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_2D_H_INCLUDED__
6 : #define __IRR_POINT_2D_H_INCLUDED__
7 :
8 : #include "irrMath.h"
9 : #include "dimension2d.h"
10 :
11 : namespace irr
12 : {
13 : namespace core
14 : {
15 :
16 :
17 : //! 2d vector template class with lots of operators and methods.
18 : /** As of Irrlicht 1.6, this class supercedes position2d, which should
19 : be considered deprecated. */
20 : template <class T>
21 : class vector2d
22 : {
23 : public:
24 : //! Default constructor (null vector)
25 4693828 : vector2d() : X(0), Y(0) {}
26 : //! Constructor with two different values
27 11303461 : vector2d(T nx, T ny) : X(nx), Y(ny) {}
28 : //! Constructor with the same value for both members
29 : explicit vector2d(T n) : X(n), Y(n) {}
30 : //! Copy constructor
31 65932930 : vector2d(const vector2d<T>& other) : X(other.X), Y(other.Y) {}
32 :
33 16036 : vector2d(const dimension2d<T>& other) : X(other.Width), Y(other.Height) {}
34 :
35 : // operators
36 :
37 1331 : vector2d<T> operator-() const { return vector2d<T>(-X, -Y); }
38 :
39 3817194 : vector2d<T>& operator=(const vector2d<T>& other) { X = other.X; Y = other.Y; return *this; }
40 :
41 : vector2d<T>& operator=(const dimension2d<T>& other) { X = other.Width; Y = other.Height; return *this; }
42 :
43 257392 : vector2d<T> operator+(const vector2d<T>& other) const { return vector2d<T>(X + other.X, Y + other.Y); }
44 : vector2d<T> operator+(const dimension2d<T>& other) const { return vector2d<T>(X + other.Width, Y + other.Height); }
45 121842 : vector2d<T>& operator+=(const vector2d<T>& other) { X+=other.X; Y+=other.Y; return *this; }
46 150 : vector2d<T> operator+(const T v) const { return vector2d<T>(X + v, Y + v); }
47 : vector2d<T>& operator+=(const T v) { X+=v; Y+=v; return *this; }
48 : vector2d<T>& operator+=(const dimension2d<T>& other) { X += other.Width; Y += other.Height; return *this; }
49 :
50 7312 : vector2d<T> operator-(const vector2d<T>& other) const { return vector2d<T>(X - other.X, Y - other.Y); }
51 : vector2d<T> operator-(const dimension2d<T>& other) const { return vector2d<T>(X - other.Width, Y - other.Height); }
52 0 : vector2d<T>& operator-=(const vector2d<T>& other) { X-=other.X; Y-=other.Y; return *this; }
53 75 : vector2d<T> operator-(const T v) const { return vector2d<T>(X - v, Y - v); }
54 0 : vector2d<T>& operator-=(const T v) { X-=v; Y-=v; return *this; }
55 : vector2d<T>& operator-=(const dimension2d<T>& other) { X -= other.Width; Y -= other.Height; return *this; }
56 :
57 : vector2d<T> operator*(const vector2d<T>& other) const { return vector2d<T>(X * other.X, Y * other.Y); }
58 : vector2d<T>& operator*=(const vector2d<T>& other) { X*=other.X; Y*=other.Y; return *this; }
59 254888 : vector2d<T> operator*(const T v) const { return vector2d<T>(X * v, Y * v); }
60 : vector2d<T>& operator*=(const T v) { X*=v; Y*=v; return *this; }
61 :
62 : vector2d<T> operator/(const vector2d<T>& other) const { return vector2d<T>(X / other.X, Y / other.Y); }
63 : vector2d<T>& operator/=(const vector2d<T>& other) { X/=other.X; Y/=other.Y; return *this; }
64 300 : vector2d<T> operator/(const T v) const { return vector2d<T>(X / v, Y / v); }
65 : vector2d<T>& operator/=(const T v) { X/=v; Y/=v; return *this; }
66 :
67 : //! sort in order X, Y. Equality with rounding tolerance.
68 : bool operator<=(const vector2d<T>&other) const
69 : {
70 : return (X<other.X || core::equals(X, other.X)) ||
71 : (core::equals(X, other.X) && (Y<other.Y || core::equals(Y, other.Y)));
72 : }
73 :
74 : //! sort in order X, Y. Equality with rounding tolerance.
75 : bool operator>=(const vector2d<T>&other) const
76 : {
77 : return (X>other.X || core::equals(X, other.X)) ||
78 : (core::equals(X, other.X) && (Y>other.Y || core::equals(Y, other.Y)));
79 : }
80 :
81 : //! sort in order X, Y. Difference must be above rounding tolerance.
82 4089583 : bool operator<(const vector2d<T>&other) const
83 : {
84 5339602 : return (X<other.X && !core::equals(X, other.X)) ||
85 5339602 : (core::equals(X, other.X) && Y<other.Y && !core::equals(Y, other.Y));
86 : }
87 :
88 : //! sort in order X, Y. Difference must be above rounding tolerance.
89 : bool operator>(const vector2d<T>&other) const
90 : {
91 : return (X>other.X && !core::equals(X, other.X)) ||
92 : (core::equals(X, other.X) && Y>other.Y && !core::equals(Y, other.Y));
93 : }
94 :
95 2346744 : bool operator==(const vector2d<T>& other) const { return equals(other); }
96 2444 : bool operator!=(const vector2d<T>& other) const { return !equals(other); }
97 :
98 : // functions
99 :
100 : //! Checks if this vector equals the other one.
101 : /** Takes floating point rounding errors into account.
102 : \param other Vector to compare with.
103 : \return True if the two vector are (almost) equal, else false. */
104 2349188 : bool equals(const vector2d<T>& other) const
105 : {
106 2349188 : return core::equals(X, other.X) && core::equals(Y, other.Y);
107 : }
108 :
109 89763 : vector2d<T>& set(T nx, T ny) {X=nx; Y=ny; return *this; }
110 : vector2d<T>& set(const vector2d<T>& p) { X=p.X; Y=p.Y; return *this; }
111 :
112 : //! Gets the length of the vector.
113 : /** \return The length of the vector. */
114 33732 : T getLength() const { return core::squareroot( X*X + Y*Y ); }
115 :
116 : //! Get the squared length of this vector
117 : /** This is useful because it is much faster than getLength().
118 : \return The squared length of the vector. */
119 0 : T getLengthSQ() const { return X*X + Y*Y; }
120 :
121 : //! Get the dot product of this vector with another.
122 : /** \param other Other vector to take dot product with.
123 : \return The dot product of the two vectors. */
124 : T dotProduct(const vector2d<T>& other) const
125 : {
126 : return X*other.X + Y*other.Y;
127 : }
128 :
129 : //! Gets distance from another point.
130 : /** Here, the vector is interpreted as a point in 2-dimensional space.
131 : \param other Other vector to measure from.
132 : \return Distance from other point. */
133 33732 : T getDistanceFrom(const vector2d<T>& other) const
134 : {
135 33732 : return vector2d<T>(X - other.X, Y - other.Y).getLength();
136 : }
137 :
138 : //! Returns squared distance from another point.
139 : /** Here, the vector is interpreted as a point in 2-dimensional space.
140 : \param other Other vector to measure from.
141 : \return Squared distance from other point. */
142 0 : T getDistanceFromSQ(const vector2d<T>& other) const
143 : {
144 0 : return vector2d<T>(X - other.X, Y - other.Y).getLengthSQ();
145 : }
146 :
147 : //! rotates the point anticlockwise around a center by an amount of degrees.
148 : /** \param degrees Amount of degrees to rotate by, anticlockwise.
149 : \param center Rotation center.
150 : \return This vector after transformation. */
151 89763 : vector2d<T>& rotateBy(f64 degrees, const vector2d<T>& center=vector2d<T>())
152 : {
153 89763 : degrees *= DEGTORAD64;
154 89763 : const f64 cs = cos(degrees);
155 89763 : const f64 sn = sin(degrees);
156 :
157 89763 : X -= center.X;
158 89763 : Y -= center.Y;
159 :
160 89763 : set((T)(X*cs - Y*sn), (T)(X*sn + Y*cs));
161 :
162 89763 : X += center.X;
163 89763 : Y += center.Y;
164 89763 : return *this;
165 : }
166 :
167 : //! Normalize the vector.
168 : /** The null vector is left untouched.
169 : \return Reference to this vector, after normalization. */
170 : vector2d<T>& normalize()
171 : {
172 : f32 length = (f32)(X*X + Y*Y);
173 : if ( length == 0 )
174 : return *this;
175 : length = core::reciprocal_squareroot ( length );
176 : X = (T)(X * length);
177 : Y = (T)(Y * length);
178 : return *this;
179 : }
180 :
181 : //! Calculates the angle of this vector in degrees in the trigonometric sense.
182 : /** 0 is to the right (3 o'clock), values increase counter-clockwise.
183 : This method has been suggested by Pr3t3nd3r.
184 : \return Returns a value between 0 and 360. */
185 : f64 getAngleTrig() const
186 : {
187 : if (Y == 0)
188 : return X < 0 ? 180 : 0;
189 : else
190 : if (X == 0)
191 : return Y < 0 ? 270 : 90;
192 :
193 : if ( Y > 0)
194 : if (X > 0)
195 : return atan((irr::f64)Y/(irr::f64)X) * RADTODEG64;
196 : else
197 : return 180.0-atan((irr::f64)Y/-(irr::f64)X) * RADTODEG64;
198 : else
199 : if (X > 0)
200 : return 360.0-atan(-(irr::f64)Y/(irr::f64)X) * RADTODEG64;
201 : else
202 : return 180.0+atan(-(irr::f64)Y/-(irr::f64)X) * RADTODEG64;
203 : }
204 :
205 : //! Calculates the angle of this vector in degrees in the counter trigonometric sense.
206 : /** 0 is to the right (3 o'clock), values increase clockwise.
207 : \return Returns a value between 0 and 360. */
208 : inline f64 getAngle() const
209 : {
210 : if (Y == 0) // corrected thanks to a suggestion by Jox
211 : return X < 0 ? 180 : 0;
212 : else if (X == 0)
213 : return Y < 0 ? 90 : 270;
214 :
215 : // don't use getLength here to avoid precision loss with s32 vectors
216 : // avoid floating-point trouble as sqrt(y*y) is occasionally larger than y, so clamp
217 : const f64 tmp = core::clamp(Y / sqrt((f64)(X*X + Y*Y)), -1.0, 1.0);
218 : const f64 angle = atan( core::squareroot(1 - tmp*tmp) / tmp) * RADTODEG64;
219 :
220 : if (X>0 && Y>0)
221 : return angle + 270;
222 : else
223 : if (X>0 && Y<0)
224 : return angle + 90;
225 : else
226 : if (X<0 && Y<0)
227 : return 90 - angle;
228 : else
229 : if (X<0 && Y>0)
230 : return 270 - angle;
231 :
232 : return angle;
233 : }
234 :
235 : //! Calculates the angle between this vector and another one in degree.
236 : /** \param b Other vector to test with.
237 : \return Returns a value between 0 and 90. */
238 : inline f64 getAngleWith(const vector2d<T>& b) const
239 : {
240 : f64 tmp = (f64)(X*b.X + Y*b.Y);
241 :
242 : if (tmp == 0.0)
243 : return 90.0;
244 :
245 : tmp = tmp / core::squareroot((f64)((X*X + Y*Y) * (b.X*b.X + b.Y*b.Y)));
246 : if (tmp < 0.0)
247 : tmp = -tmp;
248 : if ( tmp > 1.0 ) // avoid floating-point trouble
249 : tmp = 1.0;
250 :
251 : return atan(sqrt(1 - tmp*tmp) / tmp) * RADTODEG64;
252 : }
253 :
254 : //! Returns if this vector interpreted as a point is on a line between two other points.
255 : /** It is assumed that the point is on the line.
256 : \param begin Beginning vector to compare between.
257 : \param end Ending vector to compare between.
258 : \return True if this vector is between begin and end, false if not. */
259 : bool isBetweenPoints(const vector2d<T>& begin, const vector2d<T>& end) const
260 : {
261 : if (begin.X != end.X)
262 : {
263 : return ((begin.X <= X && X <= end.X) ||
264 : (begin.X >= X && X >= end.X));
265 : }
266 : else
267 : {
268 : return ((begin.Y <= Y && Y <= end.Y) ||
269 : (begin.Y >= Y && Y >= end.Y));
270 : }
271 : }
272 :
273 : //! Creates an interpolated vector between this vector and another vector.
274 : /** \param other The other vector to interpolate with.
275 : \param d Interpolation value between 0.0f (all the other vector) and 1.0f (all this vector).
276 : Note that this is the opposite direction of interpolation to getInterpolated_quadratic()
277 : \return An interpolated vector. This vector is not modified. */
278 : vector2d<T> getInterpolated(const vector2d<T>& other, f64 d) const
279 : {
280 : f64 inv = 1.0f - d;
281 : return vector2d<T>((T)(other.X*inv + X*d), (T)(other.Y*inv + Y*d));
282 : }
283 :
284 : //! Creates a quadratically interpolated vector between this and two other vectors.
285 : /** \param v2 Second vector to interpolate with.
286 : \param v3 Third vector to interpolate with (maximum at 1.0f)
287 : \param d Interpolation value between 0.0f (all this vector) and 1.0f (all the 3rd vector).
288 : Note that this is the opposite direction of interpolation to getInterpolated() and interpolate()
289 : \return An interpolated vector. This vector is not modified. */
290 : vector2d<T> getInterpolated_quadratic(const vector2d<T>& v2, const vector2d<T>& v3, f64 d) const
291 : {
292 : // this*(1-d)*(1-d) + 2 * v2 * (1-d) + v3 * d * d;
293 : const f64 inv = 1.0f - d;
294 : const f64 mul0 = inv * inv;
295 : const f64 mul1 = 2.0f * d * inv;
296 : const f64 mul2 = d * d;
297 :
298 : return vector2d<T> ( (T)(X * mul0 + v2.X * mul1 + v3.X * mul2),
299 : (T)(Y * mul0 + v2.Y * mul1 + v3.Y * mul2));
300 : }
301 :
302 : //! Sets this vector to the linearly interpolated vector between a and b.
303 : /** \param a first vector to interpolate with, maximum at 1.0f
304 : \param b second vector to interpolate with, maximum at 0.0f
305 : \param d Interpolation value between 0.0f (all vector b) and 1.0f (all vector a)
306 : Note that this is the opposite direction of interpolation to getInterpolated_quadratic()
307 : */
308 : vector2d<T>& interpolate(const vector2d<T>& a, const vector2d<T>& b, f64 d)
309 : {
310 : X = (T)((f64)b.X + ( ( a.X - b.X ) * d ));
311 : Y = (T)((f64)b.Y + ( ( a.Y - b.Y ) * d ));
312 : return *this;
313 : }
314 :
315 : //! X coordinate of vector.
316 : T X;
317 :
318 : //! Y coordinate of vector.
319 : T Y;
320 : };
321 :
322 : //! Typedef for f32 2d vector.
323 : typedef vector2d<f32> vector2df;
324 :
325 : //! Typedef for integer 2d vector.
326 : typedef vector2d<s32> vector2di;
327 :
328 : template<class S, class T>
329 1331 : vector2d<T> operator*(const S scalar, const vector2d<T>& vector) { return vector*scalar; }
330 :
331 : // These methods are declared in dimension2d, but need definitions of vector2d
332 : template<class T>
333 546 : dimension2d<T>::dimension2d(const vector2d<T>& other) : Width(other.X), Height(other.Y) { }
334 :
335 : template<class T>
336 : bool dimension2d<T>::operator==(const vector2d<T>& other) const { return Width == other.X && Height == other.Y; }
337 :
338 : } // end namespace core
339 : } // end namespace irr
340 :
341 : #endif
342 :
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