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