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