1 | #ifndef _Vector3_h__
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2 | #define _Vector3_h__
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3 |
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4 | #include <iostream>
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5 | using namespace std;
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6 | #include <math.h>
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7 | #include "common.h"
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8 |
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9 |
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10 | namespace GtpVisibilityPreprocessor {
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11 |
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12 | // Forward-declare some other classes.
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13 | class Matrix4x4;
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14 | class Vector2;
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15 |
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16 |
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17 | // HACK of returning vector components as array fields.
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18 | // NOT guarrantied to work with some strange variable allignment !
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19 | #define __VECTOR_HACK
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20 |
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21 | class Vector3
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22 | {
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23 | public:
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24 | float x, y, z;
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25 |
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26 | // for compatibility with pascal's code
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27 | void setX(float q) { x=q; }
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28 | void setY(float q) { y=q; }
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29 | void setZ(float q) { z=q; }
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30 | float getX() const { return x; }
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31 | float getY() const { return y; }
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32 | float getZ() const { return z; }
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33 |
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34 | // constructors
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35 | Vector3() { }
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36 |
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37 | Vector3(float X, float Y, float Z) { x = X; y = Y; z = Z; }
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38 | Vector3(float X) { x = y = z = X; }
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39 | Vector3(const Vector3 &v) { x = v.x; y = v.y; z = v.z; }
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40 |
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41 | // Functions to get at the vector components
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42 | float& operator[] (int inx) {
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43 | #ifndef __VECTOR_HACK
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44 | if (inx == 0)
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45 | return x;
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46 | else
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47 | if (inx == 1)
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48 | return y;
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49 | else
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50 | return z;
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51 | #else
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52 | return (&x)[inx];
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53 | #endif
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54 |
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55 | }
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56 |
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57 | #ifdef __VECTOR_HACK
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58 | operator const float*() const { return (const float*) this; }
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59 | #endif
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60 |
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61 | const float& operator[] (int inx) const {
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62 | #ifndef __VECTOR_HACK
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63 | if (inx == 0)
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64 | return x;
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65 | else
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66 | if (inx == 1)
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67 | return y;
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68 | else
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69 | return z;
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70 | #else
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71 | return *(&x+inx);
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72 | #endif
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73 | }
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74 |
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75 | void ExtractVerts(float *px, float *py, int which) const;
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76 |
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77 | void SetValue(const float &a, const float &b, const float &c)
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78 | { x=a; y=b; z=c; }
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79 |
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80 | void SetValue(const float a) { x = y = z = a; }
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81 |
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82 | // returns the axis, where the vector has the largest value
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83 | int DrivingAxis(void) const;
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84 |
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85 | // returns the axis, where the vector has the smallest value
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86 | int TinyAxis(void) const;
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87 |
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88 | inline float MaxComponent(void) const {
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89 | // return (x > y && x > z) ? x : ((y > z) ? y : z);
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90 | return (x > y) ? ( (x > z) ? x : z) : ( (y > z) ? y : z);
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91 | }
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92 |
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93 | inline Vector3 Abs(void) const {
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94 | return Vector3(fabs(x), fabs(y), fabs(z));
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95 | }
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96 |
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97 | // normalizes the vector of unit size corresponding to given vector
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98 | inline void Normalize();
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99 |
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100 | /**
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101 | ===> Using ArbitraryNormal() for constructing coord systems
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102 | ===> is obsoleted by RightHandedBase() method (<JK> 12/20/03).
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103 |
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104 | Return an arbitrary normal to `v'.
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105 | In fact it tries v x (0,0,1) an if the result is too small,
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106 | it definitely does v x (0,1,0). It will always work for
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107 | non-degenareted vector and is much faster than to use
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108 | TangentVectors.
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109 |
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110 | @param v(in) The vector we want to find normal for.
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111 | @return The normal vector to v.
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112 | */
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113 | friend inline Vector3 ArbitraryNormal(const Vector3 &v);
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114 |
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115 | /**
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116 | Find a right handed coordinate system with (*this) being
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117 | the z-axis. For a right-handed system, U x V = (*this) holds.
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118 | This implementation is here to avoid inconsistence and confusion
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119 | when construction coordinate systems using ArbitraryNormal():
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120 | In fact:
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121 | V = ArbitraryNormal(N);
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122 | U = CrossProd(V,N);
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123 | constructs a right-handed coordinate system as well, BUT:
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124 | 1) bugs can be introduced if one mistakenly constructs a
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125 | left handed sytems e.g. by doing
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126 | U = ArbitraryNormal(N);
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127 | V = CrossProd(U,N);
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128 | 2) this implementation gives non-negative base vectors
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129 | for (*this)==(0,0,1) | (0,1,0) | (1,0,0), which is
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130 | good for debugging and is not the case with the implementation
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131 | using ArbitraryNormal()
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132 |
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133 | ===> Using ArbitraryNormal() for constructing coord systems
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134 | is obsoleted by this method (<JK> 12/20/03).
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135 | */
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136 | void RightHandedBase(Vector3& U, Vector3& V) const;
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137 |
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138 | /// Transforms a vector to the global coordinate frame.
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139 | /**
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140 | Given a local coordinate frame (U,V,N) (i.e. U,V,N are
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141 | the x,y,z axes of the local coordinate system) and
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142 | a vector 'loc' in the local coordiante system, this
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143 | function returns a the coordinates of the same vector
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144 | in global frame (i.e. frame (1,0,0), (0,1,0), (0,0,1).
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145 | */
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146 | friend inline Vector3 ToGlobalFrame(const Vector3& loc,
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147 | const Vector3& U,
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148 | const Vector3& V,
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149 | const Vector3& N);
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150 |
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151 | /// Transforms a vector to a local coordinate frame.
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152 | /**
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153 | Given a local coordinate frame (U,V,N) (i.e. U,V,N are
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154 | the x,y,z axes of the local coordinate system) and
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155 | a vector 'loc' in the global coordiante system, this
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156 | function returns a the coordinates of the same vector
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157 | in the local frame.
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158 | */
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159 | friend inline Vector3 ToLocalFrame(const Vector3& loc,
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160 | const Vector3& U,
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161 | const Vector3& V,
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162 | const Vector3& N);
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163 |
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164 | /// the magnitude=size of the vector
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165 | friend inline float Magnitude(const Vector3 &v);
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166 | /// the squared magnitude of the vector .. for efficiency in some cases
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167 | friend inline float SqrMagnitude(const Vector3 &v);
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168 | /// Magnitude(v1-v2)
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169 | friend inline float Distance(const Vector3 &v1, const Vector3 &v2);
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170 | /// SqrMagnitude(v1-v2)
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171 | friend inline float SqrDistance(const Vector3 &v1, const Vector3 &v2);
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172 |
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173 | // creates the vector of unit size corresponding to given vector
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174 | friend inline Vector3 Normalize(const Vector3 &A);
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175 |
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176 | // Rotate a normal vector.
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177 | friend Vector3 PlaneRotate(const Matrix4x4 &, const Vector3 &);
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178 |
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179 | // construct view vectors .. DirAt is the main viewing direction
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180 | // Viewer is the coordinates of viewer location, UpL is the vector.
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181 | friend void ViewVectors(const Vector3 &DirAt, const Vector3 &Viewer,
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182 | const Vector3 &UpL, Vector3 &ViewV,
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183 | Vector3 &ViewU, Vector3 &ViewN );
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184 |
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185 | // Given the intersection point `P', you have available normal `N'
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186 | // of unit length. Let us suppose the incoming ray has direction `D'.
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187 | // Then we can construct such two vectors `U' and `V' that
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188 | // `U',`N', and `D' are coplanar, and `V' is perpendicular
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189 | // to the vectors `N','D', and `V'. Then 'N', 'U', and 'V' create
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190 | // the orthonormal base in space R3.
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191 | friend void TangentVectors(Vector3 &U, Vector3 &V, // output
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192 | const Vector3 &normal, // input
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193 | const Vector3 &dirIncoming);
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194 | // Unary operators
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195 | Vector3 operator+ () const;
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196 | Vector3 operator- () const;
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197 |
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198 | // Assignment operators
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199 | Vector3& operator+= (const Vector3 &A);
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200 | Vector3& operator-= (const Vector3 &A);
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201 | Vector3& operator*= (const Vector3 &A);
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202 | Vector3& operator*= (float A);
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203 | Vector3& operator/= (float A);
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204 |
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205 | // Binary operators
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206 | friend inline Vector3 operator+ (const Vector3 &A, const Vector3 &B);
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207 | friend inline Vector3 operator- (const Vector3 &A, const Vector3 &B);
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208 | friend inline Vector3 operator* (const Vector3 &A, const Vector3 &B);
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209 | friend inline Vector3 operator* (const Vector3 &A, float B);
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210 | friend inline Vector3 operator* (float A, const Vector3 &B);
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211 | friend Vector3 operator* (const Matrix4x4 &, const Vector3 &);
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212 | friend inline Vector3 operator/ (const Vector3 &A, const Vector3 &B);
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213 |
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214 | friend inline int operator< (const Vector3 &A, const Vector3 &B);
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215 | friend inline int operator<= (const Vector3 &A, const Vector3 &B);
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216 |
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217 | friend inline Vector3 operator/ (const Vector3 &A, float B);
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218 | friend inline int operator== (const Vector3 &A, const Vector3 &B);
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219 | friend inline float DotProd(const Vector3 &A, const Vector3 &B);
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220 | friend inline Vector3 CrossProd (const Vector3 &A, const Vector3 &B);
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221 |
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222 | friend ostream& operator<< (ostream &s, const Vector3 &A);
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223 | friend istream& operator>> (istream &s, Vector3 &A);
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224 |
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225 | friend void Minimize(Vector3 &min, const Vector3 &candidate);
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226 | friend void Maximize(Vector3 &max, const Vector3 &candidate);
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227 |
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228 | friend inline int EpsilonEqualV3(const Vector3 &v1, const Vector3 &v2, float thr);
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229 | friend inline int EpsilonEqualV3(const Vector3 &v1, const Vector3 &v2);
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230 |
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231 | friend Vector3 UniformRandomVector(const Vector3 &normal);
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232 | friend Vector3 UniformRandomVector();
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233 |
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234 |
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235 | };
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236 |
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237 | inline Vector3
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238 | ArbitraryNormal(const Vector3 &N)
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239 | {
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240 | float dist2 = N.x * N.x + N.y * N.y;
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241 | if (dist2 > 0.0001) {
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242 | float inv_size = 1.0f/sqrtf(dist2);
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243 | return Vector3(N.y * inv_size, -N.x * inv_size, 0); // N x (0,0,1)
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244 | }
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245 | float inv_size = 1.0f/sqrtf(N.z * N.z + N.x * N.x);
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246 | return Vector3(-N.z * inv_size, 0, N.x * inv_size); // N x (0,1,0)
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247 | }
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248 |
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249 |
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250 | inline Vector3
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251 | ToGlobalFrame(const Vector3 &loc,
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252 | const Vector3 &U,
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253 | const Vector3 &V,
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254 | const Vector3 &N)
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255 | {
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256 | return loc.x * U + loc.y * V + loc.z * N;
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257 | }
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258 |
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259 | inline Vector3
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260 | ToLocalFrame(const Vector3 &loc,
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261 | const Vector3 &U,
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262 | const Vector3 &V,
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263 | const Vector3 &N)
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264 | {
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265 | return Vector3( loc.x * U.x + loc.y * U.y + loc.z * U.z,
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266 | loc.x * V.x + loc.y * V.y + loc.z * V.z,
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267 | loc.x * N.x + loc.y * N.y + loc.z * N.z);
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268 | }
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269 |
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270 | inline float
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271 | Magnitude(const Vector3 &v)
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272 | {
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273 | return sqrtf(v.x * v.x + v.y * v.y + v.z * v.z);
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274 | }
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275 |
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276 | inline float
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277 | SqrMagnitude(const Vector3 &v)
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278 | {
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279 | return v.x * v.x + v.y * v.y + v.z * v.z;
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280 | }
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281 |
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282 | inline float
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283 | Distance(const Vector3 &v1, const Vector3 &v2)
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284 | {
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285 | return sqrtf(sqr(v1.x-v2.x) + sqr(v1.y-v2.y) + sqr(v1.z-v2.z));
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286 | }
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287 |
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288 | inline float
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289 | SqrDistance(const Vector3 &v1, const Vector3 &v2)
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290 | {
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291 | return sqr(v1.x-v2.x)+sqr(v1.y-v2.y)+sqr(v1.z-v2.z);
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292 | }
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293 |
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294 | inline Vector3
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295 | Normalize(const Vector3 &A)
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296 | {
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297 | return A * (1.0f/Magnitude(A));
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298 | }
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299 |
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300 | inline float
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301 | DotProd(const Vector3 &A, const Vector3 &B)
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302 | {
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303 | return A.x * B.x + A.y * B.y + A.z * B.z;
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304 | }
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305 |
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306 | // angle between two vectors with respect to a surface normal in the
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307 | // range [0 .. 2 * pi]
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308 | inline float
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309 | Angle(const Vector3 &A, const Vector3 &B, const Vector3 &norm)
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310 | {
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311 | Vector3 cross = CrossProd(A, B);
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312 |
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313 | float signedAngle;
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314 |
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315 | if (DotProd(cross, norm) > 0)
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316 | signedAngle = atan2(-Magnitude(CrossProd(A, B)), DotProd(A, B));
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317 | else
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318 | signedAngle = atan2(Magnitude(CrossProd(A, B)), DotProd(A, B));
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319 |
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320 | if (signedAngle < 0)
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321 | return 2 * PI + signedAngle;
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322 |
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323 | return signedAngle;
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324 | }
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325 |
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326 | inline Vector3
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327 | Vector3::operator+() const
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328 | {
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329 | return *this;
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330 | }
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331 |
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332 | inline Vector3
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333 | Vector3::operator-() const
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334 | {
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335 | return Vector3(-x, -y, -z);
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336 | }
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337 |
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338 | inline Vector3&
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339 | Vector3::operator+=(const Vector3 &A)
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340 | {
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341 | x += A.x; y += A.y; z += A.z;
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342 | return *this;
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343 | }
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344 |
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345 | inline Vector3&
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346 | Vector3::operator-=(const Vector3 &A)
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347 | {
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348 | x -= A.x; y -= A.y; z -= A.z;
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349 | return *this;
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350 | }
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351 |
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352 | inline Vector3&
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353 | Vector3::operator*= (float A)
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354 | {
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355 | x *= A; y *= A; z *= A;
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356 | return *this;
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357 | }
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358 |
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359 | inline Vector3&
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360 | Vector3::operator/=(float A)
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361 | {
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362 | float a = 1.0f/A;
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363 | x *= a; y *= a; z *= a;
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364 | return *this;
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365 | }
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366 |
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367 | inline Vector3&
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368 | Vector3::operator*= (const Vector3 &A)
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369 | {
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370 | x *= A.x; y *= A.y; z *= A.z;
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371 | return *this;
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372 | }
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373 |
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374 | inline Vector3
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375 | operator+ (const Vector3 &A, const Vector3 &B)
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376 | {
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377 | return Vector3(A.x + B.x, A.y + B.y, A.z + B.z);
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378 | }
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379 |
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380 | inline Vector3
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381 | operator- (const Vector3 &A, const Vector3 &B)
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382 | {
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383 | return Vector3(A.x - B.x, A.y - B.y, A.z - B.z);
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384 | }
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385 |
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386 | inline Vector3
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387 | operator* (const Vector3 &A, const Vector3 &B)
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388 | {
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389 | return Vector3(A.x * B.x, A.y * B.y, A.z * B.z);
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390 | }
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391 |
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392 | inline Vector3
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393 | operator* (const Vector3 &A, float B)
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394 | {
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395 | return Vector3(A.x * B, A.y * B, A.z * B);
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396 | }
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397 |
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398 | inline Vector3
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399 | operator* (float A, const Vector3 &B)
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400 | {
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401 | return Vector3(B.x * A, B.y * A, B.z * A);
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402 | }
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403 |
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404 | inline Vector3
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405 | operator/ (const Vector3 &A, const Vector3 &B)
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406 | {
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407 | return Vector3(A.x / B.x, A.y / B.y, A.z / B.z);
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408 | }
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409 |
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410 | inline Vector3
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411 | operator/ (const Vector3 &A, float B)
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412 | {
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413 | float b = 1.0f / B;
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414 | return Vector3(A.x * b, A.y * b, A.z * b);
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415 | }
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416 |
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417 | inline int
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418 | operator< (const Vector3 &A, const Vector3 &B)
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419 | {
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420 | return A.x < B.x && A.y < B.y && A.z < B.z;
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421 | }
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422 |
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423 | inline int
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424 | operator<= (const Vector3 &A, const Vector3 &B)
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425 | {
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426 | return A.x <= B.x && A.y <= B.y && A.z <= B.z;
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427 | }
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428 |
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429 | // Might replace floating-point == with comparisons of
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430 | // magnitudes, if needed.
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431 | inline int operator== (const Vector3 &A, const Vector3 &B)
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432 | {
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433 | return (A.x == B.x) && (A.y == B.y) && (A.z == B.z);
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434 | }
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435 |
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436 | inline Vector3
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437 | CrossProd (const Vector3 &A, const Vector3 &B)
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438 | {
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439 | return
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440 | Vector3(A.y * B.z - A.z * B.y,
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441 | A.z * B.x - A.x * B.z,
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442 | A.x * B.y - A.y * B.x);
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443 | }
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444 |
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445 | inline void
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446 | Vector3::Normalize()
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447 | {
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448 | float sqrmag = x * x + y * y + z * z;
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449 | if (sqrmag > 0.0f)
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450 | (*this) *= 1.0f / sqrtf(sqrmag);
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451 | }
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452 |
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453 |
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454 | // Overload << operator for C++-style output
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455 | inline ostream&
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456 | operator<< (ostream &s, const Vector3 &A)
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457 | {
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458 | return s << "(" << A.x << ", " << A.y << ", " << A.z << ")";
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459 | }
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460 |
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461 | // Overload >> operator for C++-style input
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462 | inline istream&
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463 | operator>> (istream &s, Vector3 &A)
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464 | {
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465 | char a;
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466 | // read "(x, y, z)"
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467 | return s >> a >> A.x >> a >> A.y >> a >> A.z >> a;
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468 | }
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469 |
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470 | inline int
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471 | EpsilonEqualV3(const Vector3 &v1, const Vector3 &v2, float thr)
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472 | {
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473 | if ( fabsf(v1.x-v2.x) > thr )
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474 | return false;
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475 | if ( fabsf(v1.y-v2.y) > thr )
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476 | return false;
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477 | if ( fabsf(v1.z-v2.z) > thr )
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478 | return false;
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479 | return true;
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480 | }
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481 |
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482 | inline int
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483 | EpsilonEqualV3(const Vector3 &v1, const Vector3 &v2)
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484 | {
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485 | return EpsilonEqualV3(v1, v2, Limits::Small);
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486 | }
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487 |
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488 |
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489 |
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490 | }
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491 |
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492 | #endif
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