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annotate src/vector.nim @ 16:617c6dcddbe2

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add: matrix multiplications, tests
author Sam <sam@basx.dev>
date Fri, 30 Dec 2022 15:56:17 +0700
parents a571db114152
children
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1 import std/random
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2 import std/math
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3 import std/strutils
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4 import std/macros
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5 import std/typetraits
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6 import std/tables
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7
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8
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9 type
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10 Vec2*[T: SomeNumber] = array[2, T]
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11 Vec3*[T: SomeNumber] = array[3, T]
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12 Vec4*[T: SomeNumber] = array[4, T]
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13 Vec* = Vec2|Vec3|Vec4
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14
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15 # define some often used constants
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16 func ConstOne2[T: SomeNumber](): auto {.compiletime.} = Vec2[T]([T(1), T(1)])
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17 func ConstOne3[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(1), T(1), T(1)])
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18 func ConstOne4[T: SomeNumber](): auto {.compiletime.} = Vec4[T]([T(1), T(1), T(1), T(1)])
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19 func ConstX[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(1), T(0), T(0)])
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20 func ConstY[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(0), T(1), T(0)])
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21 func ConstZ[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(0), T(0), T(1)])
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22 func ConstR[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(1), T(0), T(0)])
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23 func ConstG[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(0), T(1), T(0)])
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24 func ConstB[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(0), T(0), T(1)])
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25
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26 # generates constants: Xf, Xf32, Xf64, Xi, Xi8, Xi16, Xi32, Xi64
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27 # Also for Y, Z, R, G, B and One
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28 # not sure if this is necessary or even a good idea...
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29 macro generateAllConsts() =
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30 result = newStmtList()
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31 for component in ["X", "Y", "Z", "R", "G", "B", "One2", "One3", "One4"]:
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32 for theType in ["int", "int8", "int16", "int32", "int64", "float", "float32", "float64"]:
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33 var typename = theType[0 .. 0]
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34 if theType[^2].isDigit:
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35 typename = typename & theType[^2]
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36 if theType[^1].isDigit:
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37 typename = typename & theType[^1]
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38 result.add(
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39 newConstStmt(
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40 postfix(ident(component & typename), "*"),
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41 newCall(nnkBracketExpr.newTree(ident("Const" & component), ident(theType)))
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42 )
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43 )
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44
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45 generateAllConsts()
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46
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47 const X* = ConstX[float]()
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48 const Y* = ConstY[float]()
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49 const Z* = ConstZ[float]()
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50 const One2* = ConstOne2[float]()
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51 const One3* = ConstOne3[float]()
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52 const One4* = ConstOne4[float]()
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53
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54 func newVec2*[T](x, y: T): auto = Vec2([x, y])
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55 func newVec3*[T](x, y, z: T): auto = Vec3([x, y, z])
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56 func newVec4*[T](x, y, z, w: T): auto = Vec4([x, y, z, w])
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57
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58 func to*[T](v: Vec2): auto = Vec2([T(v[0]), T(v[1])])
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59 func to*[T](v: Vec3): auto = Vec3([T(v[0]), T(v[1]), T(v[2])])
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60 func to*[T](v: Vec4): auto = Vec4([T(v[0]), T(v[1]), T(v[2]), T(v[3])])
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61
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62 func toString[T](value: T): string =
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63 var items: seq[string]
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64 for item in value:
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65 items.add($item)
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66 $T & "(" & join(items, " ") & ")"
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67
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68 func `$`*(v: Vec2[SomeNumber]): string = toString[Vec2[SomeNumber]](v)
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69 func `$`*(v: Vec3[SomeNumber]): string = toString[Vec3[SomeNumber]](v)
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70 func `$`*(v: Vec4[SomeNumber]): string = toString[Vec4[SomeNumber]](v)
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71
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72 func length*(vec: Vec2[SomeFloat]): auto = sqrt(vec[0] * vec[0] + vec[1] * vec[1])
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73 func length*(vec: Vec2[SomeInteger]): auto = sqrt(float(vec[0] * vec[0] + vec[1] * vec[1]))
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74 func length*(vec: Vec3[SomeFloat]): auto = sqrt(vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2])
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75 func length*(vec: Vec3[SomeInteger]): auto = sqrt(float(vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2]))
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76 func length*(vec: Vec4[SomeFloat]): auto = sqrt(vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2] + vec[3] * vec[3])
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77 func length*(vec: Vec4[SomeInteger]): auto = sqrt(float(vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2] + vec[3] * vec[3]))
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78
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79 func normalized*[T](vec: Vec2[T]): auto =
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80 let l = vec.length
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81 when T is SomeFloat:
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82 Vec2[T]([vec[0] / l, vec[1] / l])
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83 else:
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84 Vec2[float]([float(vec[0]) / l, float(vec[1]) / l])
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85 func normalized*[T](vec: Vec3[T]): auto =
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86 let l = vec.length
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87 when T is SomeFloat:
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88 Vec3[T]([vec[0] / l, vec[1] / l, vec[2] / l])
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89 else:
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90 Vec3[float]([float(vec[0]) / l, float(vec[1]) / l, float(vec[2]) / l])
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91 func normalized*[T](vec: Vec4[T]): auto =
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92 let l = vec.length
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93 when T is SomeFloat:
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94 Vec4[T]([vec[0] / l, vec[1] / l, vec[2] / l, vec[3] / l])
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95 else:
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96 Vec4[float]([float(vec[0]) / l, float(vec[1]) / l, float(vec[2]) / l, float(vec[3]) / l])
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97
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98 # scalar operations
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99 func `+`*(a: Vec2, b: SomeNumber): auto = Vec2([a[0] + b, a[1] + b])
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100 func `+`*(a: Vec3, b: SomeNumber): auto = Vec3([a[0] + b, a[1] + b, a[2] + b])
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101 func `+`*(a: Vec4, b: SomeNumber): auto = Vec4([a[0] + b, a[1] + b, a[2] + b, a[3] + b])
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102 func `-`*(a: Vec2, b: SomeNumber): auto = Vec2([a[0] - b, a[1] - b])
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103 func `-`*(a: Vec3, b: SomeNumber): auto = Vec3([a[0] - b, a[1] - b, a[2] - b])
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104 func `-`*(a: Vec4, b: SomeNumber): auto = Vec4([a[0] - b, a[1] - b, a[2] - b, a[3] - b])
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105 func `*`*(a: Vec2, b: SomeNumber): auto = Vec2([a[0] * b, a[1] * b])
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106 func `*`*(a: Vec3, b: SomeNumber): auto = Vec3([a[0] * b, a[1] * b, a[2] * b])
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107 func `*`*(a: Vec4, b: SomeNumber): auto = Vec4([a[0] * b, a[1] * b, a[2] * b, a[3] * b])
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108 func `/`*[T: SomeInteger](a: Vec2[T], b: SomeInteger): auto = Vec2([a[0] div b, a[1] div b])
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109 func `/`*[T: SomeFloat](a: Vec2[T], b: SomeFloat): auto = Vec2([a[0] / b, a[1] / b])
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110 func `/`*[T: SomeInteger](a: Vec3[T], b: SomeInteger): auto = Vec3([a[0] div b, a[1] div b, a[2] div b])
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111 func `/`*[T: SomeFloat](a: Vec3[T], b: SomeFloat): auto = Vec3([a[0] / b, a[1] / b, a[2] / b])
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112 func `/`*[T: SomeInteger](a: Vec4[T], b: SomeInteger): auto = Vec4([a[0] div b, a[1] div b, a[2] div b, a[3] div b])
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113 func `/`*[T: SomeFloat](a: Vec4[T], b: SomeFloat): auto = Vec4([a[0] / b, a[1] / b, a[2] / b, a[3] / b])
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114
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115 func `+`*(a: SomeNumber, b: Vec2): auto = Vec2([a + b[0], a + b[1]])
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116 func `+`*(a: SomeNumber, b: Vec3): auto = Vec3([a + b[0], a + b[1], a + b[2]])
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117 func `+`*(a: SomeNumber, b: Vec4): auto = Vec4([a + b[0], a + b[1], a + b[2], a + b[3]])
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118 func `-`*(a: SomeNumber, b: Vec2): auto = Vec2([a - b[0], a - b[1]])
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119 func `-`*(a: SomeNumber, b: Vec3): auto = Vec3([a - b[0], a - b[1], a - b[2]])
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120 func `-`*(a: SomeNumber, b: Vec4): auto = Vec4([a - b[0], a - b[1], a - b[2], a - b[3]])
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121 func `*`*(a: SomeNumber, b: Vec2): auto = Vec2([a * b[0], a * b[1]])
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122 func `*`*(a: SomeNumber, b: Vec3): auto = Vec3([a * b[0], a * b[1], a * b[2]])
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123 func `*`*(a: SomeNumber, b: Vec4): auto = Vec4([a * b[0], a * b[1], a * b[2], a * b[3]])
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124 func `/`*[T: SomeInteger](a: SomeInteger, b: Vec2[T]): auto = Vec2([a div b[0], a div b[1]])
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125 func `/`*[T: SomeFloat](a: SomeFloat, b: Vec2[T]): auto = Vec2([a / b[0], a / b[1]])
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126 func `/`*[T: SomeInteger](a: SomeInteger, b: Vec3[T]): auto = Vec3([a div b[0], a div b[1], a div b[2]])
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127 func `/`*[T: SomeFloat](a: SomeFloat, b: Vec3[T]): auto = Vec3([a / b[0], a / b[1], a / b[2]])
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128 func `/`*[T: SomeInteger](a: SomeInteger, b: Vec4[T]): auto = Vec4([a div b[0], a div b[1], a div b[2], a div b[3]])
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129 func `/`*[T: SomeFloat](a: SomeFloat, b: Vec4[T]): auto = Vec4([a / b[0], a / b[1], a / b[2], a / b[3]])
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130
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131 # compontent-wise operations
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132 func `+`*(a, b: Vec2): auto = Vec2([a[0] + b[0], a[1] + b[1]])
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133 func `+`*(a, b: Vec3): auto = Vec3([a[0] + b[0], a[1] + b[1], a[2] + b[2]])
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134 func `+`*(a, b: Vec4): auto = Vec4([a[0] + b[0], a[1] + b[1], a[2] + b[2], a[3] + b[3]])
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135 func `-`*(a: Vec2): auto = Vec2([-a[0], -a[1]])
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136 func `-`*(a: Vec3): auto = Vec3([-a[0], -a[1], -a[2]])
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137 func `-`*(a: Vec4): auto = Vec4([-a[0], -a[1], -a[2], -a[3]])
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138 func `-`*(a, b: Vec2): auto = Vec2([a[0] - b[0], a[1] - b[1]])
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139 func `-`*(a, b: Vec3): auto = Vec3([a[0] - b[0], a[1] - b[1], a[2] - b[2]])
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140 func `-`*(a, b: Vec4): auto = Vec4([a[0] - b[0], a[1] - b[1], a[2] - b[2], a[3] - b[3]])
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141 func `*`*(a, b: Vec2): auto = Vec2([a[0] * b[0], a[1] * b[1]])
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142 func `*`*(a, b: Vec3): auto = Vec3([a[0] * b[0], a[1] * b[1], a[2] * b[2]])
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143 func `*`*(a, b: Vec4): auto = Vec4([a[0] * b[0], a[1] * b[1], a[2] * b[2], a[3] * b[3]])
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144 func `/`*[T: SomeInteger](a, b: Vec2[T]): auto = Vec2([a[0] div b[0], a[1] div b[1]])
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145 func `/`*[T: SomeFloat](a, b: Vec2[T]): auto = Vec2([a[0] / b[0], a[1] / b[1]])
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146 func `/`*[T: SomeInteger](a, b: Vec3[T]): auto = Vec3([a[0] div b[0], a[1] div b[1], a[2] div b[2]])
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147 func `/`*[T: SomeFloat](a, b: Vec3[T]): auto = Vec3([a[0] / b[0], a[1] / b[1], a[2] / b[2]])
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148 func `/`*[T: SomeInteger](a, b: Vec4[T]): auto = Vec4([a[0] div b[0], a[1] div b[1], a[2] div b[2], a[3] div b[3]])
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149 func `/`*[T: SomeFloat](a, b: Vec4[T]): auto = Vec4([a[0] / b[0], a[1] / b[1], a[2] / b[2], a[3] / b[3]])
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150
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151 # special operations
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152 func dot*(a, b: Vec2): auto = a[0] * b[0] + a[1] * b[1]
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153 func dot*(a, b: Vec3): auto = a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
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154 func dot*(a, b: Vec4): auto = a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3]
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155 func cross*(a, b: Vec3): auto = Vec3([
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156 a[1] * b[2] - a[2] * b[1],
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157 a[2] * b[0] - a[0] * b[2],
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158 a[0] * b[1] - a[1] * b[0],
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159 ])
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160
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161
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162 # macro to allow creation of new vectors by specifying vector components as attributes
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163 # e.g. myVec.xxy will return a new Vec3 that contains the components x, x an y of the original vector
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164 # (instead of x, y, z for a simple copy)
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165 proc vectorAttributeAccessor(accessor: string): NimNode =
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166 const ACCESSOR_INDICES = {
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167 'x': 0,
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168 'y': 1,
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169 'z': 2,
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170 'w': 3,
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171 'r': 0,
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172 'g': 1,
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173 'b': 2,
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174 'a': 3,
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175 }.toTable
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176 var ret: NimNode
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177 let accessorvalue = accessor
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178
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179 if accessorvalue.len == 0:
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180 raise newException(Exception, "empty attribute")
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181 elif accessorvalue.len == 1:
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182 ret = nnkBracket.newTree(ident("value"), newLit(ACCESSOR_INDICES[accessorvalue[0]]))
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183 if accessorvalue.len > 1:
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184 var attrs = nnkBracket.newTree()
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185 for attrname in accessorvalue:
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186 attrs.add(nnkBracketExpr.newTree(ident("value"), newLit(ACCESSOR_INDICES[attrname])))
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187 ret = nnkCall.newTree(ident("Vec" & $accessorvalue.len), attrs)
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188
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189 newProc(
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190 name=nnkPostfix.newTree(ident("*"), ident(accessor)),
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191 params=[ident("auto"), nnkIdentDefs.newTree(ident("value"), ident("Vec"), newEmptyNode())],
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192 body=newStmtList(ret),
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193 procType = nnkFuncDef,
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194 )
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195
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196 macro createVectorAttribAccessorFuncs() =
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197 const COORD_ATTRS = ["x", "y", "z", "w"]
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198 const COLOR_ATTRS = ["r", "g", "b", "a"]
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199 result = nnkStmtList.newTree()
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200 for attlist in [COORD_ATTRS, COLOR_ATTRS]:
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201 for i in attlist:
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202 result.add(vectorAttributeAccessor(i))
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203 for j in attlist:
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204 result.add(vectorAttributeAccessor(i & j))
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205 for k in attlist:
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206 result.add(vectorAttributeAccessor(i & j & k))
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207 for l in attlist:
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208 result.add(vectorAttributeAccessor(i & j & k & l))
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209
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210 createVectorAttribAccessorFuncs()
16
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211
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212 # call e.g. Vec2[int]().randomized() to get a random matrix
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213 template makeRandomInit(mattype: typedesc) =
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214 proc randomized*[T: SomeInteger](m: mattype[T]): mattype[T] =
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215 for i in 0 ..< result.len:
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216 result[i] = rand(low(typeof(m[0])) .. high(typeof(m[0])))
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217 proc randomized*[T: SomeFloat](m: mattype[T]): mattype[T] =
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218 for i in 0 ..< result.len:
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219 result[i] = rand(1.0)
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220
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221 makeRandomInit(Vec2)
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222 makeRandomInit(Vec3)
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223 makeRandomInit(Vec4)