1 // Copyright (C) 2002-2012 Nikolaus Gebhardt
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2 // This file is part of the "Irrlicht Engine".
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3 // For conditions of distribution and use, see copyright notice in irrlicht.h
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5 #ifndef __IRR_POINT_3D_H_INCLUDED__
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6 #define __IRR_POINT_3D_H_INCLUDED__
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15 //! 3d vector template class with lots of operators and methods.
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16 /** The vector3d class is used in Irrlicht for three main purposes:
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17 1) As a direction vector (most of the methods assume this).
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18 2) As a position in 3d space (which is synonymous with a direction vector from the origin to this position).
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19 3) To hold three Euler rotations, where X is pitch, Y is yaw and Z is roll.
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25 //! Default constructor (null vector).
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26 vector3d() : X(0), Y(0), Z(0) {}
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27 //! Constructor with three different values
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28 vector3d(T nx, T ny, T nz) : X(nx), Y(ny), Z(nz) {}
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29 //! Constructor with the same value for all elements
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30 explicit vector3d(T n) : X(n), Y(n), Z(n) {}
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34 vector3d<T> operator-() const { return vector3d<T>(-X, -Y, -Z); }
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36 vector3d<T> operator+(const vector3d<T>& other) const { return vector3d<T>(X + other.X, Y + other.Y, Z + other.Z); }
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37 vector3d<T>& operator+=(const vector3d<T>& other) { X+=other.X; Y+=other.Y; Z+=other.Z; return *this; }
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38 vector3d<T> operator+(const T val) const { return vector3d<T>(X + val, Y + val, Z + val); }
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39 vector3d<T>& operator+=(const T val) { X+=val; Y+=val; Z+=val; return *this; }
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41 vector3d<T> operator-(const vector3d<T>& other) const { return vector3d<T>(X - other.X, Y - other.Y, Z - other.Z); }
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42 vector3d<T>& operator-=(const vector3d<T>& other) { X-=other.X; Y-=other.Y; Z-=other.Z; return *this; }
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43 vector3d<T> operator-(const T val) const { return vector3d<T>(X - val, Y - val, Z - val); }
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44 vector3d<T>& operator-=(const T val) { X-=val; Y-=val; Z-=val; return *this; }
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46 vector3d<T> operator*(const vector3d<T>& other) const { return vector3d<T>(X * other.X, Y * other.Y, Z * other.Z); }
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47 vector3d<T>& operator*=(const vector3d<T>& other) { X*=other.X; Y*=other.Y; Z*=other.Z; return *this; }
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48 vector3d<T> operator*(const T v) const { return vector3d<T>(X * v, Y * v, Z * v); }
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49 vector3d<T>& operator*=(const T v) { X*=v; Y*=v; Z*=v; return *this; }
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51 vector3d<T> operator/(const vector3d<T>& other) const { return vector3d<T>(X / other.X, Y / other.Y, Z / other.Z); }
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52 vector3d<T>& operator/=(const vector3d<T>& other) { X/=other.X; Y/=other.Y; Z/=other.Z; return *this; }
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53 vector3d<T> operator/(const T v) const { T i=(T)1.0/v; return vector3d<T>(X * i, Y * i, Z * i); }
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54 vector3d<T>& operator/=(const T v) { T i=(T)1.0/v; X*=i; Y*=i; Z*=i; return *this; }
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56 T& operator [](u32 index)
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58 _IRR_DEBUG_BREAK_IF(index>2) // access violation
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63 const T& operator [](u32 index) const
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65 _IRR_DEBUG_BREAK_IF(index>2) // access violation
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70 //! sort in order X, Y, Z. Equality with rounding tolerance.
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71 bool operator<=(const vector3d<T>&other) const
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73 return (X<other.X || core::equals(X, other.X)) ||
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74 (core::equals(X, other.X) && (Y<other.Y || core::equals(Y, other.Y))) ||
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75 (core::equals(X, other.X) && core::equals(Y, other.Y) && (Z<other.Z || core::equals(Z, other.Z)));
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78 //! sort in order X, Y, Z. Equality with rounding tolerance.
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79 bool operator>=(const vector3d<T>&other) const
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81 return (X>other.X || core::equals(X, other.X)) ||
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82 (core::equals(X, other.X) && (Y>other.Y || core::equals(Y, other.Y))) ||
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83 (core::equals(X, other.X) && core::equals(Y, other.Y) && (Z>other.Z || core::equals(Z, other.Z)));
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86 //! sort in order X, Y, Z. Difference must be above rounding tolerance.
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87 bool operator<(const vector3d<T>&other) const
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89 return (X<other.X && !core::equals(X, other.X)) ||
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90 (core::equals(X, other.X) && Y<other.Y && !core::equals(Y, other.Y)) ||
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91 (core::equals(X, other.X) && core::equals(Y, other.Y) && Z<other.Z && !core::equals(Z, other.Z));
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94 //! sort in order X, Y, Z. Difference must be above rounding tolerance.
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95 bool operator>(const vector3d<T>&other) const
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97 return (X>other.X && !core::equals(X, other.X)) ||
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98 (core::equals(X, other.X) && Y>other.Y && !core::equals(Y, other.Y)) ||
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99 (core::equals(X, other.X) && core::equals(Y, other.Y) && Z>other.Z && !core::equals(Z, other.Z));
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102 //! use weak float compare
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103 bool operator==(const vector3d<T>& other) const
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105 return this->equals(other);
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108 bool operator!=(const vector3d<T>& other) const
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110 return !this->equals(other);
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115 //! returns if this vector equals the other one, taking floating point rounding errors into account
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116 bool equals(const vector3d<T>& other, const T tolerance = (T)ROUNDING_ERROR_f32 ) const
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118 return core::equals(X, other.X, tolerance) &&
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119 core::equals(Y, other.Y, tolerance) &&
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120 core::equals(Z, other.Z, tolerance);
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123 vector3d<T>& set(const T nx, const T ny, const T nz) {X=nx; Y=ny; Z=nz; return *this;}
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124 vector3d<T>& set(const vector3d<T>& p) {X=p.X; Y=p.Y; Z=p.Z;return *this;}
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126 //! Get length of the vector.
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127 T getLength() const { return core::squareroot( X*X + Y*Y + Z*Z ); }
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129 //! Get squared length of the vector.
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130 /** This is useful because it is much faster than getLength().
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131 \return Squared length of the vector. */
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132 T getLengthSQ() const { return X*X + Y*Y + Z*Z; }
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134 //! Get the dot product with another vector.
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135 T dotProduct(const vector3d<T>& other) const
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137 return X*other.X + Y*other.Y + Z*other.Z;
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140 //! Get distance from another point.
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141 /** Here, the vector is interpreted as point in 3 dimensional space. */
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142 T getDistanceFrom(const vector3d<T>& other) const
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144 return vector3d<T>(X - other.X, Y - other.Y, Z - other.Z).getLength();
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147 //! Returns squared distance from another point.
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148 /** Here, the vector is interpreted as point in 3 dimensional space. */
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149 T getDistanceFromSQ(const vector3d<T>& other) const
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151 return vector3d<T>(X - other.X, Y - other.Y, Z - other.Z).getLengthSQ();
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154 //! Calculates the cross product with another vector.
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155 /** \param p Vector to multiply with.
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156 \return Crossproduct of this vector with p. */
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157 vector3d<T> crossProduct(const vector3d<T>& p) const
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159 return vector3d<T>(Y * p.Z - Z * p.Y, Z * p.X - X * p.Z, X * p.Y - Y * p.X);
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162 //! Returns if this vector interpreted as a point is on a line between two other points.
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163 /** It is assumed that the point is on the line.
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164 \param begin Beginning vector to compare between.
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165 \param end Ending vector to compare between.
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166 \return True if this vector is between begin and end, false if not. */
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167 bool isBetweenPoints(const vector3d<T>& begin, const vector3d<T>& end) const
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169 const T f = (end - begin).getLengthSQ();
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170 return getDistanceFromSQ(begin) <= f &&
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171 getDistanceFromSQ(end) <= f;
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174 //! Normalizes the vector.
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175 /** In case of the 0 vector the result is still 0, otherwise
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176 the length of the vector will be 1.
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177 \return Reference to this vector after normalization. */
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178 vector3d<T>& normalize()
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180 f64 length = X*X + Y*Y + Z*Z;
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181 if (length == 0 ) // this check isn't an optimization but prevents getting NAN in the sqrt.
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183 length = core::reciprocal_squareroot(length);
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185 X = (T)(X * length);
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186 Y = (T)(Y * length);
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187 Z = (T)(Z * length);
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191 //! Sets the length of the vector to a new value
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192 vector3d<T>& setLength(T newlength)
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195 return (*this *= newlength);
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198 //! Inverts the vector.
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199 vector3d<T>& invert()
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207 //! Rotates the vector by a specified number of degrees around the Y axis and the specified center.
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208 /** \param degrees Number of degrees to rotate around the Y axis.
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209 \param center The center of the rotation. */
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210 void rotateXZBy(f64 degrees, const vector3d<T>& center=vector3d<T>())
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212 degrees *= DEGTORAD64;
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213 f64 cs = cos(degrees);
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214 f64 sn = sin(degrees);
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217 set((T)(X*cs - Z*sn), Y, (T)(X*sn + Z*cs));
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222 //! Rotates the vector by a specified number of degrees around the Z axis and the specified center.
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223 /** \param degrees: Number of degrees to rotate around the Z axis.
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224 \param center: The center of the rotation. */
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225 void rotateXYBy(f64 degrees, const vector3d<T>& center=vector3d<T>())
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227 degrees *= DEGTORAD64;
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228 f64 cs = cos(degrees);
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229 f64 sn = sin(degrees);
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232 set((T)(X*cs - Y*sn), (T)(X*sn + Y*cs), Z);
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237 //! Rotates the vector by a specified number of degrees around the X axis and the specified center.
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238 /** \param degrees: Number of degrees to rotate around the X axis.
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239 \param center: The center of the rotation. */
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240 void rotateYZBy(f64 degrees, const vector3d<T>& center=vector3d<T>())
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242 degrees *= DEGTORAD64;
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243 f64 cs = cos(degrees);
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244 f64 sn = sin(degrees);
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247 set(X, (T)(Y*cs - Z*sn), (T)(Y*sn + Z*cs));
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252 //! Creates an interpolated vector between this vector and another vector.
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253 /** \param other The other vector to interpolate with.
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254 \param d Interpolation value between 0.0f (all the other vector) and 1.0f (all this vector).
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255 Note that this is the opposite direction of interpolation to getInterpolated_quadratic()
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256 \return An interpolated vector. This vector is not modified. */
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257 vector3d<T> getInterpolated(const vector3d<T>& other, f64 d) const
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259 const f64 inv = 1.0 - d;
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260 return vector3d<T>((T)(other.X*inv + X*d), (T)(other.Y*inv + Y*d), (T)(other.Z*inv + Z*d));
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263 //! Creates a quadratically interpolated vector between this and two other vectors.
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264 /** \param v2 Second vector to interpolate with.
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265 \param v3 Third vector to interpolate with (maximum at 1.0f)
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266 \param d Interpolation value between 0.0f (all this vector) and 1.0f (all the 3rd vector).
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267 Note that this is the opposite direction of interpolation to getInterpolated() and interpolate()
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268 \return An interpolated vector. This vector is not modified. */
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269 vector3d<T> getInterpolated_quadratic(const vector3d<T>& v2, const vector3d<T>& v3, f64 d) const
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271 // this*(1-d)*(1-d) + 2 * v2 * (1-d) + v3 * d * d;
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272 const f64 inv = (T) 1.0 - d;
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273 const f64 mul0 = inv * inv;
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274 const f64 mul1 = (T) 2.0 * d * inv;
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275 const f64 mul2 = d * d;
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277 return vector3d<T> ((T)(X * mul0 + v2.X * mul1 + v3.X * mul2),
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278 (T)(Y * mul0 + v2.Y * mul1 + v3.Y * mul2),
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279 (T)(Z * mul0 + v2.Z * mul1 + v3.Z * mul2));
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282 //! Sets this vector to the linearly interpolated vector between a and b.
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283 /** \param a first vector to interpolate with, maximum at 1.0f
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284 \param b second vector to interpolate with, maximum at 0.0f
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285 \param d Interpolation value between 0.0f (all vector b) and 1.0f (all vector a)
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286 Note that this is the opposite direction of interpolation to getInterpolated_quadratic()
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288 vector3d<T>& interpolate(const vector3d<T>& a, const vector3d<T>& b, f64 d)
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290 X = (T)((f64)b.X + ( ( a.X - b.X ) * d ));
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291 Y = (T)((f64)b.Y + ( ( a.Y - b.Y ) * d ));
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292 Z = (T)((f64)b.Z + ( ( a.Z - b.Z ) * d ));
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297 //! Get the rotations that would make a (0,0,1) direction vector point in the same direction as this direction vector.
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298 /** Thanks to Arras on the Irrlicht forums for this method. This utility method is very useful for
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299 orienting scene nodes towards specific targets. For example, if this vector represents the difference
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300 between two scene nodes, then applying the result of getHorizontalAngle() to one scene node will point
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301 it at the other one.
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303 // Where target and seeker are of type ISceneNode*
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304 const vector3df toTarget(target->getAbsolutePosition() - seeker->getAbsolutePosition());
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305 const vector3df requiredRotation = toTarget.getHorizontalAngle();
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306 seeker->setRotation(requiredRotation);
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308 \return A rotation vector containing the X (pitch) and Y (raw) rotations (in degrees) that when applied to a
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309 +Z (e.g. 0, 0, 1) direction vector would make it point in the same direction as this vector. The Z (roll) rotation
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310 is always 0, since two Euler rotations are sufficient to point in any given direction. */
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311 vector3d<T> getHorizontalAngle() const
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315 // tmp avoids some precision troubles on some compilers when working with T=s32
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316 f64 tmp = (atan2((f64)X, (f64)Z) * RADTODEG64);
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321 if (angle.Y >= 360)
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324 const f64 z1 = core::squareroot(X*X + Z*Z);
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326 tmp = (atan2((f64)z1, (f64)Y) * RADTODEG64 - 90.0);
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331 if (angle.X >= 360)
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337 //! Get the spherical coordinate angles
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338 /** This returns Euler degrees for the point represented by
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339 this vector. The calculation assumes the pole at (0,1,0) and
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340 returns the angles in X and Y.
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342 vector3d<T> getSphericalCoordinateAngles() const
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345 const f64 length = X*X + Y*Y + Z*Z;
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351 angle.Y = (T)(atan2((f64)Z,(f64)X) * RADTODEG64);
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356 angle.X = (T)(acos(Y * core::reciprocal_squareroot(length)) * RADTODEG64);
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361 //! Builds a direction vector from (this) rotation vector.
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362 /** This vector is assumed to be a rotation vector composed of 3 Euler angle rotations, in degrees.
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363 The implementation performs the same calculations as using a matrix to do the rotation.
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365 \param[in] forwards The direction representing "forwards" which will be rotated by this vector.
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366 If you do not provide a direction, then the +Z axis (0, 0, 1) will be assumed to be forwards.
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367 \return A direction vector calculated by rotating the forwards direction by the 3 Euler angles
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368 (in degrees) represented by this vector. */
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369 vector3d<T> rotationToDirection(const vector3d<T> & forwards = vector3d<T>(0, 0, 1)) const
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371 const f64 cr = cos( core::DEGTORAD64 * X );
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372 const f64 sr = sin( core::DEGTORAD64 * X );
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373 const f64 cp = cos( core::DEGTORAD64 * Y );
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374 const f64 sp = sin( core::DEGTORAD64 * Y );
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375 const f64 cy = cos( core::DEGTORAD64 * Z );
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376 const f64 sy = sin( core::DEGTORAD64 * Z );
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378 const f64 srsp = sr*sp;
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379 const f64 crsp = cr*sp;
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381 const f64 pseudoMatrix[] = {
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382 ( cp*cy ), ( cp*sy ), ( -sp ),
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383 ( srsp*cy-cr*sy ), ( srsp*sy+cr*cy ), ( sr*cp ),
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384 ( crsp*cy+sr*sy ), ( crsp*sy-sr*cy ), ( cr*cp )};
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386 return vector3d<T>(
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387 (T)(forwards.X * pseudoMatrix[0] +
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388 forwards.Y * pseudoMatrix[3] +
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389 forwards.Z * pseudoMatrix[6]),
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390 (T)(forwards.X * pseudoMatrix[1] +
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391 forwards.Y * pseudoMatrix[4] +
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392 forwards.Z * pseudoMatrix[7]),
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393 (T)(forwards.X * pseudoMatrix[2] +
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394 forwards.Y * pseudoMatrix[5] +
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395 forwards.Z * pseudoMatrix[8]));
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398 //! Fills an array of 4 values with the vector data (usually floats).
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399 /** Useful for setting in shader constants for example. The fourth value
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400 will always be 0. */
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401 void getAs4Values(T* array) const
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409 //! Fills an array of 3 values with the vector data (usually floats).
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410 /** Useful for setting in shader constants for example.*/
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411 void getAs3Values(T* array) const
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419 //! X coordinate of the vector
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422 //! Y coordinate of the vector
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425 //! Z coordinate of the vector
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429 //! partial specialization for integer vectors
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430 // Implementer note: inline keyword needed due to template specialization for s32. Otherwise put specialization into a .cpp
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432 inline vector3d<s32> vector3d<s32>::operator /(s32 val) const {return core::vector3d<s32>(X/val,Y/val,Z/val);}
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434 inline vector3d<s32>& vector3d<s32>::operator /=(s32 val) {X/=val;Y/=val;Z/=val; return *this;}
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437 inline vector3d<s32> vector3d<s32>::getSphericalCoordinateAngles() const
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439 vector3d<s32> angle;
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440 const f64 length = X*X + Y*Y + Z*Z;
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446 angle.Y = round32((f32)(atan2((f64)Z,(f64)X) * RADTODEG64));
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451 angle.X = round32((f32)(acos(Y * core::reciprocal_squareroot(length)) * RADTODEG64));
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456 //! Typedef for a f32 3d vector.
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457 typedef vector3d<f32> vector3df;
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459 //! Typedef for an integer 3d vector.
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460 typedef vector3d<s32> vector3di;
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462 //! Function multiplying a scalar and a vector component-wise.
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463 template<class S, class T>
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464 vector3d<T> operator*(const S scalar, const vector3d<T>& vector) { return vector*scalar; }
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466 } // end namespace core
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467 } // end namespace irr
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projects / irrlicht.git / blob