[9ec35db] | 1 | #pragma once |
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| 2 | #include <math.hfa> |
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| 3 | #include <iostream.hfa> |
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| 4 | |
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[1dd929e] | 5 | trait zeroassn(otype T) { |
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| 6 | T ?=?(T&, zero_t); |
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| 7 | }; |
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| 8 | trait fromint(otype T) { |
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[9ec35db] | 9 | void ?{}(T&, int); |
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[1dd929e] | 10 | }; |
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| 11 | trait zero_assign(otype T) { |
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[9ec35db] | 12 | T ?=?(T&, zero_t); |
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[1dd929e] | 13 | }; |
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| 14 | trait subtract(otype T) { |
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[9ec35db] | 15 | T ?-?(T, T); |
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| 16 | T -?(T); |
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[1dd929e] | 17 | }; |
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| 18 | trait add(otype T) { |
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[9ec35db] | 19 | T ?+?(T, T); |
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[1dd929e] | 20 | }; |
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| 21 | trait multiply(otype T) { |
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[9ec35db] | 22 | T ?*?(T, T); |
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[1dd929e] | 23 | }; |
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| 24 | trait divide(otype T) { |
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[9ec35db] | 25 | T ?/?(T, T); |
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[1dd929e] | 26 | }; |
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| 27 | trait lessthan(otype T) { |
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[9ec35db] | 28 | int ?<?(T, T); |
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[1dd929e] | 29 | }; |
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| 30 | trait equality(otype T) { |
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| 31 | int ?==?(T, T); |
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| 32 | }; |
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| 33 | trait sqrt(otype T) { |
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[9ec35db] | 34 | T sqrt(T); |
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| 35 | }; |
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| 36 | |
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| 37 | static inline { |
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| 38 | // int |
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| 39 | int ?=?(int& n, zero_t) { return n = 0.f; } |
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| 40 | /* float */ |
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| 41 | void ?{}(float& a, int b) { a = b; } |
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| 42 | float ?=?(float& n, zero_t) { return n = 0.f; } |
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| 43 | /* double */ |
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| 44 | void ?{}(double& a, int b) { a = b; } |
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| 45 | double ?=?(double& n, zero_t) { return n = 0L; } |
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| 46 | // long double |
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| 47 | void ?{}(long double& a, int b) { a = b; } |
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| 48 | long double ?=?(long double& n, zero_t) { return n = 0L; } |
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| 49 | } |
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| 50 | |
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[1dd929e] | 51 | forall(otype T) { |
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[9ec35db] | 52 | struct vec2 { |
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| 53 | T x, y; |
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| 54 | }; |
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| 55 | } |
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| 56 | |
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[1dd929e] | 57 | forall(otype T) { |
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[9ec35db] | 58 | static inline { |
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| 59 | |
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| 60 | // Constructors |
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| 61 | |
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| 62 | void ?{}(vec2(T)& v, T x, T y) { |
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| 63 | v.[x, y] = [x, y]; |
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| 64 | } |
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[1dd929e] | 65 | |
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| 66 | forall(| zero_assign(T)) |
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[9ec35db] | 67 | void ?{}(vec2(T)& vec, zero_t) with (vec) { |
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| 68 | x = y = 0; |
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| 69 | } |
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[1dd929e] | 70 | |
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[9ec35db] | 71 | void ?{}(vec2(T)& vec, T val) with (vec) { |
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| 72 | x = y = val; |
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| 73 | } |
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[1dd929e] | 74 | |
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[9ec35db] | 75 | void ?{}(vec2(T)& vec, vec2(T) other) with (vec) { |
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| 76 | [x,y] = other.[x,y]; |
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| 77 | } |
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| 78 | |
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| 79 | // Assignment |
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| 80 | void ?=?(vec2(T)& vec, vec2(T) other) with (vec) { |
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| 81 | [x,y] = other.[x,y]; |
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| 82 | } |
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[1dd929e] | 83 | forall(| zero_assign(T)) |
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[9ec35db] | 84 | void ?=?(vec2(T)& vec, zero_t) with (vec) { |
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| 85 | x = y = 0; |
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| 86 | } |
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| 87 | |
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| 88 | // Primitive mathematical operations |
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| 89 | |
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| 90 | // Subtraction |
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[1dd929e] | 91 | |
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| 92 | forall(| subtract(T)) { |
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[9ec35db] | 93 | vec2(T) ?-?(vec2(T) u, vec2(T) v) { // TODO( can't make this const ref ) |
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| 94 | return [u.x - v.x, u.y - v.y]; |
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| 95 | } |
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| 96 | vec2(T)& ?-=?(vec2(T)& u, vec2(T) v) { |
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| 97 | u = u - v; |
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| 98 | return u; |
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| 99 | } |
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| 100 | vec2(T) -?(vec2(T)& v) with (v) { |
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| 101 | return [-x, -y]; |
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| 102 | } |
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[1dd929e] | 103 | } |
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[9ec35db] | 104 | |
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| 105 | // Addition |
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[1dd929e] | 106 | forall(| add(T)) { |
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[9ec35db] | 107 | vec2(T) ?+?(vec2(T) u, vec2(T) v) { // TODO( can't make this const ref ) |
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| 108 | return [u.x + v.x, u.y + v.y]; |
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| 109 | } |
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| 110 | vec2(T)& ?+=?(vec2(T)& u, vec2(T) v) { |
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| 111 | u = u + v; |
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| 112 | return u; |
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| 113 | } |
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[1dd929e] | 114 | } |
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[9ec35db] | 115 | |
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| 116 | // Scalar Multiplication |
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[1dd929e] | 117 | forall(| multiply(T)) { |
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[9ec35db] | 118 | vec2(T) ?*?(vec2(T) v, T scalar) with (v) { // TODO (can't make this const ref) |
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| 119 | return [x * scalar, y * scalar]; |
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| 120 | } |
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| 121 | vec2(T) ?*?(T scalar, vec2(T) v) { // TODO (can't make this const ref) |
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| 122 | return v * scalar; |
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| 123 | } |
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| 124 | vec2(T)& ?*=?(vec2(T)& v, T scalar) { |
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| 125 | v = v * scalar; |
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| 126 | return v; |
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| 127 | } |
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[1dd929e] | 128 | } |
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[9ec35db] | 129 | |
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| 130 | // Scalar Division |
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[1dd929e] | 131 | forall(| divide(T)) { |
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[9ec35db] | 132 | vec2(T) ?/?(vec2(T) v, T scalar) with (v) { |
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| 133 | return [x / scalar, y / scalar]; |
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| 134 | } |
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| 135 | vec2(T)& ?/=?(vec2(T)& v, T scalar) with (v) { |
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| 136 | v = v / scalar; |
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| 137 | return v; |
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| 138 | } |
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[1dd929e] | 139 | } |
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| 140 | |
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[9ec35db] | 141 | // Relational Operators |
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[1dd929e] | 142 | forall(| equality(T)) { |
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[9ec35db] | 143 | bool ?==?(vec2(T) u, vec2(T) v) with (u) { |
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| 144 | return x == v.x && y == v.y; |
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| 145 | } |
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| 146 | bool ?!=?(vec2(T) u, vec2(T) v) { |
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| 147 | return !(u == v); |
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| 148 | } |
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[1dd929e] | 149 | } |
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[9ec35db] | 150 | |
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[1dd929e] | 151 | forall(| add(T) | multiply(T)) |
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[9ec35db] | 152 | T dot(vec2(T) u, vec2(T) v) { |
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| 153 | return u.x * v.x + u.y * v.y; |
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| 154 | } |
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| 155 | |
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[1dd929e] | 156 | forall(| sqrt(T) | add(T) | multiply(T)) |
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[9ec35db] | 157 | T length(vec2(T) v) { |
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| 158 | return sqrt(dot(v, v)); |
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| 159 | } |
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| 160 | |
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[1dd929e] | 161 | forall(| add(T) | multiply(T)) |
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[9ec35db] | 162 | T length_squared(vec2(T) v) { |
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| 163 | return dot(v, v); |
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| 164 | } |
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| 165 | |
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[1dd929e] | 166 | forall(| subtract(T) | sqrt(T) | add(T) | multiply(T)) |
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[9ec35db] | 167 | T distance(vec2(T) v1, vec2(T) v2) { |
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| 168 | return length(v1 - v2); |
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| 169 | } |
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| 170 | |
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[1dd929e] | 171 | forall(| sqrt(T) | divide(T) | add(T) | multiply(T)) |
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[9ec35db] | 172 | vec2(T) normalize(vec2(T) v) { |
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| 173 | return v / sqrt(dot(v, v)); |
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| 174 | } |
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| 175 | |
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| 176 | // Project vector u onto vector v |
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[1dd929e] | 177 | forall(| sqrt(T) | divide(T) | add(T) | multiply(T)) |
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[9ec35db] | 178 | vec2(T) project(vec2(T) u, vec2(T) v) { |
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| 179 | vec2(T) v_norm = normalize(v); |
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| 180 | return v_norm * dot(u, v_norm); |
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| 181 | } |
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| 182 | |
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| 183 | // Reflect incident vector v with respect to surface with normal n |
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[1dd929e] | 184 | forall(| sqrt(T) | divide(T) | add(T) | multiply(T) | subtract(T) | fromint(T)) |
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[9ec35db] | 185 | vec2(T) reflect(vec2(T) v, vec2(T) n) { |
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| 186 | return v - (T){2} * project(v, n); |
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| 187 | } |
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| 188 | |
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| 189 | // Refract incident vector v with respect to surface with normal n |
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| 190 | // eta is the ratio of indices of refraction between starting material and |
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| 191 | // entering material (i.e., from air to water, eta = 1/1.33) |
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| 192 | // v and n must already be normalized |
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[1dd929e] | 193 | forall(| sqrt(T) | add(T) | multiply(T) | subtract(T) | fromint(T) | lessthan(T) | zeroassn(T)) |
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[9ec35db] | 194 | vec2(T) refract(vec2(T) v, vec2(T) n, T eta) { |
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| 195 | T dotValue = dot(n, v); |
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| 196 | T k = (T){1} - eta * eta * ((T){1} - dotValue * dotValue); |
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| 197 | if (k < (T){0}) { |
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| 198 | return 0; |
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| 199 | } |
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| 200 | return eta * v - (eta * dotValue + sqrt(k)) * n; |
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| 201 | } |
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| 202 | |
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| 203 | // Given a perturbed normal and a geometric normal, |
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| 204 | // flip the perturbed normal if the geometric normal is pointing away |
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| 205 | // from the observer. |
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| 206 | // n is the perturbed vector that we want to align |
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| 207 | // i is the incident vector |
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| 208 | // ng is the geometric normal of the surface |
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[1dd929e] | 209 | forall(| add(T) | multiply(T) | lessthan(T) | fromint(T) | subtract(T)) |
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[9ec35db] | 210 | vec2(T) faceforward(vec2(T) n, vec2(T) i, vec2(T) ng) { |
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| 211 | return dot(ng, i) < (T){0} ? n : -n; |
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| 212 | } |
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[1dd929e] | 213 | |
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[9ec35db] | 214 | } |
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| 215 | } |
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| 216 | |
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[d131480] | 217 | forall(dtype ostype, otype T | writeable(T, ostype)) { |
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[9ec35db] | 218 | ostype & ?|?( ostype & os, vec2(T) v) with (v) { |
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| 219 | return os | '<' | x | ',' | y | '>'; |
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| 220 | } |
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| 221 | void ?|?( ostype & os, vec2(T) v ) with (v) { |
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| 222 | (ostype &)(os | v); ends(os); |
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| 223 | } |
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| 224 | } |
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