 operator+(const SGVec3<T>& v)
227 /// Unary -, do nearly nothing
231 operator-(const SGVec3<T>& v)
232 { return SGVec3<T>(-v(0), -v(1), -v(2)); }
238 operator+(const SGVec3<T>& v1, const SGVec3<T>& v2)
239 { return SGVec3<T>(v1(0)+v2(0), v1(1)+v2(1), v1(2)+v2(2)); }
245 operator-(const SGVec3<T>& v1, const SGVec3<T>& v2)
246 { return SGVec3<T>(v1(0)-v2(0), v1(1)-v2(1), v1(2)-v2(2)); }
248 /// Scalar multiplication
249 template<typename S, typename T>
252 operator*(S s, const SGVec3<T>& v)
253 { return SGVec3<T>(s*v(0), s*v(1), s*v(2)); }
255 /// Scalar multiplication
256 template<typename S, typename T>
259 operator*(const SGVec3<T>& v, S s)
260 { return SGVec3<T>(s*v(0), s*v(1), s*v(2)); }
262 /// component wise min
266 min(const SGVec3<T>& v1, const SGVec3<T>& v2)
268 return SGVec3<T>(SGMisc<T>::min(v1(0), v2(0)),
269 SGMisc<T>::min(v1(1), v2(1)),
270 SGMisc<T>::min(v1(2), v2(2)));
272 template<typename S, typename T>
275 min(const SGVec3<T>& v, S s)
277 return SGVec3<T>(SGMisc<T>::min(s, v(0)),
278 SGMisc<T>::min(s, v(1)),
279 SGMisc<T>::min(s, v(2)));
281 template<typename S, typename T>
284 min(S s, const SGVec3<T>& v)
286 return SGVec3<T>(SGMisc<T>::min(s, v(0)),
287 SGMisc<T>::min(s, v(1)),
288 SGMisc<T>::min(s, v(2)));
291 /// component wise max
295 max(const SGVec3<T>& v1, const SGVec3<T>& v2)
297 return SGVec3<T>(SGMisc<T>::max(v1(0), v2(0)),
298 SGMisc<T>::max(v1(1), v2(1)),
299 SGMisc<T>::max(v1(2), v2(2)));
301 template<typename S, typename T>
304 max(const SGVec3<T>& v, S s)
306 return SGVec3<T>(SGMisc<T>::max(s, v(0)),
307 SGMisc<T>::max(s, v(1)),
308 SGMisc<T>::max(s, v(2)));
310 template<typename S, typename T>
313 max(S s, const SGVec3<T>& v)
315 return SGVec3<T>(SGMisc<T>::max(s, v(0)),
316 SGMisc<T>::max(s, v(1)),
317 SGMisc<T>::max(s, v(2)));
320 /// Scalar dot product
324 dot(const SGVec3<T>& v1, const SGVec3<T>& v2)
325 { return v1(0)*v2(0) + v1(1)*v2(1) + v1(2)*v2(2); }
327 /// The euclidean norm of the vector, that is what most people call length
331 norm(const SGVec3<T>& v)
332 { return sqrt(dot(v, v)); }
334 /// The euclidean norm of the vector, that is what most people call length
338 length(const SGVec3<T>& v)
339 { return sqrt(dot(v, v)); }
341 /// The 1-norm of the vector, this one is the fastest length function we
342 /// can implement on modern cpu's
346 norm1(const SGVec3<T>& v)
347 { return fabs(v(0)) + fabs(v(1)) + fabs(v(2)); }
349 /// The inf-norm of the vector
353 normI(const SGVec3<T>& v)
354 { return SGMisc<T>::max(fabs(v(0)), fabs(v(1)), fabs(v(2))); }
356 /// Vector cross product
360 cross(const SGVec3<T>& v1, const SGVec3<T>& v2)
362 return SGVec3<T>(v1(1)*v2(2) - v1(2)*v2(1),
363 v1(2)*v2(0) - v1(0)*v2(2),
364 v1(0)*v2(1) - v1(1)*v2(0));
367 /// return any normalized vector perpendicular to v
371 perpendicular(const SGVec3<T>& v)
373 T absv1 = fabs(v(0));
374 T absv2 = fabs(v(1));
375 T absv3 = fabs(v(2));
377 if (absv2 < absv1 && absv3 < absv1) {
379 return (1/sqrt(1+quot*quot))*SGVec3<T>(quot, -1, 0);
380 } else if (absv1 < absv2 && absv3 < absv2) {
382 return (1/sqrt(1+quot*quot))*SGVec3<T>(0, quot, -1);
383 } else if (absv1 < absv3 && absv2 < absv3) {
385 return (1/sqrt(1+quot*quot))*SGVec3<T>(-1, 0, quot);
387 // the all zero case ...
388 return SGVec3<T>(0, 0, 0);
392 /// The euclidean norm of the vector, that is what most people call length
396 normalize(const SGVec3<T>& v)
397 { return (1/norm(v))*v; }
399 /// Return true if exactly the same
403 operator==(const SGVec3<T>& v1, const SGVec3<T>& v2)
404 { return v1(0) == v2(0) && v1(1) == v2(1) && v1(2) == v2(2); }
406 /// Return true if not exactly the same
410 operator!=(const SGVec3<T>& v1, const SGVec3<T>& v2)
411 { return ! (v1 == v2); }
413 /// Return true if equal to the relative tolerance tol
417 equivalent(const SGVec3<T>& v1, const SGVec3<T>& v2, T rtol, T atol)
418 { return norm1(v1 - v2) < rtol*(norm1(v1) + norm1(v2)) + atol; }
420 /// Return true if equal to the relative tolerance tol
424 equivalent(const SGVec3<T>& v1, const SGVec3<T>& v2, T rtol)
425 { return norm1(v1 - v2) < rtol*(norm1(v1) + norm1(v2)); }
427 /// Return true if about equal to roundoff of the underlying type
431 equivalent(const SGVec3<T>& v1, const SGVec3<T>& v2)
433 T tol = 100*SGLimits<T>::epsilon();
434 return equivalent(v1, v2, tol, tol);
437 /// The euclidean distance of the two vectors
441 dist(const SGVec3<T>& v1, const SGVec3<T>& v2)
442 { return norm(v1 - v2); }
444 /// The squared euclidean distance of the two vectors
448 distSqr(const SGVec3<T>& v1, const SGVec3<T>& v2)
449 { SGVec3<T> tmp = v1 - v2; return dot(tmp, tmp); }
455 isNaN(const SGVec3<T>& v)
457 return SGMisc<T>::isNaN(v(0)) ||
458 SGMisc<T>::isNaN(v(1)) || SGMisc<T>::isNaN(v(2));
462 /// Output to an ostream
463 template<typename char_type, typename traits_type, typename T>
465 std::basic_ostream<char_type, traits_type>&
466 operator<<(std::basic_ostream<char_type, traits_type>& s, const SGVec3<T>& v)
467 { return s << "[ " << v(0) << ", " << v(1) << ", " << v(2) << " ]"; }
471 toVec3f(const SGVec3d& v)
472 { return SGVec3f((float)v(0), (float)v(1), (float)v(2)); }
476 toVec3d(const SGVec3f& v)
477 { return SGVec3d(v(0), v(1), v(2)); }