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| 1 | #ifndef __TOUCHLIB_VECTOR2D__
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|---|---|
| 2 | #define __TOUCHLIB_VECTOR2D__
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| 3 | |
| 4 | |
| 5 | #include <math.h> |
| 6 | |
| 7 | // The following code was originally written by Nikolaus Gebhardt as part of Irrlicht.
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| 8 | // See www.irrlicht3d.org
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| 9 | |
| 10 | // The Irrlicht Engine License
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| 11 | // Copyright © 2002-2005 Nikolaus Gebhardt
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| 12 | // This software is provided 'as-is', without any express or implied warranty. In no event will the authors be held
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| 13 | // liable for any damages arising from the use of this software.
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| 14 | //
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| 15 | // Permission is granted to anyone to use this software for any purpose, including commercial applications, and to
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| 16 | // alter it and redistribute it freely, subject to the following restrictions:
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| 17 | //
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| 18 | // 1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software.
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| 19 | // If you use this software in a product, an acknowledgment in the product documentation would be appreciated but
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| 20 | // is not required.
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| 21 | // 2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
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| 22 | // 3. This notice may not be removed or altered from any source distribution.
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| 23 | |
| 24 | |
| 25 | const float GRAD_PI = 180.0f / 3.14159f; |
| 26 | const float GRAD_PI2 = 3.14159f / 180.0f; |
| 27 | //const float PI = 3.14159f;
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| 28 | const float ROUNDING_ERROR = 0.0001f; |
| 29 | |
| 30 | |
| 31 | template <class T> |
| 32 | class vector2d |
| 33 | {
|
| 34 | public:
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| 35 | |
| 36 | vector2d(): X(0), Y(0) {}; |
| 37 | vector2d(T nx, T ny) : X(nx), Y(ny) {};
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| 38 | vector2d(const vector2d<T>& other) :X(other.X), Y(other.Y) {};
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| 39 | |
| 40 | // operators
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| 41 | |
| 42 | vector2d<T> operator-() const { return vector2d<T>(-X, -Y); } |
| 43 | |
| 44 | vector2d<T>& operator=(const vector2d<T>& other) { X = other.X; Y = other.Y; return *this; } |
| 45 | |
| 46 | vector2d<T> operator+(const vector2d<T>& other) const { return vector2d<T>(X + other.X, Y + other.Y); } |
| 47 | vector2d<T>& operator+=(const vector2d<T>& other) { X+=other.X; Y+=other.Y; return *this; } |
| 48 | |
| 49 | vector2d<T> operator-(const vector2d<T>& other) const { return vector2d<T>(X - other.X, Y - other.Y); } |
| 50 | vector2d<T>& operator-=(const vector2d<T>& other) { X-=other.X; Y-=other.Y; return *this; } |
| 51 | |
| 52 | vector2d<T> operator*(const vector2d<T>& other) const { return vector2d<T>(X * other.X, Y * other.Y); } |
| 53 | vector2d<T>& operator*=(const vector2d<T>& other) { X*=other.X; Y*=other.Y; return *this; } |
| 54 | vector2d<T> operator*(const T v) const { return vector2d<T>(X * v, Y * v); } |
| 55 | vector2d<T>& operator*=(const T v) { X*=v; Y*=v; 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 | 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 | bool operator==(const vector2d<T>& other) const { return other.X==X && other.Y==Y; } |
| 63 | bool operator!=(const vector2d<T>& other) const { return other.X!=X || other.Y!=Y; } |
| 64 | |
| 65 | // functions
|
| 66 | |
| 67 | void set(const T& nx, const T& ny) {X=nx; Y=ny; } |
| 68 | void set(const vector2d<T>& p) { X=p.X; Y=p.Y;} |
| 69 | |
| 70 | //! Returns the length of the vector
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| 71 | //! \return Returns the length of the vector.
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| 72 | float getLength() const { return sqrt(X*X + Y*Y); } |
| 73 | float getLengthSQ() const { return (X*X + Y*Y); } |
| 74 | |
| 75 | //! Returns the dot product of this vector with an other.
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| 76 | T dotProduct(const vector2d<T>& other) const |
| 77 | {
|
| 78 | return X*other.X + Y*other.Y;
|
| 79 | } |
| 80 | |
| 81 | //! Calculates the cross product with another vector
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| 82 | T crossProduct(const vector2d<T>& p) const |
| 83 | {
|
| 84 | return X * p.Y - Y * p.X;
|
| 85 | } |
| 86 | |
| 87 | |
| 88 | //! Returns distance from an other point. Here, the vector is interpreted as
|
| 89 | //! point in 2 dimensional space.
|
| 90 | float getDistanceFrom(const vector2d<T>& other) const |
| 91 | {
|
| 92 | float vx = X - other.X; float vy = Y - other.Y; |
| 93 | return sqrt(vx*vx + vy*vy);
|
| 94 | } |
| 95 | |
| 96 | //! Returns distance from an other point. Here, the vector is interpreted as
|
| 97 | //! point in 2 dimensional space.
|
| 98 | float getDistanceFromSQ(const vector2d<T>& other) const |
| 99 | {
|
| 100 | float vx = X - other.X;
|
| 101 | float vy = Y - other.Y;
|
| 102 | |
| 103 | return (vx*vx + vy*vy);
|
| 104 | } |
| 105 | |
| 106 | //! rotates the point around a center by an amount of degrees.
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| 107 | void rotateBy(float degrees, const vector2d<T>& center) |
| 108 | {
|
| 109 | degrees *= GRAD_PI2; |
| 110 | T cs = (T)cos(degrees); |
| 111 | T sn = (T)sin(degrees); |
| 112 | |
| 113 | X -= center.X; |
| 114 | Y -= center.Y; |
| 115 | |
| 116 | set(X*cs - Y*sn, X*sn + Y*cs); |
| 117 | |
| 118 | X += center.X; |
| 119 | Y += center.Y; |
| 120 | } |
| 121 | |
| 122 | //! normalizes the vector.
|
| 123 | vector2d<T>& normalize() |
| 124 | {
|
| 125 | T l = (T)getLength(); |
| 126 | if (l == 0) |
| 127 | return *this;
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| 128 | |
| 129 | l = (T)1.0 / l; |
| 130 | X *= l; |
| 131 | Y *= l; |
| 132 | return *this;
|
| 133 | } |
| 134 | |
| 135 | //! Calculates the angle of this vector in grad in the trigonometric sense.
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| 136 | //! This method has been suggested by Pr3t3nd3r.
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| 137 | //! \return Returns a value between 0 and 360.
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| 138 | inline float getAngleTrig() const |
| 139 | {
|
| 140 | if (X == 0.0) |
| 141 | return Y < 0.0 ? 270.0 : 90.0; |
| 142 | else
|
| 143 | if (Y == 0) |
| 144 | return X < 0.0 ? 180.0 : 0.0; |
| 145 | |
| 146 | if ( Y > 0.0) |
| 147 | if (X > 0.0) |
| 148 | return atan(Y/X) * GRAD_PI;
|
| 149 | else
|
| 150 | return 180.0-atan(Y/-X) * GRAD_PI; |
| 151 | else
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| 152 | if (X > 0.0) |
| 153 | return 360.0-atan(-Y/X) * GRAD_PI; |
| 154 | else
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| 155 | return 180.0+atan(-Y/-X) * GRAD_PI; |
| 156 | } |
| 157 | |
| 158 | //! Calculates the angle of this vector in grad in the counter trigonometric sense.
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| 159 | //! \return Returns a value between 0 and 360.
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| 160 | inline float getAngle() const |
| 161 | {
|
| 162 | if (Y == 0.0) // corrected thanks to a suggestion by Jox |
| 163 | return X < 0.0 ? 180.0 : 0.0; |
| 164 | else if (X == 0.0) |
| 165 | return Y < 0.0 ? 90.0 : 270.0; |
| 166 | |
| 167 | float tmp = Y / sqrt(X*X + Y*Y);
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| 168 | tmp = atan(sqrt(1 - tmp*tmp) / tmp) * GRAD_PI;
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| 169 | |
| 170 | if (X>0.0 && Y>0.0) |
| 171 | return tmp + 270; |
| 172 | else
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| 173 | if (X>0.0 && Y<0.0) |
| 174 | return tmp + 90; |
| 175 | else
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| 176 | if (X<0.0 && Y<0.0) |
| 177 | return 90 - tmp; |
| 178 | else
|
| 179 | if (X<0.0 && Y>0.0) |
| 180 | return 270 - tmp; |
| 181 | |
| 182 | return tmp;
|
| 183 | } |
| 184 | |
| 185 | //! Calculates the angle between this vector and another one in grad.
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| 186 | //! \return Returns a value between 0 and 90.
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| 187 | inline float getAngleWith(const vector2d<T>& b) const |
| 188 | {
|
| 189 | float tmp = X*b.X + Y*b.Y;
|
| 190 | |
| 191 | if (tmp == 0.0) |
| 192 | return 90.0; |
| 193 | |
| 194 | tmp = tmp / sqrt((X*X + Y*Y) * (b.X*b.X + b.Y*b.Y)); |
| 195 | if (tmp < 0.0) tmp = -tmp; |
| 196 | |
| 197 | return atan(sqrt(1 - tmp*tmp) / tmp) * GRAD_PI; |
| 198 | } |
| 199 | |
| 200 | |
| 201 | //! returns interpolated vector
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| 202 | //! \param other: other vector to interpolate between
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| 203 | //! \param d: value between 0.0f and 1.0f.
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| 204 | vector2d<T> getInterpolated(const vector2d<T>& other, float d) const |
| 205 | {
|
| 206 | float inv = 1.0f - d; |
| 207 | return vector2d<T>(other.X*inv + X*d,
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| 208 | other.Y*inv + Y*d); |
| 209 | } |
| 210 | |
| 211 | //! Returns if this vector interpreted as a point is on a line between two other points.
|
| 212 | /** It is assumed that the point is on the line. */
|
| 213 | bool isBetweenPoints(const vector2d<T>& begin, const vector2d<T>& end) const |
| 214 | {
|
| 215 | float f = (float)(end - begin).getLengthSQ(); |
| 216 | return (float)getDistanceFromSQ(begin) < f && |
| 217 | (float)getDistanceFromSQ(end) < f;
|
| 218 | } |
| 219 | |
| 220 | static bool isOnSameSide(vector2d<T> p1, vector2d<T> p2, vector2d<T> a, vector2d<T> b) |
| 221 | {
|
| 222 | vector2d<T> ba = b - a; |
| 223 | |
| 224 | float cp1 = ba.crossProduct(p1-a);
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| 225 | float cp2 = ba.crossProduct(p2-a);
|
| 226 | |
| 227 | if (cp1*cp2 >= 0.0f) |
| 228 | return true; |
| 229 | else
|
| 230 | return false; |
| 231 | } |
| 232 | |
| 233 | |
| 234 | // member variables
|
| 235 | T X, Y; |
| 236 | }; |
| 237 | |
| 238 | //! Typedef for float 2d vector.
|
| 239 | typedef vector2d<float> vector2df; |
| 240 | //! Typedef for integer 2d vector.
|
| 241 | typedef vector2d<int> vector2di; |
| 242 | |
| 243 | #endif
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