Line data Source code
1 : // Copyright (C) 2002-2012 Nikolaus Gebhardt
2 : // This file is part of the "Irrlicht Engine".
3 : // For conditions of distribution and use, see copyright notice in irrlicht.h
4 :
5 : #ifndef __IRR_POINT_3D_H_INCLUDED__
6 : #define __IRR_POINT_3D_H_INCLUDED__
7 :
8 : #include "irrMath.h"
9 :
10 : namespace irr
11 : {
12 : namespace core
13 : {
14 :
15 : //! 3d vector template class with lots of operators and methods.
16 : /** The vector3d class is used in Irrlicht for three main purposes:
17 : 1) As a direction vector (most of the methods assume this).
18 : 2) As a position in 3d space (which is synonymous with a direction vector from the origin to this position).
19 : 3) To hold three Euler rotations, where X is pitch, Y is yaw and Z is roll.
20 : */
21 : template <class T>
22 : class vector3d
23 : {
24 : public:
25 : //! Default constructor (null vector).
26 131911956 : vector3d() : X(0), Y(0), Z(0) {}
27 : //! Constructor with three different values
28 721271007 : vector3d(T nx, T ny, T nz) : X(nx), Y(ny), Z(nz) {}
29 : //! Constructor with the same value for all elements
30 0 : explicit vector3d(T n) : X(n), Y(n), Z(n) {}
31 : //! Copy constructor
32 527713061 : vector3d(const vector3d<T>& other) : X(other.X), Y(other.Y), Z(other.Z) {}
33 :
34 : // operators
35 :
36 635020 : vector3d<T> operator-() const { return vector3d<T>(-X, -Y, -Z); }
37 :
38 124328128 : vector3d<T>& operator=(const vector3d<T>& other) { X = other.X; Y = other.Y; Z = other.Z; return *this; }
39 :
40 272974542 : vector3d<T> operator+(const vector3d<T>& other) const { return vector3d<T>(X + other.X, Y + other.Y, Z + other.Z); }
41 15974524 : vector3d<T>& operator+=(const vector3d<T>& other) { X+=other.X; Y+=other.Y; Z+=other.Z; return *this; }
42 0 : vector3d<T> operator+(const T val) const { return vector3d<T>(X + val, Y + val, Z + val); }
43 : vector3d<T>& operator+=(const T val) { X+=val; Y+=val; Z+=val; return *this; }
44 :
45 188304500 : vector3d<T> operator-(const vector3d<T>& other) const { return vector3d<T>(X - other.X, Y - other.Y, Z - other.Z); }
46 819211 : vector3d<T>& operator-=(const vector3d<T>& other) { X-=other.X; Y-=other.Y; Z-=other.Z; return *this; }
47 0 : vector3d<T> operator-(const T val) const { return vector3d<T>(X - val, Y - val, Z - val); }
48 : vector3d<T>& operator-=(const T val) { X-=val; Y-=val; Z-=val; return *this; }
49 :
50 : vector3d<T> operator*(const vector3d<T>& other) const { return vector3d<T>(X * other.X, Y * other.Y, Z * other.Z); }
51 346300 : vector3d<T>& operator*=(const vector3d<T>& other) { X*=other.X; Y*=other.Y; Z*=other.Z; return *this; }
52 34154412 : vector3d<T> operator*(const T v) const { return vector3d<T>(X * v, Y * v, Z * v); }
53 246098 : vector3d<T>& operator*=(const T v) { X*=v; Y*=v; Z*=v; return *this; }
54 :
55 : vector3d<T> operator/(const vector3d<T>& other) const { return vector3d<T>(X / other.X, Y / other.Y, Z / other.Z); }
56 : vector3d<T>& operator/=(const vector3d<T>& other) { X/=other.X; Y/=other.Y; Z/=other.Z; return *this; }
57 3510829 : vector3d<T> operator/(const T v) const { T i=(T)1.0/v; return vector3d<T>(X * i, Y * i, Z * i); }
58 0 : vector3d<T>& operator/=(const T v) { T i=(T)1.0/v; X*=i; Y*=i; Z*=i; return *this; }
59 :
60 : //! sort in order X, Y, Z. Equality with rounding tolerance.
61 : bool operator<=(const vector3d<T>&other) const
62 : {
63 : return (X<other.X || core::equals(X, other.X)) ||
64 : (core::equals(X, other.X) && (Y<other.Y || core::equals(Y, other.Y))) ||
65 : (core::equals(X, other.X) && core::equals(Y, other.Y) && (Z<other.Z || core::equals(Z, other.Z)));
66 : }
67 :
68 : //! sort in order X, Y, Z. Equality with rounding tolerance.
69 : bool operator>=(const vector3d<T>&other) const
70 : {
71 : return (X>other.X || core::equals(X, other.X)) ||
72 : (core::equals(X, other.X) && (Y>other.Y || core::equals(Y, other.Y))) ||
73 : (core::equals(X, other.X) && core::equals(Y, other.Y) && (Z>other.Z || core::equals(Z, other.Z)));
74 : }
75 :
76 : //! sort in order X, Y, Z. Difference must be above rounding tolerance.
77 11189529 : bool operator<(const vector3d<T>&other) const
78 : {
79 15040871 : return (X<other.X && !core::equals(X, other.X)) ||
80 16697895 : (core::equals(X, other.X) && Y<other.Y && !core::equals(Y, other.Y)) ||
81 31731704 : (core::equals(X, other.X) && core::equals(Y, other.Y) && Z<other.Z && !core::equals(Z, other.Z));
82 : }
83 :
84 : //! sort in order X, Y, Z. Difference must be above rounding tolerance.
85 : bool operator>(const vector3d<T>&other) const
86 : {
87 : return (X>other.X && !core::equals(X, other.X)) ||
88 : (core::equals(X, other.X) && Y>other.Y && !core::equals(Y, other.Y)) ||
89 : (core::equals(X, other.X) && core::equals(Y, other.Y) && Z>other.Z && !core::equals(Z, other.Z));
90 : }
91 :
92 : //! use weak float compare
93 68074320 : bool operator==(const vector3d<T>& other) const
94 : {
95 68074320 : return this->equals(other);
96 : }
97 :
98 447027 : bool operator!=(const vector3d<T>& other) const
99 : {
100 447027 : return !this->equals(other);
101 : }
102 :
103 : // functions
104 :
105 : //! returns if this vector equals the other one, taking floating point rounding errors into account
106 68518543 : bool equals(const vector3d<T>& other, const T tolerance = (T)ROUNDING_ERROR_f32 ) const
107 : {
108 68518543 : return core::equals(X, other.X, tolerance) &&
109 12713063 : core::equals(Y, other.Y, tolerance) &&
110 81229806 : core::equals(Z, other.Z, tolerance);
111 : }
112 :
113 18936380 : vector3d<T>& set(const T nx, const T ny, const T nz) {X=nx; Y=ny; Z=nz; return *this;}
114 : vector3d<T>& set(const vector3d<T>& p) {X=p.X; Y=p.Y; Z=p.Z;return *this;}
115 :
116 : //! Get length of the vector.
117 3178973 : T getLength() const { return core::squareroot( X*X + Y*Y + Z*Z ); }
118 :
119 : //! Get squared length of the vector.
120 : /** This is useful because it is much faster than getLength().
121 : \return Squared length of the vector. */
122 : T getLengthSQ() const { return X*X + Y*Y + Z*Z; }
123 :
124 : //! Get the dot product with another vector.
125 281948 : T dotProduct(const vector3d<T>& other) const
126 : {
127 281948 : return X*other.X + Y*other.Y + Z*other.Z;
128 : }
129 :
130 : //! Get distance from another point.
131 : /** Here, the vector is interpreted as point in 3 dimensional space. */
132 1246232 : T getDistanceFrom(const vector3d<T>& other) const
133 : {
134 1246232 : return vector3d<T>(X - other.X, Y - other.Y, Z - other.Z).getLength();
135 : }
136 :
137 : //! Returns squared distance from another point.
138 : /** Here, the vector is interpreted as point in 3 dimensional space. */
139 : T getDistanceFromSQ(const vector3d<T>& other) const
140 : {
141 : return vector3d<T>(X - other.X, Y - other.Y, Z - other.Z).getLengthSQ();
142 : }
143 :
144 : //! Calculates the cross product with another vector.
145 : /** \param p Vector to multiply with.
146 : \return Crossproduct of this vector with p. */
147 53482 : vector3d<T> crossProduct(const vector3d<T>& p) const
148 : {
149 53482 : return vector3d<T>(Y * p.Z - Z * p.Y, Z * p.X - X * p.Z, X * p.Y - Y * p.X);
150 : }
151 :
152 : //! Returns if this vector interpreted as a point is on a line between two other points.
153 : /** It is assumed that the point is on the line.
154 : \param begin Beginning vector to compare between.
155 : \param end Ending vector to compare between.
156 : \return True if this vector is between begin and end, false if not. */
157 : bool isBetweenPoints(const vector3d<T>& begin, const vector3d<T>& end) const
158 : {
159 : const T f = (end - begin).getLengthSQ();
160 : return getDistanceFromSQ(begin) <= f &&
161 : getDistanceFromSQ(end) <= f;
162 : }
163 :
164 : //! Normalizes the vector.
165 : /** In case of the 0 vector the result is still 0, otherwise
166 : the length of the vector will be 1.
167 : \return Reference to this vector after normalization. */
168 8890076 : vector3d<T>& normalize()
169 : {
170 8890076 : f64 length = X*X + Y*Y + Z*Z;
171 8890076 : if (length == 0 ) // this check isn't an optimization but prevents getting NAN in the sqrt.
172 23785 : return *this;
173 8866291 : length = core::reciprocal_squareroot(length);
174 :
175 8866291 : X = (T)(X * length);
176 8866291 : Y = (T)(Y * length);
177 8866291 : Z = (T)(Z * length);
178 8866291 : return *this;
179 : }
180 :
181 : //! Sets the length of the vector to a new value
182 0 : vector3d<T>& setLength(T newlength)
183 : {
184 0 : normalize();
185 0 : return (*this *= newlength);
186 : }
187 :
188 : //! Inverts the vector.
189 : vector3d<T>& invert()
190 : {
191 : X *= -1;
192 : Y *= -1;
193 : Z *= -1;
194 : return *this;
195 : }
196 :
197 : //! Rotates the vector by a specified number of degrees around the Y axis and the specified center.
198 : /** \param degrees Number of degrees to rotate around the Y axis.
199 : \param center The center of the rotation. */
200 2396897 : void rotateXZBy(f64 degrees, const vector3d<T>& center=vector3d<T>())
201 : {
202 2396897 : degrees *= DEGTORAD64;
203 2396897 : f64 cs = cos(degrees);
204 2396897 : f64 sn = sin(degrees);
205 2396897 : X -= center.X;
206 2396897 : Z -= center.Z;
207 2396897 : set((T)(X*cs - Z*sn), Y, (T)(X*sn + Z*cs));
208 2396901 : X += center.X;
209 2396901 : Z += center.Z;
210 2396901 : }
211 :
212 : //! Rotates the vector by a specified number of degrees around the Z axis and the specified center.
213 : /** \param degrees: Number of degrees to rotate around the Z axis.
214 : \param center: The center of the rotation. */
215 5561726 : void rotateXYBy(f64 degrees, const vector3d<T>& center=vector3d<T>())
216 : {
217 5561726 : degrees *= DEGTORAD64;
218 5561726 : f64 cs = cos(degrees);
219 5561726 : f64 sn = sin(degrees);
220 5561726 : X -= center.X;
221 5561726 : Y -= center.Y;
222 5561726 : set((T)(X*cs - Y*sn), (T)(X*sn + Y*cs), Z);
223 5561726 : X += center.X;
224 5561726 : Y += center.Y;
225 5561726 : }
226 :
227 : //! Rotates the vector by a specified number of degrees around the X axis and the specified center.
228 : /** \param degrees: Number of degrees to rotate around the X axis.
229 : \param center: The center of the rotation. */
230 4312704 : void rotateYZBy(f64 degrees, const vector3d<T>& center=vector3d<T>())
231 : {
232 4312704 : degrees *= DEGTORAD64;
233 4312704 : f64 cs = cos(degrees);
234 4312704 : f64 sn = sin(degrees);
235 4312704 : Z -= center.Z;
236 4312704 : Y -= center.Y;
237 4312704 : set(X, (T)(Y*cs - Z*sn), (T)(Y*sn + Z*cs));
238 4312704 : Z += center.Z;
239 4312704 : Y += center.Y;
240 4312704 : }
241 :
242 : //! Creates an interpolated vector between this vector and another vector.
243 : /** \param other The other vector to interpolate with.
244 : \param d Interpolation value between 0.0f (all the other vector) and 1.0f (all this vector).
245 : Note that this is the opposite direction of interpolation to getInterpolated_quadratic()
246 : \return An interpolated vector. This vector is not modified. */
247 : vector3d<T> getInterpolated(const vector3d<T>& other, f64 d) const
248 : {
249 : const f64 inv = 1.0 - d;
250 : return vector3d<T>((T)(other.X*inv + X*d), (T)(other.Y*inv + Y*d), (T)(other.Z*inv + Z*d));
251 : }
252 :
253 : //! Creates a quadratically interpolated vector between this and two other vectors.
254 : /** \param v2 Second vector to interpolate with.
255 : \param v3 Third vector to interpolate with (maximum at 1.0f)
256 : \param d Interpolation value between 0.0f (all this vector) and 1.0f (all the 3rd vector).
257 : Note that this is the opposite direction of interpolation to getInterpolated() and interpolate()
258 : \return An interpolated vector. This vector is not modified. */
259 : vector3d<T> getInterpolated_quadratic(const vector3d<T>& v2, const vector3d<T>& v3, f64 d) const
260 : {
261 : // this*(1-d)*(1-d) + 2 * v2 * (1-d) + v3 * d * d;
262 : const f64 inv = (T) 1.0 - d;
263 : const f64 mul0 = inv * inv;
264 : const f64 mul1 = (T) 2.0 * d * inv;
265 : const f64 mul2 = d * d;
266 :
267 : return vector3d<T> ((T)(X * mul0 + v2.X * mul1 + v3.X * mul2),
268 : (T)(Y * mul0 + v2.Y * mul1 + v3.Y * mul2),
269 : (T)(Z * mul0 + v2.Z * mul1 + v3.Z * mul2));
270 : }
271 :
272 : //! Sets this vector to the linearly interpolated vector between a and b.
273 : /** \param a first vector to interpolate with, maximum at 1.0f
274 : \param b second vector to interpolate with, maximum at 0.0f
275 : \param d Interpolation value between 0.0f (all vector b) and 1.0f (all vector a)
276 : Note that this is the opposite direction of interpolation to getInterpolated_quadratic()
277 : */
278 : vector3d<T>& interpolate(const vector3d<T>& a, const vector3d<T>& b, f64 d)
279 : {
280 : X = (T)((f64)b.X + ( ( a.X - b.X ) * d ));
281 : Y = (T)((f64)b.Y + ( ( a.Y - b.Y ) * d ));
282 : Z = (T)((f64)b.Z + ( ( a.Z - b.Z ) * d ));
283 : return *this;
284 : }
285 :
286 :
287 : //! Get the rotations that would make a (0,0,1) direction vector point in the same direction as this direction vector.
288 : /** Thanks to Arras on the Irrlicht forums for this method. This utility method is very useful for
289 : orienting scene nodes towards specific targets. For example, if this vector represents the difference
290 : between two scene nodes, then applying the result of getHorizontalAngle() to one scene node will point
291 : it at the other one.
292 : Example code:
293 : // Where target and seeker are of type ISceneNode*
294 : const vector3df toTarget(target->getAbsolutePosition() - seeker->getAbsolutePosition());
295 : const vector3df requiredRotation = toTarget.getHorizontalAngle();
296 : seeker->setRotation(requiredRotation);
297 :
298 : \return A rotation vector containing the X (pitch) and Y (raw) rotations (in degrees) that when applied to a
299 : +Z (e.g. 0, 0, 1) direction vector would make it point in the same direction as this vector. The Z (roll) rotation
300 : is always 0, since two Euler rotations are sufficient to point in any given direction. */
301 : vector3d<T> getHorizontalAngle() const
302 : {
303 : vector3d<T> angle;
304 :
305 : const f64 tmp = (atan2((f64)X, (f64)Z) * RADTODEG64);
306 : angle.Y = (T)tmp;
307 :
308 : if (angle.Y < 0)
309 : angle.Y += 360;
310 : if (angle.Y >= 360)
311 : angle.Y -= 360;
312 :
313 : const f64 z1 = core::squareroot(X*X + Z*Z);
314 :
315 : angle.X = (T)(atan2((f64)z1, (f64)Y) * RADTODEG64 - 90.0);
316 :
317 : if (angle.X < 0)
318 : angle.X += 360;
319 : if (angle.X >= 360)
320 : angle.X -= 360;
321 :
322 : return angle;
323 : }
324 :
325 : //! Get the spherical coordinate angles
326 : /** This returns Euler degrees for the point represented by
327 : this vector. The calculation assumes the pole at (0,1,0) and
328 : returns the angles in X and Y.
329 : */
330 : vector3d<T> getSphericalCoordinateAngles() const
331 : {
332 : vector3d<T> angle;
333 : const f64 length = X*X + Y*Y + Z*Z;
334 :
335 : if (length)
336 : {
337 : if (X!=0)
338 : {
339 : angle.Y = (T)(atan2((f64)Z,(f64)X) * RADTODEG64);
340 : }
341 : else if (Z<0)
342 : angle.Y=180;
343 :
344 : angle.X = (T)(acos(Y * core::reciprocal_squareroot(length)) * RADTODEG64);
345 : }
346 : return angle;
347 : }
348 :
349 : //! Builds a direction vector from (this) rotation vector.
350 : /** This vector is assumed to be a rotation vector composed of 3 Euler angle rotations, in degrees.
351 : The implementation performs the same calculations as using a matrix to do the rotation.
352 :
353 : \param[in] forwards The direction representing "forwards" which will be rotated by this vector.
354 : If you do not provide a direction, then the +Z axis (0, 0, 1) will be assumed to be forwards.
355 : \return A direction vector calculated by rotating the forwards direction by the 3 Euler angles
356 : (in degrees) represented by this vector. */
357 : vector3d<T> rotationToDirection(const vector3d<T> & forwards = vector3d<T>(0, 0, 1)) const
358 : {
359 : const f64 cr = cos( core::DEGTORAD64 * X );
360 : const f64 sr = sin( core::DEGTORAD64 * X );
361 : const f64 cp = cos( core::DEGTORAD64 * Y );
362 : const f64 sp = sin( core::DEGTORAD64 * Y );
363 : const f64 cy = cos( core::DEGTORAD64 * Z );
364 : const f64 sy = sin( core::DEGTORAD64 * Z );
365 :
366 : const f64 srsp = sr*sp;
367 : const f64 crsp = cr*sp;
368 :
369 : const f64 pseudoMatrix[] = {
370 : ( cp*cy ), ( cp*sy ), ( -sp ),
371 : ( srsp*cy-cr*sy ), ( srsp*sy+cr*cy ), ( sr*cp ),
372 : ( crsp*cy+sr*sy ), ( crsp*sy-sr*cy ), ( cr*cp )};
373 :
374 : return vector3d<T>(
375 : (T)(forwards.X * pseudoMatrix[0] +
376 : forwards.Y * pseudoMatrix[3] +
377 : forwards.Z * pseudoMatrix[6]),
378 : (T)(forwards.X * pseudoMatrix[1] +
379 : forwards.Y * pseudoMatrix[4] +
380 : forwards.Z * pseudoMatrix[7]),
381 : (T)(forwards.X * pseudoMatrix[2] +
382 : forwards.Y * pseudoMatrix[5] +
383 : forwards.Z * pseudoMatrix[8]));
384 : }
385 :
386 : //! Fills an array of 4 values with the vector data (usually floats).
387 : /** Useful for setting in shader constants for example. The fourth value
388 : will always be 0. */
389 : void getAs4Values(T* array) const
390 : {
391 : array[0] = X;
392 : array[1] = Y;
393 : array[2] = Z;
394 : array[3] = 0;
395 : }
396 :
397 : //! Fills an array of 3 values with the vector data (usually floats).
398 : /** Useful for setting in shader constants for example.*/
399 : void getAs3Values(T* array) const
400 : {
401 : array[0] = X;
402 : array[1] = Y;
403 : array[2] = Z;
404 : }
405 :
406 :
407 : //! X coordinate of the vector
408 : T X;
409 :
410 : //! Y coordinate of the vector
411 : T Y;
412 :
413 : //! Z coordinate of the vector
414 : T Z;
415 : };
416 :
417 : //! partial specialization for integer vectors
418 : // Implementor note: inline keyword needed due to template specialization for s32. Otherwise put specialization into a .cpp
419 : template <>
420 : inline vector3d<s32> vector3d<s32>::operator /(s32 val) const {return core::vector3d<s32>(X/val,Y/val,Z/val);}
421 : template <>
422 : inline vector3d<s32>& vector3d<s32>::operator /=(s32 val) {X/=val;Y/=val;Z/=val; return *this;}
423 :
424 : template <>
425 : inline vector3d<s32> vector3d<s32>::getSphericalCoordinateAngles() const
426 : {
427 : vector3d<s32> angle;
428 : const f64 length = X*X + Y*Y + Z*Z;
429 :
430 : if (length)
431 : {
432 : if (X!=0)
433 : {
434 : angle.Y = round32((f32)(atan2((f64)Z,(f64)X) * RADTODEG64));
435 : }
436 : else if (Z<0)
437 : angle.Y=180;
438 :
439 : angle.X = round32((f32)(acos(Y * core::reciprocal_squareroot(length)) * RADTODEG64));
440 : }
441 : return angle;
442 : }
443 :
444 : //! Typedef for a f32 3d vector.
445 : typedef vector3d<f32> vector3df;
446 :
447 : //! Typedef for an integer 3d vector.
448 : typedef vector3d<s32> vector3di;
449 :
450 : //! Function multiplying a scalar and a vector component-wise.
451 : template<class S, class T>
452 832960 : vector3d<T> operator*(const S scalar, const vector3d<T>& vector) { return vector*scalar; }
453 :
454 : } // end namespace core
455 : } // end namespace irr
456 :
457 : #endif
458 :
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