[9ec35db] | 1 | #pragma once |
---|
| 2 | #include <math.hfa> |
---|
| 3 | #include <iostream.hfa> |
---|
| 4 | |
---|
| 5 | trait vec2_t(otype T) { |
---|
| 6 | void ?{}(T&, int); |
---|
| 7 | T ?=?(T&, zero_t); |
---|
| 8 | T ?-?(T, T); |
---|
| 9 | T -?(T); |
---|
| 10 | T ?+?(T, T); |
---|
| 11 | T ?*?(T, T); |
---|
| 12 | T ?/?(T, T); |
---|
| 13 | int ?==?(T, T); |
---|
| 14 | int ?<?(T, T); |
---|
| 15 | T sqrt(T); |
---|
| 16 | }; |
---|
| 17 | |
---|
| 18 | static inline { |
---|
| 19 | // int |
---|
| 20 | int ?=?(int& n, zero_t) { return n = 0.f; } |
---|
| 21 | int sqrt(int a) { return sqrt((float)a); } |
---|
| 22 | /* float */ |
---|
| 23 | void ?{}(float& a, int b) { a = b; } |
---|
| 24 | float ?=?(float& n, zero_t) { return n = 0.f; } |
---|
| 25 | /* double */ |
---|
| 26 | void ?{}(double& a, int b) { a = b; } |
---|
| 27 | double ?=?(double& n, zero_t) { return n = 0L; } |
---|
| 28 | // long double |
---|
| 29 | void ?{}(long double& a, int b) { a = b; } |
---|
| 30 | long double ?=?(long double& n, zero_t) { return n = 0L; } |
---|
| 31 | } |
---|
| 32 | |
---|
| 33 | forall(otype T | vec2_t(T)) { |
---|
| 34 | struct vec2 { |
---|
| 35 | T x, y; |
---|
| 36 | }; |
---|
| 37 | } |
---|
| 38 | |
---|
| 39 | /* static inline { */ |
---|
| 40 | forall(otype T | vec2_t(T)) { |
---|
| 41 | static inline { |
---|
| 42 | |
---|
| 43 | // Constructors |
---|
| 44 | |
---|
| 45 | void ?{}(vec2(T)& v, T x, T y) { |
---|
| 46 | v.[x, y] = [x, y]; |
---|
| 47 | } |
---|
| 48 | void ?{}(vec2(T)& vec, zero_t) with (vec) { |
---|
| 49 | x = y = 0; |
---|
| 50 | } |
---|
| 51 | void ?{}(vec2(T)& vec, T val) with (vec) { |
---|
| 52 | x = y = val; |
---|
| 53 | } |
---|
| 54 | void ?{}(vec2(T)& vec, vec2(T) other) with (vec) { |
---|
| 55 | [x,y] = other.[x,y]; |
---|
| 56 | } |
---|
| 57 | |
---|
| 58 | // Assignment |
---|
| 59 | void ?=?(vec2(T)& vec, vec2(T) other) with (vec) { |
---|
| 60 | [x,y] = other.[x,y]; |
---|
| 61 | } |
---|
| 62 | void ?=?(vec2(T)& vec, zero_t) with (vec) { |
---|
| 63 | x = y = 0; |
---|
| 64 | } |
---|
| 65 | |
---|
| 66 | // Primitive mathematical operations |
---|
| 67 | |
---|
| 68 | // Subtraction |
---|
| 69 | vec2(T) ?-?(vec2(T) u, vec2(T) v) { // TODO( can't make this const ref ) |
---|
| 70 | return [u.x - v.x, u.y - v.y]; |
---|
| 71 | } |
---|
| 72 | vec2(T)& ?-=?(vec2(T)& u, vec2(T) v) { |
---|
| 73 | u = u - v; |
---|
| 74 | return u; |
---|
| 75 | } |
---|
| 76 | vec2(T) -?(vec2(T)& v) with (v) { |
---|
| 77 | return [-x, -y]; |
---|
| 78 | } |
---|
| 79 | |
---|
| 80 | // Addition |
---|
| 81 | vec2(T) ?+?(vec2(T) u, vec2(T) v) { // TODO( can't make this const ref ) |
---|
| 82 | return [u.x + v.x, u.y + v.y]; |
---|
| 83 | } |
---|
| 84 | vec2(T)& ?+=?(vec2(T)& u, vec2(T) v) { |
---|
| 85 | u = u + v; |
---|
| 86 | return u; |
---|
| 87 | } |
---|
| 88 | |
---|
| 89 | // Scalar Multiplication |
---|
| 90 | vec2(T) ?*?(vec2(T) v, T scalar) with (v) { // TODO (can't make this const ref) |
---|
| 91 | return [x * scalar, y * scalar]; |
---|
| 92 | } |
---|
| 93 | vec2(T) ?*?(T scalar, vec2(T) v) { // TODO (can't make this const ref) |
---|
| 94 | return v * scalar; |
---|
| 95 | } |
---|
| 96 | vec2(T)& ?*=?(vec2(T)& v, T scalar) { |
---|
| 97 | v = v * scalar; |
---|
| 98 | return v; |
---|
| 99 | } |
---|
| 100 | |
---|
| 101 | |
---|
| 102 | // Scalar Division |
---|
| 103 | vec2(T) ?/?(vec2(T) v, T scalar) with (v) { |
---|
| 104 | return [x / scalar, y / scalar]; |
---|
| 105 | } |
---|
| 106 | vec2(T)& ?/=?(vec2(T)& v, T scalar) with (v) { |
---|
| 107 | v = v / scalar; |
---|
| 108 | return v; |
---|
| 109 | } |
---|
| 110 | // Relational Operators |
---|
| 111 | bool ?==?(vec2(T) u, vec2(T) v) with (u) { |
---|
| 112 | return x == v.x && y == v.y; |
---|
| 113 | } |
---|
| 114 | bool ?!=?(vec2(T) u, vec2(T) v) { |
---|
| 115 | return !(u == v); |
---|
| 116 | } |
---|
| 117 | |
---|
| 118 | T dot(vec2(T) u, vec2(T) v) { |
---|
| 119 | return u.x * v.x + u.y * v.y; |
---|
| 120 | } |
---|
| 121 | |
---|
| 122 | T length(vec2(T) v) { |
---|
| 123 | return sqrt(dot(v, v)); |
---|
| 124 | } |
---|
| 125 | |
---|
| 126 | T length_squared(vec2(T) v) { |
---|
| 127 | return dot(v, v); |
---|
| 128 | } |
---|
| 129 | |
---|
| 130 | T distance(vec2(T) v1, vec2(T) v2) { |
---|
| 131 | return length(v1 - v2); |
---|
| 132 | } |
---|
| 133 | |
---|
| 134 | vec2(T) normalize(vec2(T) v) { |
---|
| 135 | return v / sqrt(dot(v, v)); |
---|
| 136 | } |
---|
| 137 | |
---|
| 138 | // Project vector u onto vector v |
---|
| 139 | vec2(T) project(vec2(T) u, vec2(T) v) { |
---|
| 140 | vec2(T) v_norm = normalize(v); |
---|
| 141 | return v_norm * dot(u, v_norm); |
---|
| 142 | } |
---|
| 143 | |
---|
| 144 | // Reflect incident vector v with respect to surface with normal n |
---|
| 145 | vec2(T) reflect(vec2(T) v, vec2(T) n) { |
---|
| 146 | return v - (T){2} * project(v, n); |
---|
| 147 | } |
---|
| 148 | |
---|
| 149 | // Refract incident vector v with respect to surface with normal n |
---|
| 150 | // eta is the ratio of indices of refraction between starting material and |
---|
| 151 | // entering material (i.e., from air to water, eta = 1/1.33) |
---|
| 152 | // v and n must already be normalized |
---|
| 153 | vec2(T) refract(vec2(T) v, vec2(T) n, T eta) { |
---|
| 154 | T dotValue = dot(n, v); |
---|
| 155 | T k = (T){1} - eta * eta * ((T){1} - dotValue * dotValue); |
---|
| 156 | if (k < (T){0}) { |
---|
| 157 | return 0; |
---|
| 158 | } |
---|
| 159 | return eta * v - (eta * dotValue + sqrt(k)) * n; |
---|
| 160 | } |
---|
| 161 | |
---|
| 162 | // Given a perturbed normal and a geometric normal, |
---|
| 163 | // flip the perturbed normal if the geometric normal is pointing away |
---|
| 164 | // from the observer. |
---|
| 165 | // n is the perturbed vector that we want to align |
---|
| 166 | // i is the incident vector |
---|
| 167 | // ng is the geometric normal of the surface |
---|
| 168 | vec2(T) faceforward(vec2(T) n, vec2(T) i, vec2(T) ng) { |
---|
| 169 | return dot(ng, i) < (T){0} ? n : -n; |
---|
| 170 | } |
---|
| 171 | } |
---|
| 172 | } |
---|
| 173 | |
---|
| 174 | forall(dtype ostype, otype T | writeable(T, ostype) | vec2_t(T)) { |
---|
| 175 | ostype & ?|?( ostype & os, vec2(T) v) with (v) { |
---|
| 176 | return os | '<' | x | ',' | y | '>'; |
---|
| 177 | } |
---|
| 178 | void ?|?( ostype & os, vec2(T) v ) with (v) { |
---|
| 179 | (ostype &)(os | v); ends(os); |
---|
| 180 | } |
---|
| 181 | } |
---|