[2746] | 1 | #ifndef _Vector3_h__
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| 2 | #define _Vector3_h__
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| 3 |
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[2911] | 4 |
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[2746] | 5 | #include "common.h"
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| 6 | #include <math.h>
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| 7 |
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| 8 |
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[2776] | 9 | namespace CHCDemoEngine
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[2756] | 10 | {
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| 11 |
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[2746] | 12 | // Forward-declare some other classes.
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| 13 | class Matrix4x4;
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| 14 |
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| 15 |
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| 16 | /** Vector class.
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| 17 | */
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| 18 | class Vector3
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| 19 | {
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| 20 | public:
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| 21 |
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| 22 | ///////////
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| 23 | //-- members;
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| 24 |
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| 25 | float x;
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| 26 | float y;
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| 27 | float z;
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| 28 |
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| 29 |
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| 30 | /////////////////////////
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| 31 |
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| 32 | void SetX(float q) { x = q; }
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| 33 | void SetY(float q) { y = q; }
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| 34 | void SetZ(float q) { z = q; }
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| 35 |
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| 36 | float GetX() const { return x; }
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| 37 | float GetY() const { return y; }
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| 38 | float GetZ() const { return z; }
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| 39 |
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| 40 |
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| 41 | //////////////
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| 42 | //-- constructors
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| 43 |
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| 44 | Vector3() { }
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| 45 |
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[2753] | 46 | Vector3(float x, float y, float z): x(x), y(y), z(z)
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| 47 | {}
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| 48 |
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[2916] | 49 | explicit Vector3(float v): x(v), y(v), z(v){}
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[2746] | 50 | /** Copy constructor.
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| 51 | */
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| 52 | Vector3(const Vector3 &v): x(v.x), y(v.y), z(v.z)
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| 53 | {}
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| 54 |
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| 55 | // Functions to get at the std::vector components
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| 56 | float& operator[] (const int inx)
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| 57 | {
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| 58 | return (&x)[inx];
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| 59 | }
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| 60 |
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| 61 | operator const float*() const
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| 62 | {
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| 63 | return (const float*) this;
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| 64 | }
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| 65 |
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| 66 | const float &operator[] (const int inx) const
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| 67 | {
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| 68 | return *(&x + inx);
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| 69 | }
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| 70 |
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| 71 | void ExtractVerts(float *px, float *py, int which) const;
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| 72 |
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| 73 | void SetValue(float a, float b, float c)
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| 74 | {
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| 75 | x = a; y = b; z = c;
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| 76 | }
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| 77 |
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| 78 | void SetValue(float a)
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| 79 | {
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| 80 | x = y = z = a;
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| 81 | }
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| 82 |
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[2920] | 83 |
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[2746] | 84 | /** Returns the axis, where the std::vector has the largest value.
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| 85 | */
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| 86 | int DrivingAxis(void) const;
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| 87 | /** returns the axis, where the std::vector has the smallest value
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| 88 | */
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| 89 | int TinyAxis(void) const;
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| 90 | /** Returns largest component in this vector
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| 91 | */
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| 92 | inline float MaxComponent(void) const
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| 93 | {
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| 94 | return (x > y) ? ( (x > z) ? x : z) : ( (y > z) ? y : z);
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| 95 | }
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| 96 | /** Returns copy of this vector where all components are positiv.
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| 97 | */
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| 98 | inline Vector3 Abs(void) const
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| 99 | {
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| 100 | return Vector3(fabs(x), fabs(y), fabs(z));
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| 101 | }
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[2752] | 102 | /** normalizes the std::vector of unit size corresponding to given std::vector
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| 103 | */
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[2746] | 104 | inline void Normalize();
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| 105 | /** Returns false if this std::vector has a nan component.
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| 106 | */
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| 107 | bool CheckValidity() const;
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| 108 | /**
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| 109 | Find a right handed coordinate system with (*this) being
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| 110 | the z-axis. For a right-handed system, U x V = (*this) holds.
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| 111 | This implementation is here to avoid inconsistence and confusion
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| 112 | when construction coordinate systems using ArbitraryNormal():
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| 113 | In fact:
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| 114 | V = ArbitraryNormal(N);
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| 115 | U = CrossProd(V,N);
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| 116 | constructs a right-handed coordinate system as well, BUT:
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| 117 | 1) bugs can be introduced if one mistakenly constructs a
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| 118 | left handed sytems e.g. by doing
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| 119 | U = ArbitraryNormal(N);
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| 120 | V = CrossProd(U,N);
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| 121 | 2) this implementation gives non-negative base vectors
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| 122 | for (*this)==(0,0,1) | (0,1,0) | (1,0,0), which is
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| 123 | good for debugging and is not the case with the implementation
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| 124 | using ArbitraryNormal()
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| 125 |
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| 126 | ===> Using ArbitraryNormal() for constructing coord systems
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| 127 | is obsoleted by this method (<JK> 12/20/03).
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| 128 | */
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| 129 | void RightHandedBase(Vector3& U, Vector3& V) const;
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[2752] | 130 |
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| 131 |
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| 132 | // Unary operators
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[2746] | 133 |
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[2752] | 134 | Vector3 operator+ () const;
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| 135 | Vector3 operator- () const;
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| 136 |
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| 137 | // Assignment operators
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| 138 |
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| 139 | Vector3& operator+= (const Vector3 &A);
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| 140 | Vector3& operator-= (const Vector3 &A);
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| 141 | Vector3& operator*= (const Vector3 &A);
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| 142 | Vector3& operator*= (float A);
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| 143 | Vector3& operator/= (float A);
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| 144 |
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[2920] | 145 | static inline Vector3 UNIT_X() { return Vector3(1, 0, 0); }
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| 146 | static inline Vector3 UNIT_Y() { return Vector3(0, 1, 0); }
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| 147 | static inline Vector3 UNIT_Z() { return Vector3(0, 0, 1); }
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| 148 | static inline Vector3 ZERO() { return Vector3(0, 0, 0); }
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[2752] | 149 |
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[2920] | 150 |
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[2752] | 151 | //////////
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| 152 | //-- friends
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| 153 |
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| 154 | /**
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| 155 | ===> Using ArbitraryNormal() for constructing coord systems
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| 156 | ===> is obsoleted by RightHandedBase() method (<JK> 12/20/03).
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| 157 |
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| 158 | Return an arbitrary normal to `v'.
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| 159 | In fact it tries v x (0,0,1) an if the result is too small,
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| 160 | it definitely does v x (0,1,0). It will always work for
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| 161 | non-degenareted std::vector and is much faster than to use
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| 162 | TangentVectors.
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| 163 |
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| 164 | @param v(in) The std::vector we want to find normal for.
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| 165 | @return The normal std::vector to v.
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| 166 | */
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| 167 | friend inline Vector3 ArbitraryNormal(const Vector3 &v);
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| 168 |
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[2746] | 169 | /// Transforms a std::vector to the global coordinate frame.
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| 170 | /**
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| 171 | Given a local coordinate frame (U,V,N) (i.e. U,V,N are
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| 172 | the x,y,z axes of the local coordinate system) and
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| 173 | a std::vector 'loc' in the local coordiante system, this
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| 174 | function returns a the coordinates of the same std::vector
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| 175 | in global frame (i.e. frame (1,0,0), (0,1,0), (0,0,1).
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| 176 | */
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| 177 | friend inline Vector3 ToGlobalFrame(const Vector3& loc,
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[2752] | 178 | const Vector3& U,
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| 179 | const Vector3& V,
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| 180 | const Vector3& N);
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[2746] | 181 |
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| 182 | /// Transforms a std::vector to a local coordinate frame.
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| 183 | /**
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| 184 | Given a local coordinate frame (U,V,N) (i.e. U,V,N are
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| 185 | the x,y,z axes of the local coordinate system) and
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| 186 | a std::vector 'loc' in the global coordiante system, this
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| 187 | function returns a the coordinates of the same std::vector
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| 188 | in the local frame.
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| 189 | */
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| 190 | friend inline Vector3 ToLocalFrame(const Vector3& loc,
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[2752] | 191 | const Vector3& U,
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| 192 | const Vector3& V,
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| 193 | const Vector3& N);
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[2746] | 194 |
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| 195 | /// the magnitude=size of the std::vector
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| 196 | friend inline float Magnitude(const Vector3 &v);
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| 197 | /// the squared magnitude of the std::vector .. for efficiency in some cases
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| 198 | friend inline float SqrMagnitude(const Vector3 &v);
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| 199 | /// Magnitude(v1-v2)
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| 200 | friend inline float Distance(const Vector3 &v1, const Vector3 &v2);
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| 201 | /// SqrMagnitude(v1-v2)
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| 202 | friend inline float SqrDistance(const Vector3 &v1, const Vector3 &v2);
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[2752] | 203 | /// creates the std::vector of unit size corresponding to given std::vector
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[2746] | 204 | friend inline Vector3 Normalize(const Vector3 &A);
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[2752] | 205 | /// // Rotate a direction vector
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[2746] | 206 | friend Vector3 PlaneRotate(const Matrix4x4 &, const Vector3 &);
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| 207 |
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| 208 | // construct view vectors .. DirAt is the main viewing direction
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| 209 | // Viewer is the coordinates of viewer location, UpL is the std::vector.
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| 210 | friend void ViewVectors(const Vector3 &DirAt,
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| 211 | const Vector3 &Viewer,
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| 212 | const Vector3 &UpL,
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| 213 | Vector3 &ViewV,
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| 214 | Vector3 &ViewU,
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| 215 | Vector3 &ViewN);
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| 216 |
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| 217 | // Given the intersection point `P', you have available normal `N'
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| 218 | // of unit length. Let us suppose the incoming ray has direction `D'.
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| 219 | // Then we can construct such two vectors `U' and `V' that
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| 220 | // `U',`N', and `D' are coplanar, and `V' is perpendicular
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| 221 | // to the vectors `N','D', and `V'. Then 'N', 'U', and 'V' create
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| 222 | // the orthonormal base in space R3.
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[2752] | 223 | friend void TangentVectors(Vector3 &U, Vector3 &V, // output
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[2746] | 224 | const Vector3 &normal, // input
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| 225 | const Vector3 &dirIncoming);
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| 226 |
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| 227 |
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| 228 | // Binary operators
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[2752] | 229 |
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[2746] | 230 | friend inline Vector3 operator+ (const Vector3 &A, const Vector3 &B);
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| 231 | friend inline Vector3 operator- (const Vector3 &A, const Vector3 &B);
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| 232 | friend inline Vector3 operator* (const Vector3 &A, const Vector3 &B);
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| 233 | friend inline Vector3 operator* (const Vector3 &A, float B);
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| 234 | friend inline Vector3 operator* (float A, const Vector3 &B);
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| 235 | friend Vector3 operator* (const Matrix4x4 &, const Vector3 &);
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| 236 | friend inline Vector3 operator/ (const Vector3 &A, const Vector3 &B);
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| 237 |
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| 238 | friend inline int operator< (const Vector3 &A, const Vector3 &B);
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| 239 | friend inline int operator<= (const Vector3 &A, const Vector3 &B);
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| 240 |
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| 241 | friend inline Vector3 operator/ (const Vector3 &A, float B);
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| 242 | friend inline int operator== (const Vector3 &A, const Vector3 &B);
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| 243 | friend inline float DotProd(const Vector3 &A, const Vector3 &B);
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| 244 | friend inline Vector3 CrossProd (const Vector3 &A, const Vector3 &B);
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| 245 |
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| 246 | friend std::ostream& operator<< (std::ostream &s, const Vector3 &A);
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| 247 | friend std::istream& operator>> (std::istream &s, Vector3 &A);
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| 248 |
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| 249 | friend void Minimize(Vector3 &min, const Vector3 &candidate);
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| 250 | friend void Maximize(Vector3 &max, const Vector3 &candidate);
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| 251 |
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| 252 | friend inline int EpsilonEqualV3(const Vector3 &v1, const Vector3 &v2, float thr);
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| 253 | friend inline int EpsilonEqualV3(const Vector3 &v1, const Vector3 &v2);
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| 254 |
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| 255 | friend Vector3 CosineRandomVector(const Vector3 &normal);
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| 256 | friend Vector3 UniformRandomVector(const Vector3 &normal);
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| 257 | friend Vector3 UniformRandomVector();
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| 258 |
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| 259 | friend Vector3 UniformRandomVector(float r1, float r2);
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| 260 |
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| 261 | friend Vector3 CosineRandomVector(float r1, float r2, const Vector3 &normal);
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| 262 | };
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| 263 |
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| 264 |
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| 265 |
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| 266 | // forward declaration
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| 267 | extern Vector3 UniformRandomVector(const Vector3 &normal);
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| 268 | extern Vector3 UniformRandomVector();
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| 269 | extern Vector3 UniformRandomVector(const float r1, const float r2);
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| 270 |
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| 271 | inline Vector3 ArbitraryNormal(const Vector3 &N)
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| 272 | {
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| 273 | float dist2 = N.x * N.x + N.y * N.y;
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| 274 |
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| 275 | if (dist2 > 0.0001f)
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| 276 | {
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| 277 | float inv_size = 1.0f / sqrtf(dist2);
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| 278 | return Vector3(N.y * inv_size, -N.x * inv_size, 0); // N x (0,0,1)
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| 279 | }
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| 280 |
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| 281 | float inv_size = 1.0f / sqrtf(N.z * N.z + N.x * N.x);
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| 282 | return Vector3(-N.z * inv_size, 0, N.x * inv_size); // N x (0,1,0)
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| 283 | }
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| 284 |
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| 285 |
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| 286 | inline void Vector3::RightHandedBase(Vector3& U, Vector3& V) const
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| 287 | {
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| 288 | // HACK
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| 289 | V = ArbitraryNormal(*this);
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| 290 | U = CrossProd(V, *this);
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| 291 | }
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| 292 |
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| 293 |
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| 294 | inline Vector3 ToGlobalFrame(const Vector3 &loc,
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| 295 | const Vector3 &U,
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| 296 | const Vector3 &V,
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| 297 | const Vector3 &N)
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| 298 | {
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| 299 | return loc.x * U + loc.y * V + loc.z * N;
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| 300 | }
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| 301 |
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| 302 |
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| 303 | inline Vector3 ToLocalFrame(const Vector3 &loc,
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| 304 | const Vector3 &U,
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| 305 | const Vector3 &V,
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| 306 | const Vector3 &N)
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| 307 | {
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| 308 | return Vector3(loc.x * U.x + loc.y * U.y + loc.z * U.z,
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| 309 | loc.x * V.x + loc.y * V.y + loc.z * V.z,
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| 310 | loc.x * N.x + loc.y * N.y + loc.z * N.z);
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| 311 | }
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| 312 |
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| 313 |
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| 314 | inline float Magnitude(const Vector3 &v)
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| 315 | {
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| 316 | return sqrtf(v.x * v.x + v.y * v.y + v.z * v.z);
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| 317 | }
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| 318 |
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| 319 |
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| 320 | inline float SqrMagnitude(const Vector3 &v)
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| 321 | {
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[2844] | 322 | return v.x * v.x + v.y * v.y + v.z * v.z;
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[2746] | 323 | }
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| 324 |
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| 325 |
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| 326 | inline float Distance(const Vector3 &v1, const Vector3 &v2)
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| 327 | {
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[2844] | 328 | //return sqrtf(sqrt(v1.x - v2.x) + sqrt(v1.y - v2.y) + sqrt(v1.z - v2.z));
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| 329 | return Magnitude(v1 - v2);
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[2746] | 330 | }
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| 331 |
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| 332 |
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| 333 | inline float SqrDistance(const Vector3 &v1, const Vector3 &v2)
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| 334 | {
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[2844] | 335 | //return sqrt(v1.x - v2.x) + sqrt(v1.y - v2.y) + sqrt(v1.z - v2.z);
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| 336 | return SqrMagnitude(v1 - v2);
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[2746] | 337 | }
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| 338 |
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| 339 |
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| 340 | inline Vector3 Normalize(const Vector3 &A)
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| 341 | {
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[2844] | 342 | return A * (1.0f / Magnitude(A));
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[2746] | 343 | }
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| 344 |
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| 345 |
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| 346 | inline float DotProd(const Vector3 &A, const Vector3 &B)
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| 347 | {
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[2844] | 348 | return A.x * B.x + A.y * B.y + A.z * B.z;
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[2746] | 349 | }
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| 350 |
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| 351 |
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| 352 | // angle between two vectors with respect to a surface normal in the
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| 353 | // range [0 .. 2 * pi]
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| 354 | inline float Angle(const Vector3 &A, const Vector3 &B, const Vector3 &norm)
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| 355 | {
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| 356 | Vector3 cross = CrossProd(A, B);
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| 357 |
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| 358 | float signedAngle;
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| 359 |
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| 360 | if (DotProd(cross, norm) > 0)
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| 361 | signedAngle = atan2(-Magnitude(CrossProd(A, B)), DotProd(A, B));
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| 362 | else
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| 363 | signedAngle = atan2(Magnitude(CrossProd(A, B)), DotProd(A, B));
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| 364 |
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| 365 | if (signedAngle < 0)
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[2751] | 366 | return 2 * M_PI + signedAngle;
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[2746] | 367 |
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| 368 | return signedAngle;
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| 369 | }
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| 370 |
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| 371 |
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| 372 | inline Vector3 Vector3::operator+() const
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| 373 | {
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| 374 | return *this;
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| 375 | }
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| 376 |
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| 377 |
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| 378 | inline Vector3 Vector3::operator-() const
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| 379 | {
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| 380 | return Vector3(-x, -y, -z);
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| 381 | }
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| 382 |
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| 383 |
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| 384 | inline Vector3 &Vector3::operator+=(const Vector3 &A)
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| 385 | {
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| 386 | x += A.x; y += A.y; z += A.z;
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| 387 | return *this;
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| 388 | }
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| 389 |
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| 390 |
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| 391 | inline Vector3& Vector3::operator-=(const Vector3 &A)
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| 392 | {
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| 393 | x -= A.x; y -= A.y; z -= A.z;
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| 394 |
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| 395 | return *this;
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| 396 | }
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| 397 |
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| 398 |
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| 399 | inline Vector3& Vector3::operator*= (float A)
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| 400 | {
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| 401 | x *= A; y *= A; z *= A;
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| 402 | return *this;
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| 403 | }
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| 404 |
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| 405 |
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| 406 | inline Vector3& Vector3::operator/=(float A)
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| 407 | {
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| 408 | float a = 1.0f / A;
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| 409 |
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| 410 | x *= a; y *= a; z *= a;
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| 411 |
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| 412 | return *this;
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| 413 | }
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| 414 |
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| 415 |
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| 416 | inline Vector3& Vector3::operator*= (const Vector3 &A)
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| 417 | {
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| 418 | x *= A.x; y *= A.y; z *= A.z;
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| 419 | return *this;
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| 420 | }
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| 421 |
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| 422 |
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| 423 | inline Vector3 operator+ (const Vector3 &A, const Vector3 &B)
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| 424 | {
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| 425 | return Vector3(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 |
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| 429 | inline Vector3 operator- (const Vector3 &A, const Vector3 &B)
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| 430 | {
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| 431 | return Vector3(A.x - B.x, A.y - B.y, A.z - B.z);
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| 432 | }
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| 433 |
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| 434 |
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| 435 | inline Vector3 operator* (const Vector3 &A, const Vector3 &B)
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| 436 | {
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| 437 | return Vector3(A.x * B.x, A.y * B.y, A.z * B.z);
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| 438 | }
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| 439 |
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| 440 |
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| 441 | inline Vector3 operator* (const Vector3 &A, float B)
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| 442 | {
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| 443 | return Vector3(A.x * B, A.y * B, A.z * B);
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| 444 | }
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| 445 |
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| 446 |
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| 447 | inline Vector3 operator* (float A, const Vector3 &B)
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| 448 | {
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| 449 | return Vector3(B.x * A, B.y * A, B.z * A);
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| 450 | }
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| 451 |
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| 452 |
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| 453 | inline Vector3 operator/ (const Vector3 &A, const Vector3 &B)
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| 454 | {
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| 455 | return Vector3(A.x / B.x, A.y / B.y, A.z / B.z);
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| 456 | }
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| 457 |
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| 458 |
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| 459 | inline Vector3 operator/ (const Vector3 &A, float B)
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| 460 | {
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| 461 | float b = 1.0f / B;
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| 462 | return Vector3(A.x * b, A.y * b, A.z * b);
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| 463 | }
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| 464 |
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| 465 |
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| 466 | inline int operator< (const Vector3 &A, const Vector3 &B)
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| 467 | {
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| 468 | return A.x < B.x && A.y < B.y && A.z < B.z;
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| 469 | }
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| 470 |
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| 471 |
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| 472 | inline int operator<= (const Vector3 &A, const Vector3 &B)
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| 473 | {
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| 474 | return A.x <= B.x && A.y <= B.y && A.z <= B.z;
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| 475 | }
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| 476 |
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| 477 |
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| 478 | // Might replace floating-point == with comparisons of
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| 479 | // magnitudes, if needed.
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| 480 | inline int operator== (const Vector3 &A, const Vector3 &B)
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| 481 | {
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| 482 | return (A.x == B.x) && (A.y == B.y) && (A.z == B.z);
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| 483 | }
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| 484 |
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| 485 |
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| 486 | inline Vector3 CrossProd (const Vector3 &A, const Vector3 &B)
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| 487 | {
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| 488 | return Vector3(A.y * B.z - A.z * B.y,
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| 489 | A.z * B.x - A.x * B.z,
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| 490 | A.x * B.y - A.y * B.x);
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| 491 | }
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| 492 |
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| 493 |
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| 494 | inline void Vector3::Normalize()
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| 495 | {
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| 496 | float sqrmag = x * x + y * y + z * z;
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| 497 |
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| 498 | if (sqrmag > 0.0f)
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| 499 | (*this) *= 1.0f / sqrtf(sqrmag);
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| 500 | }
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| 501 |
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| 502 |
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| 503 | // Overload << operator for C++-style output
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| 504 | inline std::ostream& operator<< (std::ostream &s, const Vector3 &A)
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| 505 | {
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| 506 | return s << "(" << A.x << ", " << A.y << ", " << A.z << ")";
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| 507 | }
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| 508 |
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| 509 |
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| 510 | // Overload >> operator for C++-style input
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| 511 | inline std::istream& operator>> (std::istream &s, Vector3 &A)
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| 512 | {
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| 513 | char a;
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| 514 | // read "(x, y, z)"
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| 515 | return s >> a >> A.x >> a >> A.y >> a >> A.z >> a;
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| 516 | }
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| 517 |
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| 518 |
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| 519 | inline int EpsilonEqualV3(const Vector3 &v1, const Vector3 &v2, float thr)
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| 520 | {
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| 521 | if (fabsf(v1.x-v2.x) > thr)
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| 522 | return false;
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| 523 | if (fabsf(v1.y-v2.y) > thr)
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| 524 | return false;
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| 525 | if (fabsf(v1.z-v2.z) > thr)
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| 526 | return false;
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| 527 |
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| 528 | return true;
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| 529 | }
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| 530 |
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| 531 |
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| 532 | inline int EpsilonEqualV3(const Vector3 &v1, const Vector3 &v2)
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| 533 | {
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| 534 | return EpsilonEqualV3(v1, v2, Limits::Small);
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| 535 | }
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| 536 |
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| 537 |
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[2751] | 538 | }
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[2746] | 539 |
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| 540 | #endif
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