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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5 | struct vec2 { |
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6 | float x, y; |
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7 | }; |
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8 | |
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9 | // Constructors |
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10 | |
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11 | void ?{}( vec2 & v, float x, float y) { |
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12 | v.[x, y] = [x, y]; |
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13 | } |
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14 | void ?{}(vec2& vec, zero_t) with (vec) { |
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15 | x = y = 0; |
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16 | } |
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17 | void ?{}(vec2& vec, float val) with (vec) { |
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18 | x = y = val; |
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19 | } |
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20 | void ?{}(vec2& vec, vec2& other) with (vec) { |
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21 | [x,y] = other.[x,y]; |
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22 | } |
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23 | |
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24 | // Assignment |
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25 | void ?=?(vec2& vec, const vec2& other) with (vec) { |
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26 | [x,y] = other.[x,y]; |
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27 | } |
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28 | |
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29 | // Primitive mathematical operations |
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30 | |
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31 | // Subtraction |
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32 | vec2 ?-?(const vec2& u, const vec2& v) { |
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33 | return [u.x - v.x, u.y - v.y]; |
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34 | } |
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35 | vec2& ?-=?(vec2& u, const vec2& v) { |
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36 | u = u - v; |
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37 | return u; |
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38 | } |
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39 | vec2 -?(const vec2& v) with (v) { |
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40 | return [-x, -y]; |
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41 | } |
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42 | |
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43 | // Addition |
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44 | vec2 ?+?(const vec2& u, const vec2& v) { |
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45 | return [u.x + v.x, u.y + v.y]; |
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46 | } |
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47 | vec2& ?+=?(vec2& u, const vec2& v) { |
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48 | u = u + v; |
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49 | return u; |
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50 | } |
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51 | |
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52 | // Scalar Multiplication |
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53 | vec2 ?*?(const vec2& v, float scalar) with (v) { |
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54 | return [x * scalar, y * scalar]; |
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55 | } |
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56 | vec2& ?*=?(vec2& v, float scalar) with (v) { |
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57 | v = v * scalar; |
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58 | return v; |
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59 | } |
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60 | vec2 ?*?(float scalar, const vec2& v) { |
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61 | return v * scalar; |
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62 | } |
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63 | |
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64 | |
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65 | // Scalar Division |
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66 | vec2 ?/?(const vec2& v, float scalar) with (v) { |
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67 | return [x / scalar, y / scalar]; |
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68 | } |
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69 | vec2& ?/=?(vec2& v, float scalar) with (v) { |
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70 | v = v / scalar; |
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71 | return v; |
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72 | } |
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73 | |
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74 | // Relational Operators |
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75 | bool ?==?(const vec2& u, const vec2& v) with (u) { |
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76 | return x == v.x && y == v.y; |
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77 | } |
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78 | bool ?!=?(const vec2& u, const vec2& v) { |
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79 | return !(u == v); |
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80 | } |
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81 | |
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82 | // Printing the vector (ostream) |
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83 | forall( dtype ostype | ostream( ostype ) ) { |
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84 | ostype & ?|?( ostype & os, const vec2& v) with (v) { |
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85 | if ( sepPrt( os ) ) fmt( os, "%s", sepGetCur( os ) ); |
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86 | fmt( os, "<%g,%g>", x, y); |
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87 | return os; |
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88 | } |
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89 | void ?|?( ostype & os, const vec2& v ) { |
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90 | (ostype &)(os | v); ends( os ); |
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91 | } |
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92 | } |
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93 | |
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94 | /* //---------------------- Geometric Functions ---------------------- */ |
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95 | /* // These functions implement the Geometric Functions section of GLSL for 2D vectors*/ |
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96 | |
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97 | static inline float dot(const vec2& u, const vec2& v) { |
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98 | return u.x * v.x + u.y * v.y; |
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99 | } |
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100 | |
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101 | static inline float length(const vec2& v) { |
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102 | return sqrt(dot(v, v)); |
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103 | } |
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104 | |
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105 | static inline float distance(const vec2& v1, const vec2& v2) { |
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106 | return length(v1 - v2); |
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107 | } |
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108 | |
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109 | static inline vec2 normalize(const vec2& v) { |
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110 | return v / sqrt(dot(v, v)); |
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111 | } |
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112 | |
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113 | // Project vector u onto vector v |
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114 | static inline vec2 project(const vec2& u, const vec2& v) { |
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115 | vec2 v_norm = normalize(v); |
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116 | return v_norm * dot(u, v_norm); |
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117 | } |
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118 | |
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119 | // Reflect incident vector v with respect to surface with normal n |
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120 | static inline vec2 reflect(const vec2& v, const vec2& n) { |
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121 | return v - 2 * project(v, n); |
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122 | } |
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123 | |
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124 | // Refract incident vector v with respect to surface with normal n |
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125 | // eta is the ratio of indices of refraction between starting material and |
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126 | // entering material (i.e., from air to water, eta = 1/1.33) |
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127 | static inline vec2 refract(const vec2& v, const vec2& n, float eta) { |
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128 | float dotValue = dot(n, v); |
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129 | float k = 1 - eta * eta * (1 - dotValue * dotValue); |
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130 | if (k < 0) { |
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131 | return 0; |
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132 | } |
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133 | return eta * v - (eta * dotValue + sqrt(k)) * n; |
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134 | } |
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135 | |
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136 | // Used to render perturbed surfaces by ensuring that a perturbed normal |
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137 | // is pointing in the same direction as the geometric normal of the |
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138 | // surface. |
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139 | // n is the perturbed vector that we want to align |
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140 | // i is the incident vector |
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141 | // ng is the geometric normal of the surface |
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142 | static inline vec2 faceforward(const vec2& n, const vec2& i, float ng) { |
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143 | return dot(n, i) < 0 ? ng : -ng; |
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144 | } |
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