1 | #pragma once |
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2 | |
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3 | #include <math.hfa> |
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4 | |
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5 | trait fromint(otype T) { |
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6 | void ?{}(T&, int); |
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7 | }; |
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8 | trait zeroinit(otype T) { |
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9 | void ?{}(T&, zero_t); |
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10 | }; |
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11 | trait zero_assign(otype T) { |
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12 | T ?=?(T&, zero_t); |
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13 | }; |
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14 | trait subtract(otype T) { |
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15 | T ?-?(T, T); |
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16 | }; |
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17 | trait negate(otype T) { |
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18 | T -?(T); |
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19 | }; |
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20 | trait add(otype T) { |
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21 | T ?+?(T, T); |
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22 | }; |
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23 | trait multiply(otype T) { |
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24 | T ?*?(T, T); |
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25 | }; |
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26 | trait divide(otype T) { |
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27 | T ?/?(T, T); |
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28 | }; |
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29 | trait lessthan(otype T) { |
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30 | int ?<?(T, T); |
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31 | }; |
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32 | trait equality(otype T) { |
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33 | int ?==?(T, T); |
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34 | }; |
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35 | trait sqrt(otype T) { |
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36 | T sqrt(T); |
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37 | }; |
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38 | |
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39 | static inline { |
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40 | // int |
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41 | int ?=?(int& n, zero_t) { return n = 0.f; } |
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42 | /* float */ |
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43 | void ?{}(float& a, int b) { a = b; } |
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44 | float ?=?(float& n, zero_t) { return n = 0.f; } |
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45 | /* double */ |
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46 | void ?{}(double& a, int b) { a = b; } |
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47 | double ?=?(double& n, zero_t) { return n = 0L; } |
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48 | // long double |
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49 | void ?{}(long double& a, int b) { a = b; } |
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50 | long double ?=?(long double& n, zero_t) { return n = 0L; } |
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51 | } |
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52 | |
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53 | trait dottable(otype V, otype T) { |
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54 | T dot(V, V); |
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55 | }; |
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56 | |
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57 | static inline { |
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58 | |
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59 | forall(otype T | sqrt(T), otype V | dottable(V, T)) |
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60 | T length(V v) { |
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61 | return sqrt(dot(v, v)); |
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62 | } |
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63 | |
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64 | forall(otype T, otype V | dottable(V, T)) |
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65 | T length_squared(V v) { |
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66 | return dot(v, v); |
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67 | } |
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68 | |
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69 | forall(otype T, otype V | { T length(V); } | subtract(V)) |
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70 | T distance(V v1, V v2) { |
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71 | return length(v1 - v2); |
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72 | } |
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73 | |
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74 | |
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75 | forall(otype T, otype V | { T length(V); V ?/?(V, T); }) |
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76 | V normalize(V v) { |
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77 | return v / length(v); |
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78 | } |
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79 | |
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80 | // Project vector u onto vector v |
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81 | forall(otype T, otype V | dottable(V, T) | { V normalize(V); V ?*?(V, T); }) |
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82 | V project(V u, V v) { |
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83 | V v_norm = normalize(v); |
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84 | return v_norm * dot(u, v_norm); |
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85 | } |
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86 | |
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87 | // Reflect incident vector v with respect to surface with normal n |
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88 | forall(otype T | fromint(T), otype V | { V project(V, V); V ?*?(T, V); V ?-?(V,V); }) |
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89 | V reflect(V v, V n) { |
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90 | return v - (T){2} * project(v, n); |
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91 | } |
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92 | |
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93 | // Refract incident vector v with respect to surface with normal n |
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94 | // eta is the ratio of indices of refraction between starting material and |
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95 | // entering material (i.e., from air to water, eta = 1/1.33) |
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96 | // v and n must already be normalized |
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97 | forall(otype T | fromint(T) | subtract(T) | multiply(T) | add(T) | lessthan(T) | sqrt(T), |
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98 | otype V | dottable(V, T) | { V ?*?(T, V); V ?-?(V,V); void ?{}(V&, zero_t); }) |
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99 | V refract(V v, V n, T eta) { |
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100 | T dotValue = dot(n, v); |
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101 | T k = (T){1} - eta * eta * ((T){1} - dotValue * dotValue); |
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102 | if (k < (T){0}) { |
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103 | return 0; |
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104 | } |
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105 | return eta * v - (eta * dotValue + sqrt(k)) * n; |
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106 | } |
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107 | |
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108 | // Given a perturbed normal and a geometric normal, |
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109 | // flip the perturbed normal if the geometric normal is pointing away |
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110 | // from the observer. |
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111 | // n is the perturbed vector that we want to align |
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112 | // i is the incident vector |
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113 | // ng is the geometric normal of the surface |
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114 | /* forall(| add(T) | multiply(T) | lessthan(T) | fromint(T) | subtract(T)) */ |
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115 | forall(otype T | lessthan(T) | zeroinit(T), otype V | dottable(V, T) | negate(V)) |
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116 | V faceforward(V n, V i, V ng) { |
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117 | return dot(ng, i) < (T){0} ? n : -n; |
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118 | } |
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119 | |
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120 | } // inline |
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