[3012] | 1 | #ifndef _SimpleVec_h__
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| 2 | #define _SimpleVec_h__
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| 3 |
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| 4 |
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| 5 | #include <math.h>
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| 6 | #include <vector>
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| 7 | #include <iostream>
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| 8 |
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| 9 |
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| 10 | /** Vector class.
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| 11 | */
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| 12 | class SimpleVec
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| 13 | {
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| 14 | public:
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| 15 |
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| 16 | ///////////
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| 17 | //-- members;
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| 18 |
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| 19 | float x;
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| 20 | float y;
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| 21 | float z;
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| 22 |
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| 23 |
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| 24 | /////////////////////////
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| 25 |
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| 26 | void SetX(float q) { x = q; }
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| 27 | void SetY(float q) { y = q; }
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| 28 | void SetZ(float q) { z = q; }
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| 29 |
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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 |
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| 35 | //////////////
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| 36 | //-- constructors
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| 37 |
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| 38 | SimpleVec() { }
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| 39 |
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| 40 | SimpleVec(float x, float y, float z): x(x), y(y), z(z)
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| 41 | {}
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| 42 |
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| 43 | explicit SimpleVec(float v): x(v), y(v), z(v){}
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| 44 | /** Copy constructor.
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| 45 | */
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| 46 | SimpleVec(const SimpleVec &v): x(v.x), y(v.y), z(v.z)
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| 47 | {}
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| 48 |
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| 49 | // Functions to get at the std::vector components
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| 50 | float& operator[] (const int inx)
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| 51 | {
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| 52 | return (&x)[inx];
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| 53 | }
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| 54 |
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| 55 | operator const float*() const
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| 56 | {
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| 57 | return (const float*) this;
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| 58 | }
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| 59 |
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| 60 | const float &operator[] (const int inx) const
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| 61 | {
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| 62 | return *(&x + inx);
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| 63 | }
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| 64 |
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| 65 | void ExtractVerts(float *px, float *py, int which) const;
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| 66 |
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| 67 | void SetValue(float a, float b, float c)
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| 68 | {
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| 69 | x = a; y = b; z = c;
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| 70 | }
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| 71 |
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| 72 | void SetValue(float a)
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| 73 | {
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| 74 | x = y = z = a;
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| 75 | }
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| 76 |
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| 77 |
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| 78 | /** Returns the axis, where the std::vector has the largest value.
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| 79 | */
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| 80 | int DrivingAxis(void) const;
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| 81 | /** returns the axis, where the std::vector has the smallest value
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| 82 | */
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| 83 | int TinyAxis(void) const;
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| 84 | /** Returns largest component in this vector
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| 85 | */
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| 86 | inline float MaxComponent(void) const
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| 87 | {
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| 88 | return (x > y) ? ( (x > z) ? x : z) : ( (y > z) ? y : z);
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| 89 | }
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| 90 | /** Returns copy of this vector where all components are positiv.
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| 91 | */
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| 92 | inline SimpleVec Abs(void) const
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| 93 | {
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| 94 | return SimpleVec(fabs(x), fabs(y), fabs(z));
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| 95 | }
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| 96 | /** normalizes the std::vector of unit size corresponding to given std::vector
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| 97 | */
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| 98 | inline void Normalize();
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| 99 | /** Returns false if this std::vector has a nan component.
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| 100 | */
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| 101 | bool CheckValidity() const;
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| 102 | /**
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| 103 | Find a right handed coordinate system with (*this) being
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| 104 | the z-axis. For a right-handed system, U x V = (*this) holds.
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| 105 | This implementation is here to avoid inconsistence and confusion
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| 106 | when construction coordinate systems using ArbitraryNormal():
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| 107 | In fact:
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| 108 | V = ArbitraryNormal(N);
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| 109 | U = CrossProd(V,N);
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| 110 | constructs a right-handed coordinate system as well, BUT:
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| 111 | 1) bugs can be introduced if one mistakenly constructs a
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| 112 | left handed sytems e.g. by doing
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| 113 | U = ArbitraryNormal(N);
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| 114 | V = CrossProd(U,N);
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| 115 | 2) this implementation gives non-negative base vectors
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| 116 | for (*this)==(0,0,1) | (0,1,0) | (1,0,0), which is
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| 117 | good for debugging and is not the case with the implementation
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| 118 | using ArbitraryNormal()
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| 119 |
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| 120 | ===> Using ArbitraryNormal() for constructing coord systems
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| 121 | is obsoleted by this method (<JK> 12/20/03).
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| 122 | */
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| 123 | void RightHandedBase(SimpleVec& U, SimpleVec& V) const;
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| 124 |
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| 125 |
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| 126 | // Unary operators
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| 127 |
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| 128 | SimpleVec operator+ () const;
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| 129 | SimpleVec operator- () const;
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| 130 |
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| 131 | // Assignment operators
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| 132 |
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| 133 | SimpleVec& operator+= (const SimpleVec &A);
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| 134 | SimpleVec& operator-= (const SimpleVec &A);
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| 135 | SimpleVec& operator*= (const SimpleVec &A);
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| 136 | SimpleVec& operator*= (float A);
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| 137 | SimpleVec& operator/= (float A);
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| 138 |
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| 139 | static inline SimpleVec UNIT_X() { return SimpleVec(1, 0, 0); }
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| 140 | static inline SimpleVec UNIT_Y() { return SimpleVec(0, 1, 0); }
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| 141 | static inline SimpleVec UNIT_Z() { return SimpleVec(0, 0, 1); }
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| 142 | static inline SimpleVec ZERO() { return SimpleVec(0, 0, 0); }
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| 143 |
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| 144 |
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| 145 | //////////
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| 146 | //-- friends
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| 147 |
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| 148 | /**
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| 149 | ===> Using ArbitraryNormal() for constructing coord systems
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| 150 | ===> is obsoleted by RightHandedBase() method (<JK> 12/20/03).
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| 151 |
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| 152 | Return an arbitrary normal to `v'.
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| 153 | In fact it tries v x (0,0,1) an if the result is too small,
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| 154 | it definitely does v x (0,1,0). It will always work for
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| 155 | non-degenareted std::vector and is much faster than to use
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| 156 | TangentVectors.
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| 157 |
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| 158 | @param v(in) The std::vector we want to find normal for.
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| 159 | @return The normal std::vector to v.
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| 160 | */
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| 161 | friend inline SimpleVec ArbitraryNormal(const SimpleVec &v);
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| 162 |
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| 163 | /// Transforms a std::vector to the global coordinate frame.
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| 164 | /**
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| 165 | Given a local coordinate frame (U,V,N) (i.e. U,V,N are
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| 166 | the x,y,z axes of the local coordinate system) and
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| 167 | a std::vector 'loc' in the local coordiante system, this
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| 168 | function returns a the coordinates of the same std::vector
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| 169 | in global frame (i.e. frame (1,0,0), (0,1,0), (0,0,1).
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| 170 | */
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| 171 | friend inline SimpleVec ToGlobalFrame(const SimpleVec& loc,
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| 172 | const SimpleVec& U,
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| 173 | const SimpleVec& V,
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| 174 | const SimpleVec& N);
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| 175 |
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| 176 | /// Transforms a std::vector to a local coordinate frame.
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| 177 | /**
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| 178 | Given a local coordinate frame (U,V,N) (i.e. U,V,N are
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| 179 | the x,y,z axes of the local coordinate system) and
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| 180 | a std::vector 'loc' in the global coordiante system, this
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| 181 | function returns a the coordinates of the same std::vector
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| 182 | in the local frame.
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| 183 | */
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| 184 | friend inline SimpleVec ToLocalFrame(const SimpleVec& loc,
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| 185 | const SimpleVec& U,
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| 186 | const SimpleVec& V,
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| 187 | const SimpleVec& N);
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| 188 |
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| 189 | /// the magnitude=size of the std::vector
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| 190 | friend inline float Magnitude(const SimpleVec &v);
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| 191 | /// the squared magnitude of the std::vector .. for efficiency in some cases
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| 192 | friend inline float SqrMagnitude(const SimpleVec &v);
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| 193 | /// Magnitude(v1-v2)
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| 194 | friend inline float Distance(const SimpleVec &v1, const SimpleVec &v2);
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| 195 | /// SqrMagnitude(v1-v2)
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| 196 | friend inline float SqrDistance(const SimpleVec &v1, const SimpleVec &v2);
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| 197 | /// creates the std::vector of unit size corresponding to given std::vector
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| 198 | friend inline SimpleVec Normalize(const SimpleVec &A);
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| 199 |
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| 200 |
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| 201 | // construct view vectors .. DirAt is the main viewing direction
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| 202 | // Viewer is the coordinates of viewer location, UpL is the std::vector.
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| 203 | friend void ViewVectors(const SimpleVec &DirAt,
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| 204 | const SimpleVec &Viewer,
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| 205 | const SimpleVec &UpL,
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| 206 | SimpleVec &ViewV,
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| 207 | SimpleVec &ViewU,
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| 208 | SimpleVec &ViewN);
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| 209 |
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| 210 | // Given the intersection point `P', you have available normal `N'
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| 211 | // of unit length. Let us suppose the incoming ray has direction `D'.
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| 212 | // Then we can construct such two vectors `U' and `V' that
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| 213 | // `U',`N', and `D' are coplanar, and `V' is perpendicular
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| 214 | // to the vectors `N','D', and `V'. Then 'N', 'U', and 'V' create
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| 215 | // the orthonormal base in space R3.
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| 216 | friend void TangentVectors(SimpleVec &U, SimpleVec &V, // output
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| 217 | const SimpleVec &normal, // input
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| 218 | const SimpleVec &dirIncoming);
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| 219 |
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| 220 |
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| 221 | // Binary operators
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| 222 |
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| 223 | friend inline SimpleVec operator+ (const SimpleVec &A, const SimpleVec &B);
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| 224 | friend inline SimpleVec operator- (const SimpleVec &A, const SimpleVec &B);
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| 225 | friend inline SimpleVec operator* (const SimpleVec &A, const SimpleVec &B);
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| 226 | friend inline SimpleVec operator* (const SimpleVec &A, float B);
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| 227 | friend inline SimpleVec operator* (float A, const SimpleVec &B);
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| 228 | friend inline SimpleVec operator/ (const SimpleVec &A, const SimpleVec &B);
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| 229 |
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| 230 | friend inline int operator< (const SimpleVec &A, const SimpleVec &B);
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| 231 | friend inline int operator<= (const SimpleVec &A, const SimpleVec &B);
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| 232 |
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| 233 | friend inline SimpleVec operator/ (const SimpleVec &A, float B);
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| 234 | friend inline int operator== (const SimpleVec &A, const SimpleVec &B);
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| 235 | friend inline float DotProd(const SimpleVec &A, const SimpleVec &B);
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| 236 | friend inline SimpleVec CrossProd (const SimpleVec &A, const SimpleVec &B);
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| 237 |
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| 238 | friend std::ostream& operator<< (std::ostream &s, const SimpleVec &A);
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| 239 | friend std::istream& operator>> (std::istream &s, SimpleVec &A);
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| 240 |
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| 241 | friend void Minimize(SimpleVec &min, const SimpleVec &candidate);
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| 242 | friend void Maximize(SimpleVec &max, const SimpleVec &candidate);
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| 243 |
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| 244 | friend inline int EpsilonEqualV3(const SimpleVec &v1, const SimpleVec &v2, float thr);
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| 245 | friend inline int EpsilonEqualV3(const SimpleVec &v1, const SimpleVec &v2);
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| 246 | };
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| 247 |
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| 248 |
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| 249 | inline SimpleVec ArbitraryNormal(const SimpleVec &N)
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| 250 | {
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| 251 | float dist2 = N.x * N.x + N.y * N.y;
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| 252 |
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| 253 | if (dist2 > 0.0001f)
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| 254 | {
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| 255 | float inv_size = 1.0f / sqrtf(dist2);
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| 256 | return SimpleVec(N.y * inv_size, -N.x * inv_size, 0); // N x (0,0,1)
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| 257 | }
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| 258 |
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| 259 | float inv_size = 1.0f / sqrtf(N.z * N.z + N.x * N.x);
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| 260 | return SimpleVec(-N.z * inv_size, 0, N.x * inv_size); // N x (0,1,0)
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| 261 | }
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| 262 |
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| 263 |
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| 264 |
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| 265 | inline float Magnitude(const SimpleVec &v)
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| 266 | {
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| 267 | return sqrtf(v.x * v.x + v.y * v.y + v.z * v.z);
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| 268 | }
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| 269 |
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| 270 |
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| 271 | inline float SqrMagnitude(const SimpleVec &v)
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| 272 | {
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| 273 | return 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 |
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| 277 | inline float Distance(const SimpleVec &v1, const SimpleVec &v2)
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| 278 | {
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| 279 | //return sqrtf(sqrt(v1.x - v2.x) + sqrt(v1.y - v2.y) + sqrt(v1.z - v2.z));
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| 280 | return Magnitude(v1 - v2);
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| 281 | }
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| 282 |
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| 283 |
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| 284 | inline float SqrDistance(const SimpleVec &v1, const SimpleVec &v2)
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| 285 | {
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| 286 | //return sqrt(v1.x - v2.x) + sqrt(v1.y - v2.y) + sqrt(v1.z - v2.z);
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| 287 | return SqrMagnitude(v1 - v2);
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| 288 | }
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| 289 |
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| 290 |
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| 291 | inline SimpleVec Normalize(const SimpleVec &A)
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| 292 | {
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| 293 | return A * (1.0f / Magnitude(A));
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| 294 | }
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| 295 |
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| 296 |
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| 297 | inline float DotProd(const SimpleVec &A, const SimpleVec &B)
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| 298 | {
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| 299 | return A.x * B.x + A.y * B.y + A.z * B.z;
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| 300 | }
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| 301 |
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| 302 |
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| 303 | // angle between two vectors with respect to a surface normal in the
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| 304 | // range [0 .. 2 * pi]
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| 305 | inline float Angle(const SimpleVec &A, const SimpleVec &B, const SimpleVec &norm)
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| 306 | {
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| 307 | SimpleVec cross = CrossProd(A, B);
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| 308 |
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| 309 | float signedAngle;
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| 310 |
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| 311 | if (DotProd(cross, norm) > 0)
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| 312 | signedAngle = atan2(-Magnitude(CrossProd(A, B)), DotProd(A, B));
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| 313 | else
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| 314 | signedAngle = atan2(Magnitude(CrossProd(A, B)), DotProd(A, B));
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| 315 |
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| 316 | if (signedAngle < 0)
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| 317 | return 2 * 3.145f + signedAngle;
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| 318 |
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| 319 | return signedAngle;
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| 320 | }
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| 321 |
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| 322 |
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| 323 | inline SimpleVec SimpleVec::operator+() const
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| 324 | {
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| 325 | return *this;
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| 326 | }
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| 327 |
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| 328 |
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| 329 | inline SimpleVec SimpleVec::operator-() const
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| 330 | {
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| 331 | return SimpleVec(-x, -y, -z);
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| 332 | }
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| 333 |
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| 334 |
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| 335 | inline SimpleVec &SimpleVec::operator+=(const SimpleVec &A)
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| 336 | {
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| 337 | x += A.x; y += A.y; z += A.z;
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| 338 | return *this;
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| 339 | }
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| 340 |
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| 341 |
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| 342 | inline SimpleVec& SimpleVec::operator-=(const SimpleVec &A)
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| 343 | {
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| 344 | x -= A.x; y -= A.y; z -= A.z;
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| 345 |
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| 346 | return *this;
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| 347 | }
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| 348 |
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| 349 |
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| 350 | inline SimpleVec& SimpleVec::operator*= (float A)
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| 351 | {
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| 352 | x *= A; y *= A; z *= A;
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| 353 | return *this;
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| 354 | }
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| 355 |
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| 356 |
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| 357 | inline SimpleVec& SimpleVec::operator/=(float A)
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| 358 | {
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| 359 | float a = 1.0f / A;
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| 360 |
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| 361 | x *= a; y *= a; z *= a;
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| 362 |
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| 363 | return *this;
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| 364 | }
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| 365 |
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| 366 |
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| 367 | inline SimpleVec& SimpleVec::operator*= (const SimpleVec &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 |
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| 374 | inline SimpleVec operator+ (const SimpleVec &A, const SimpleVec &B)
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| 375 | {
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| 376 | return SimpleVec(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 |
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| 380 | inline SimpleVec operator- (const SimpleVec &A, const SimpleVec &B)
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| 381 | {
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| 382 | return SimpleVec(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 |
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| 386 | inline SimpleVec operator* (const SimpleVec &A, const SimpleVec &B)
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| 387 | {
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| 388 | return SimpleVec(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 |
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| 392 | inline SimpleVec operator* (const SimpleVec &A, float B)
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| 393 | {
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| 394 | return SimpleVec(A.x * B, A.y * B, A.z * B);
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| 395 | }
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| 396 |
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| 397 |
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| 398 | inline SimpleVec operator* (float A, const SimpleVec &B)
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| 399 | {
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| 400 | return SimpleVec(B.x * A, B.y * A, B.z * A);
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| 401 | }
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| 402 |
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| 403 |
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| 404 | inline SimpleVec operator/ (const SimpleVec &A, const SimpleVec &B)
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| 405 | {
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| 406 | return SimpleVec(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 |
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| 410 | inline SimpleVec operator/ (const SimpleVec &A, float B)
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| 411 | {
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| 412 | float b = 1.0f / B;
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| 413 | return SimpleVec(A.x * b, A.y * b, A.z * b);
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| 414 | }
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| 415 |
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| 416 |
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| 417 | inline int operator< (const SimpleVec &A, const SimpleVec &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 |
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| 423 | inline int operator<= (const SimpleVec &A, const SimpleVec &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 |
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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 SimpleVec &A, const SimpleVec &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 |
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| 437 | inline SimpleVec CrossProd (const SimpleVec &A, const SimpleVec &B)
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| 438 | {
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| 439 | return SimpleVec(A.y * B.z - A.z * B.y,
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| 440 | A.z * B.x - A.x * B.z,
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| 441 | A.x * B.y - A.y * B.x);
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| 442 | }
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| 443 |
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| 444 |
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| 445 | inline void SimpleVec::Normalize()
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| 446 | {
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| 447 | float sqrmag = x * x + y * y + z * z;
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| 448 |
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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 std::ostream& operator<< (std::ostream &s, const SimpleVec &A)
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| 456 | {
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| 457 | return s << "(" << A.x << ", " << A.y << ", " << A.z << ")";
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| 458 | }
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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 std::istream& operator>> (std::istream &s, SimpleVec &A)
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| 463 | {
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| 464 | char a;
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| 465 | // read "(x, y, z)"
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| 466 | return s >> a >> A.x >> a >> A.y >> a >> A.z >> a;
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| 467 | }
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| 468 |
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| 469 |
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| 470 | inline int EpsilonEqualV3(const SimpleVec &v1, const SimpleVec &v2, float thr)
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| 471 | {
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| 472 | if (fabsf(v1.x-v2.x) > thr)
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| 473 | return false;
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| 474 | if (fabsf(v1.y-v2.y) > thr)
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| 475 | return false;
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| 476 | if (fabsf(v1.z-v2.z) > thr)
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| 477 | return false;
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| 478 |
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| 479 | return true;
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| 480 | }
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| 481 |
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| 482 |
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| 483 | inline int EpsilonEqualV3(const SimpleVec &v1, const SimpleVec &v2)
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| 484 | {
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| 485 | return EpsilonEqualV3(v1, v2, 1e-6f);
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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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