engine/include/support/vector2d.h

   1 // Copyright (C) 2002-2007 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
  10 namespace irr
  11 {
  12 namespace core
  13 {
  14
  15
  16 //! 2d vector template class with lots of operators and methods.
  17 template <class T>
  18 class vector2d
  19 {
  20 public:
  21
  22         vector2d() : X(0), Y(0) {}
  23         vector2d(T nx, T ny) : X(nx), Y(ny) {}
  24         vector2d(const vector2d<T>& other) : X(other.X), Y(other.Y) {}
  25
  26         // operators
  27
  28         vector2d<T> operator-() const { return vector2d<T>(-X, -Y); }
  29
  30         vector2d<T>& operator=(const vector2d<T>& other) { X = other.X; Y = other.Y; return *this; }
  31
  32         vector2d<T> operator+(const vector2d<T>& other) const { return vector2d<T>(X + other.X, Y + other.Y); }
  33         vector2d<T>& operator+=(const vector2d<T>& other) { X+=other.X; Y+=other.Y; return *this; }
  34         vector2d<T> operator+(const T v) const { return vector2d<T>(X + v, Y + v); }
  35         vector2d<T>& operator+=(const T v) { X+=v; Y+=v; return *this; }
  36
  37         vector2d<T> operator-(const vector2d<T>& other) const { return vector2d<T>(X - other.X, Y - other.Y); }
  38         vector2d<T>& operator-=(const vector2d<T>& other) { X-=other.X; Y-=other.Y; return *this; }
  39         vector2d<T> operator-(const T v) const { return vector2d<T>(X - v, Y - v); }
  40         vector2d<T>& operator-=(const T v) { X-=v; Y-=v; return *this; }
  41
  42         vector2d<T> operator*(const vector2d<T>& other) const { return vector2d<T>(X * other.X, Y * other.Y);   }
  43         vector2d<T>& operator*=(const vector2d<T>& other) { X*=other.X; Y*=other.Y; return *this; }
  44         vector2d<T> operator*(const T v) const { return vector2d<T>(X * v, Y * v);      }
  45         vector2d<T>& operator*=(const T v) { X*=v; Y*=v; return *this; }
  46
  47         vector2d<T> operator/(const vector2d<T>& other) const { return vector2d<T>(X / other.X, Y / other.Y);   }
  48         vector2d<T>& operator/=(const vector2d<T>& other) { X/=other.X; Y/=other.Y; return *this; }
  49         vector2d<T> operator/(const T v) const { return vector2d<T>(X / v, Y / v);      }
  50         vector2d<T>& operator/=(const T v) { X/=v; Y/=v; return *this; }
  51
  52         bool operator<=(const vector2d<T>&other) const { return X<=other.X && Y<=other.Y; }
  53         bool operator>=(const vector2d<T>&other) const { return X>=other.X && Y>=other.Y; }
  54
  55         bool operator<(const vector2d<T>&other) const { return X<other.X && Y<other.Y; }
  56         bool operator>(const vector2d<T>&other) const { return X>other.X && Y>other.Y; }
  57
  58         bool operator==(const vector2d<T>& other) const { return other.X==X && other.Y==Y; }
  59         bool operator!=(const vector2d<T>& other) const { return other.X!=X || other.Y!=Y; }
  60
  61         // functions
  62
  63         //! returns if this vector equals the other one, taking floating point rounding errors into account
  64         bool equals(const vector2d<T>& other) const
  65         {
  66                 return core::equals(X, other.X) && core::equals(Y, other.Y);
  67         }
  68
  69         void set(T nx, T ny) {X=nx; Y=ny; }
  70         void set(const vector2d<T>& p) { X=p.X; Y=p.Y;}
  71
  72         //! Returns the length of the vector
  73         //! \return Returns the length of the vector.
  74         T getLength() const { return (T)sqrt((f64)(X*X + Y*Y)); }
  75
  76         //! Returns the squared length of this vector
  77         /** This is useful because it is much faster than getLength(). */
  78         T getLengthSQ() const { return X*X + Y*Y; }
  79
  80         //! Returns the dot product of this vector with another.
  81         T dotProduct(const vector2d<T>& other) const
  82         {
  83                 return X*other.X + Y*other.Y;
  84         }
  85
  86         //! Returns distance from another point. Here, the vector is interpreted
  87         //! as a point in 2 dimensional space.
  88         T getDistanceFrom(const vector2d<T>& other) const
  89         {
  90                 return vector2d<T>(X - other.X, Y - other.Y).getLength();
  91         }
  92
  93         //! Returns squared distance from another point. Here, the vector is
  94         //! interpreted as a point in 2 dimensional space.
  95         T getDistanceFromSQ(const vector2d<T>& other) const
  96         {
  97                 return vector2d<T>(X - other.X, Y - other.Y).getLengthSQ();
  98         }
  99
 100         //! rotates the point around a center by an amount of degrees.
 101         void rotateBy(f64 degrees, const vector2d<T>& center)
 102         {
 103                 degrees *= DEGTORAD64;
 104                 T cs = (T)cos(degrees);
 105                 T sn = (T)sin(degrees);
 106
 107                 X -= center.X;
 108                 Y -= center.Y;
 109
 110                 set(X*cs - Y*sn, X*sn + Y*cs);
 111
 112                 X += center.X;
 113                 Y += center.Y;
 114         }
 115
 116         //! normalizes the vector.
 117         vector2d<T>& normalize()
 118         {
 119                 T l = X*X + Y*Y;
 120                 if (l == 0)
 121                         return *this;
 122                 l = core::reciprocal_squareroot ( (f32)l );
 123                 X *= l;
 124                 Y *= l;
 125                 return *this;
 126         }
 127
 128         //! Calculates the angle of this vector in grad in the trigonometric sense.
 129         //! This method has been suggested by Pr3t3nd3r.
 130         //! \return Returns a value between 0 and 360.
 131         f64 getAngleTrig() const
 132         {
 133                 if (X == 0)
 134                         return Y < 0 ? 270 : 90;
 135                 else
 136                 if (Y == 0)
 137                         return X < 0 ? 180 : 0;
 138
 139                 if ( Y > 0)
 140                         if (X > 0)
 141                                 return atan(Y/X) * RADTODEG64;
 142                         else
 143                                 return 180.0-atan(Y/-X) * RADTODEG64;
 144                 else
 145                         if (X > 0)
 146                                 return 360.0-atan(-Y/X) * RADTODEG64;
 147                         else
 148                                 return 180.0+atan(-Y/-X) * RADTODEG64;
 149         }
 150
 151         //! Calculates the angle of this vector in grad in the counter trigonometric sense.
 152         //! \return Returns a value between 0 and 360.
 153         inline f64 getAngle() const
 154         {
 155                 if (Y == 0)  // corrected thanks to a suggestion by Jox
 156                         return X < 0 ? 180 : 0;
 157                 else if (X == 0)
 158                         return Y < 0 ? 90 : 270;
 159
 160                 f64 tmp = Y / getLength();
 161                 tmp = atan(sqrt(1 - tmp*tmp) / tmp) * RADTODEG64;
 162
 163                 if (X>0 && Y>0)
 164                         return tmp + 270;
 165                 else
 166                 if (X>0 && Y<0)
 167                         return tmp + 90;
 168                 else
 169                 if (X<0 && Y<0)
 170                         return 90 - tmp;
 171                 else
 172                 if (X<0 && Y>0)
 173                         return 270 - tmp;
 174
 175                 return tmp;
 176         }
 177
 178         //! Calculates the angle between this vector and another one in grad.
 179         //! \return Returns a value between 0 and 90.
 180         inline f64 getAngleWith(const vector2d<T>& b) const
 181         {
 182                 f64 tmp = X*b.X + Y*b.Y;
 183
 184                 if (tmp == 0.0)
 185                         return 90.0;
 186
 187                 tmp = tmp / sqrt((f64)((X*X + Y*Y) * (b.X*b.X + b.Y*b.Y)));
 188                 if (tmp < 0.0)
 189                         tmp = -tmp;
 190
 191                 return atan(sqrt(1 - tmp*tmp) / tmp) * RADTODEG64;
 192         }
 193
 194         //! Returns if this vector interpreted as a point is on a line between two other points.
 195         /** It is assumed that the point is on the line. */
 196         //! \param begin: Beginning vector to compare between.
 197         //! \param end: Ending vector to compare between.
 198         //! \return True if this vector is between begin and end.  False if not.
 199         bool isBetweenPoints(const vector2d<T>& begin, const vector2d<T>& end) const
 200         {
 201                 T f = (end - begin).getLengthSQ();
 202                 return getDistanceFromSQ(begin) < f &&
 203                         getDistanceFromSQ(end) < f;
 204         }
 205
 206         //! returns interpolated vector
 207         //! \param other: other vector to interpolate between
 208         //! \param d: value between 0.0f and 1.0f.
 209         vector2d<T> getInterpolated(const vector2d<T>& other, f32 d) const
 210         {
 211                 T inv = (T) 1.0 - d;
 212                 return vector2d<T>(other.X*inv + X*d, other.Y*inv + Y*d);
 213         }
 214
 215         //! Returns (quadratically) interpolated vector between this and the two given ones.
 216         /** \param v2: second vector to interpolate with
 217         \param v3: third vector to interpolate with
 218         \param d: value between 0.0f and 1.0f. */
 219         vector2d<T> getInterpolated_quadratic(const vector2d<T>& v2, const vector2d<T>& v3, const T d) const
 220         {
 221                 // this*(1-d)*(1-d) + 2 * v2 * (1-d) + v3 * d * d;
 222                 const T inv = (T) 1.0 - d;
 223                 const T mul0 = inv * inv;
 224                 const T mul1 = (T) 2.0 * d * inv;
 225                 const T mul2 = d * d;
 226
 227                 return vector2d<T> ( X * mul0 + v2.X * mul1 + v3.X * mul2,
 228                                         Y * mul0 + v2.Y * mul1 + v3.Y * mul2);
 229         }
 230
 231         //! sets this vector to the linearly interpolated vector between a and b.
 232         /** \param a: first vector to interpolate with
 233         \param b: second vector to interpolate with
 234         \param t: value between 0.0f and 1.0f. */
 235         void interpolate(const vector2d<T>& a, const vector2d<T>& b, const f32 t)
 236         {
 237                 X = b.X + ( ( a.X - b.X ) * t );
 238                 Y = b.Y + ( ( a.Y - b.Y ) * t );
 239         }
 240
 241         // member variables
 242         T X, Y;
 243 };
 244
 245         //! Typedef for f32 2d vector.
 246         typedef vector2d<f32> vector2df;
 247         //! Typedef for integer 2d vector.
 248         typedef vector2d<s32> vector2di;
 249
 250         template<class S, class T> vector2d<T> operator*(const S scalar, const vector2d<T>& vector) { return vector*scalar; }
 251
 252 } // end namespace core
 253 } // end namespace irr
 254
 255 #endif
 256