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annotate semicongine/core/matrix.nim @ 1136:71315636ba82

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did: refactor naming in tons of places
author sam <sam@basx.dev>
date Tue, 04 Jun 2024 16:51:50 +0700
parents fe48fb1bdfda
children 114f395b9144
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1 import std/math
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2 import std/macros
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3 import std/random
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4 import std/strutils
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5 import std/strformat
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6 import std/typetraits
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7
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8 import ./vector
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9
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10 export math
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11
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12 type
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13 # layout is row-first
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14 # having an object instead of directly aliasing the array seems a bit ugly at
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15 # first, but is necessary to be able to work correctly with distinguished
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16 # types (i.e. TMat23 and TMat32 would be an alias for the same type array[6, T]
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17 # which prevents the type system from identifying the correct type at times)
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18 #
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19 # Though, great news is that objects have zero overhead!
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20 TMat2*[T: SomeNumber] = object
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21 data*: array[4, T]
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22 TMat23*[T: SomeNumber] = object
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23 data*: array[6, T]
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24 TMat32*[T: SomeNumber] = object
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25 data*: array[6, T]
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26 TMat3*[T: SomeNumber] = object
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27 data*: array[9, T]
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28 TMat34*[T: SomeNumber] = object
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29 data*: array[12, T]
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30 TMat43*[T: SomeNumber] = object
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31 data*: array[12, T]
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32 TMat4*[T: SomeNumber] = object
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33 data*: array[16, T]
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34 TMat* = TMat2|TMat3|TMat4|TMat23|TMat32|TMat34|TMat43
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35 Mat2* = TMat2[float32]
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36 Mat23* = TMat23[float32]
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37 Mat32* = TMat32[float32]
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38 Mat3* = TMat3[float32]
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39 Mat34* = TMat34[float32]
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40 Mat43* = TMat43[float32]
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41 Mat4* = TMat4[float32]
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42
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43 func MakeUnit2*[T: SomeNumber](): auto {.compiletime.} = TMat2[T](data: [
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44 T(1), T(0),
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45 T(0), T(1),
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46 ])
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47 func MakeUnit3*[T: SomeNumber](): auto {.compiletime.} = TMat3[T](data: [
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48 T(1), T(0), T(0),
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49 T(0), T(1), T(0),
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50 T(0), T(0), T(1),
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51 ])
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52 func MakeUnit4*[T: SomeNumber](): auto {.compiletime.} = TMat4[T](data: [
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53 T(1), T(0), T(0), T(0),
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54 T(0), T(1), T(0), T(0),
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55 T(0), T(0), T(1), T(0),
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56 T(0), T(0), T(0), T(1),
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57 ])
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58
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59 # generates constants: Unit
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60 # Also for Y, Z, R, G, B
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61 # not sure if this is necessary or even a good idea...
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62 macro generateAllConsts() =
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63 result = newStmtList()
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64 for theType in ["int", "int8", "int16", "int32", "int64", "float", "float32", "float64"]:
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65 var typename = theType[0 .. 0]
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66 if theType[^2].isDigit:
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67 typename = typename & theType[^2]
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68 if theType[^1].isDigit:
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69 typename = typename & theType[^1]
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70 result.add(newConstStmt(
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71 postfix(ident("Unit2" & typename), "*"),
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72 newCall(nnkBracketExpr.newTree(ident("MakeUnit2"), ident(theType)))
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73 ))
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74 result.add(newConstStmt(
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75 postfix(ident("Unit3" & typename), "*"),
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76 newCall(nnkBracketExpr.newTree(ident("MakeUnit3"), ident(theType)))
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77 ))
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78 result.add(newConstStmt(
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79 postfix(ident("Unit4" & typename), "*"),
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80 newCall(nnkBracketExpr.newTree(ident("MakeUnit4"), ident(theType)))
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81 ))
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82
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83 generateAllConsts()
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84
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85 const Unit2* = MakeUnit2[float32]()
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86 const Unit3* = MakeUnit3[float32]()
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87 const Unit4* = MakeUnit4[float32]()
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88
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89 template RowCount*(m: typedesc): int =
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90 when m is TMat2: 2
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91 elif m is TMat23: 2
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92 elif m is TMat32: 3
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93 elif m is TMat3: 3
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94 elif m is TMat34: 3
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95 elif m is TMat43: 4
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96 elif m is TMat4: 4
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97 template ColumnCount*(m: typedesc): int =
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98 when m is TMat2: 2
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99 elif m is TMat23: 3
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100 elif m is TMat32: 2
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101 elif m is TMat3: 3
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102 elif m is TMat34: 4
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103 elif m is TMat43: 3
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104 elif m is TMat4: 4
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105 template matlen(m: typedesc): int =
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106 when m is TMat2: 4
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107 elif m is TMat23: 6
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108 elif m is TMat32: 6
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109 elif m is TMat3: 9
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110 elif m is TMat34: 12
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111 elif m is TMat43: 12
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112 elif m is TMat4: 16
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113
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114
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115 func toString[T](value: T): string =
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116 var
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117 strvalues: seq[string]
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118 maxwidth = 0
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119
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120 for n in value.data:
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121 let strval = &"{n:.4f}"
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122 strvalues.add(strval)
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123 if strval.len > maxwidth:
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124 maxwidth = strval.len
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125
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126 for i in 0 ..< strvalues.len:
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127 let filler = " ".repeat(maxwidth - strvalues[i].len)
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128 if i mod T.ColumnCount == T.ColumnCount - 1:
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129 result &= filler & strvalues[i] & "\n"
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130 else:
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131 if i mod T.ColumnCount == 0:
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132 result &= " "
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133 result &= filler & strvalues[i] & " "
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134
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135 func `$`*(v: TMat2[SomeNumber]): string = toString[TMat2[SomeNumber]](v)
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136 func `$`*(v: TMat23[SomeNumber]): string = toString[TMat23[SomeNumber]](v)
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137 func `$`*(v: TMat32[SomeNumber]): string = toString[TMat32[SomeNumber]](v)
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138 func `$`*(v: TMat3[SomeNumber]): string = toString[TMat3[SomeNumber]](v)
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139 func `$`*(v: TMat34[SomeNumber]): string = toString[TMat34[SomeNumber]](v)
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140 func `$`*(v: TMat43[SomeNumber]): string = toString[TMat43[SomeNumber]](v)
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141 func `$`*(v: TMat4[SomeNumber]): string = toString[TMat4[SomeNumber]](v)
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142
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143 func `[]`*[T: TMat](m: T, row, col: int): auto = m.data[col + row * T.ColumnCount]
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144 func `[]=`*[T: TMat, U](m: var T, row, col: int, value: U) = m.data[col + row * T.ColumnCount] = value
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145 func `[]`*[T: TMat](m: T, i: int): auto = m.data[i]
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146 func `[]=`*[T: TMat, U](m: var T, i: int, value: U) = m.data[i] = value
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147
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148 func Row*[T: TMat2](m: T, i: 0..1): auto = TVec2([m[i, 0], m[i, 1]])
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149 func Row*[T: TMat32](m: T, i: 0..2): auto = TVec2([m[i, 0], m[i, 1]])
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150 func Row*[T: TMat23](m: T, i: 0..1): auto = TVec3([m[i, 0], m[i, 1], m[i, 2]])
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151 func Row*[T: TMat3](m: T, i: 0..2): auto = TVec3([m[i, 0], m[i, 1], m[i, 2]])
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152 func Row*[T: TMat43](m: T, i: 0..3): auto = TVec3([m[i, 0], m[i, 1], m[i, 2]])
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153 func Row*[T: TMat34](m: T, i: 0..2): auto = TVec4([m[i, 0], m[i, 1], m[i, 2], m[i, 3]])
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154 func Row*[T: TMat4](m: T, i: 0..3): auto = TVec4([m[i, 0], m[i, 1], m[i, 2], m[i, 3]])
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155
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156 func Col*[T: TMat2](m: T, i: 0..1): auto = TVec2([m[0, i], m[1, i]])
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157 func Col*[T: TMat23](m: T, i: 0..2): auto = TVec2([m[0, i], m[1, i]])
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158 func Col*[T: TMat32](m: T, i: 0..1): auto = TVec3([m[0, i], m[1, i], m[2, i]])
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159 func Col*[T: TMat3](m: T, i: 0..2): auto = TVec3([m[0, i], m[1, i], m[2, i]])
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160 func Col*[T: TMat34](m: T, i: 0..3): auto = TVec3([m[0, i], m[1, i], m[2, i]])
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161 func Col*[T: TMat43](m: T, i: 0..2): auto = TVec4([m[0, i], m[1, i], m[2, i], m[3, i]])
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162 func Col*[T: TMat4](m: T, i: 0..3): auto = TVec4([m[0, i], m[1, i], m[2, i], m[3, i]])
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163
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164 proc createMatMatMultiplicationOperator(leftType: typedesc, rightType: typedesc, outType: typedesc): NimNode =
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165 var data = nnkBracket.newTree()
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166 for i in 0 ..< RowCount(leftType):
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167 for j in 0 ..< rightType.ColumnCount:
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168 data.add(newCall(
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169 ident("sum"),
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170 infix(
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171 newCall(newDotExpr(ident("a"), ident("Row")), newLit(i)),
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172 "*",
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173 newCall(newDotExpr(ident("b"), ident("Col")), newLit(j))
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174 )
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175 ))
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176
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177 return newProc(
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178 postfix(nnkAccQuoted.newTree(ident("*")), "*"),
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179 params = [
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180 ident("auto"),
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181 newIdentDefs(ident("a"), ident(leftType.name)),
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182 newIdentDefs(ident("b"), ident(rightType.name))
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183 ],
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184 body = nnkObjConstr.newTree(ident(outType.name), nnkExprColonExpr.newTree(ident("data"), data)),
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185 procType = nnkFuncDef,
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186 )
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187
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188 proc createMatMatAdditionOperator(theType: typedesc): NimNode =
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189 var data = nnkBracket.newTree()
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190 for i in 0 ..< matlen(theType):
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191 data.add(
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192 infix(
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193 nnkBracketExpr.newTree(ident("a"), newLit(i)),
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194 "+",
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195 nnkBracketExpr.newTree(ident("b"), newLit(i)),
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196 ))
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197
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198 return newProc(
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199 postfix(nnkAccQuoted.newTree(ident("+")), "*"),
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200 params = [
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201 ident("auto"),
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202 newIdentDefs(ident("a"), ident(theType.name)),
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203 newIdentDefs(ident("b"), ident(theType.name))
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204 ],
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205 body = nnkObjConstr.newTree(ident(theType.name), nnkExprColonExpr.newTree(ident("data"), data)),
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206 procType = nnkFuncDef,
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207 )
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208
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209 proc createVecMatMultiplicationOperator(matType: typedesc, vecType: typedesc): NimNode =
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210 var data = nnkBracket.newTree()
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211 for i in 0 ..< matType.RowCount:
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212 data.add(newCall(
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213 ident("sum"),
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214 infix(
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215 ident("v"),
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216 "*",
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217 newCall(newDotExpr(ident("m"), ident("Row")), newLit(i))
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218 )
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219 ))
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220
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221 let resultVec = newCall(
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222 nnkBracketExpr.newTree(ident(vecType.name), ident("T")),
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223 data,
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224 )
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225 let name = postfix(nnkAccQuoted.newTree(ident("*")), "*")
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226 let genericParams = nnkGenericParams.newTree(nnkIdentDefs.newTree(ident("T"), ident("SomeNumber"), newEmptyNode()))
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227 let formalParams = nnkFormalParams.newTree(
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228 ident("auto"),
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229 newIdentDefs(ident("m"), nnkBracketExpr.newTree(ident(matType.name), ident("T"))),
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230 newIdentDefs(ident("v"), nnkBracketExpr.newTree(ident(vecType.name), ident("T"))),
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231 )
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232
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233 return nnkFuncDef.newTree(
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234 name,
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235 newEmptyNode(),
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236 genericParams,
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237 formalParams,
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238 newEmptyNode(),
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239 newEmptyNode(),
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240 resultVec
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241 )
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242
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243
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244 proc createMatScalarOperator(matType: typedesc, op: string): NimNode =
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245 result = newStmtList()
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246
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247 var data = nnkBracket.newTree()
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248 for i in 0 ..< matType.RowCount * matType.ColumnCount:
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249 data.add(infix(nnkBracketExpr.newTree(newDotExpr(ident("a"), ident("data")), newLit(i)), op, ident("b")))
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250 result.add(newProc(
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251 postfix(nnkAccQuoted.newTree(ident(op)), "*"),
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252 params = [
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253 ident("auto"),
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254 newIdentDefs(ident("a"), ident(matType.name)),
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255 newIdentDefs(ident("b"), ident("SomeNumber")),
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256 ],
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257 body = nnkObjConstr.newTree(ident(matType.name), nnkExprColonExpr.newTree(ident("data"), data)),
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258 procType = nnkFuncDef,
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259 ))
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260 result.add(newProc(
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261 postfix(nnkAccQuoted.newTree(ident(op)), "*"),
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262 params = [
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263 ident("auto"),
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264 newIdentDefs(ident("b"), ident("SomeNumber")),
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265 newIdentDefs(ident("a"), ident(matType.name)),
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266 ],
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267 body = nnkObjConstr.newTree(ident(matType.name), nnkExprColonExpr.newTree(ident("data"), data)),
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268 procType = nnkFuncDef,
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269 ))
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270 if op == "-":
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271 var data2 = nnkBracket.newTree()
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272 for i in 0 ..< matType.RowCount * matType.ColumnCount:
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273 data2.add(prefix(nnkBracketExpr.newTree(newDotExpr(ident("a"), ident("data")), newLit(i)), op))
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274 result.add(newProc(
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275 postfix(nnkAccQuoted.newTree(ident(op)), "*"),
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276 params = [
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277 ident("auto"),
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278 newIdentDefs(ident("a"), ident(matType.name)),
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279 ],
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280 body = nnkObjConstr.newTree(ident(matType.name), nnkExprColonExpr.newTree(ident("data"), data2)),
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281 procType = nnkFuncDef,
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282 ))
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283
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284 macro createAllMultiplicationOperators() =
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285 result = newStmtList()
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286
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287 for op in ["+", "-", "*", "/"]:
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288 result.add(createMatScalarOperator(TMat2, op))
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289 result.add(createMatScalarOperator(TMat23, op))
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290 result.add(createMatScalarOperator(TMat32, op))
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291 result.add(createMatScalarOperator(TMat3, op))
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292 result.add(createMatScalarOperator(TMat34, op))
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293 result.add(createMatScalarOperator(TMat43, op))
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294 result.add(createMatScalarOperator(TMat4, op))
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295
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296 result.add(createMatMatMultiplicationOperator(TMat2, TMat2, TMat2))
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297 result.add(createMatMatMultiplicationOperator(TMat2, TMat23, TMat23))
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298 result.add(createMatMatMultiplicationOperator(TMat23, TMat32, TMat2))
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299 result.add(createMatMatMultiplicationOperator(TMat23, TMat3, TMat23))
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300 result.add(createMatMatMultiplicationOperator(TMat32, TMat2, TMat32))
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301 result.add(createMatMatMultiplicationOperator(TMat32, TMat23, TMat3))
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302 result.add(createMatMatMultiplicationOperator(TMat3, TMat32, TMat32))
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303 result.add(createMatMatMultiplicationOperator(TMat3, TMat3, TMat3))
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304 result.add(createMatMatMultiplicationOperator(TMat3, TMat34, TMat34))
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305 result.add(createMatMatMultiplicationOperator(TMat43, TMat3, TMat43))
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306 result.add(createMatMatMultiplicationOperator(TMat43, TMat34, TMat4))
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307 result.add(createMatMatMultiplicationOperator(TMat4, TMat43, TMat43))
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308 result.add(createMatMatMultiplicationOperator(TMat4, TMat4, TMat4))
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309
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310 result.add(createMatMatAdditionOperator(TMat2))
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311 result.add(createMatMatAdditionOperator(TMat23))
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312 result.add(createMatMatAdditionOperator(TMat32))
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313 result.add(createMatMatAdditionOperator(TMat3))
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314 result.add(createMatMatAdditionOperator(TMat34))
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315 result.add(createMatMatAdditionOperator(TMat43))
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316 result.add(createMatMatAdditionOperator(TMat4))
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317
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318 result.add(createVecMatMultiplicationOperator(TMat2, TVec2))
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319 result.add(createVecMatMultiplicationOperator(TMat3, TVec3))
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320 result.add(createVecMatMultiplicationOperator(TMat4, TVec4))
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321
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322 createAllMultiplicationOperators()
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323
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324 func `*`*(mat: Mat4, vec: Vec3f): Vec3f =
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325 (mat * vec.ToVec4(1)).ToVec3
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326
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327 func Transposed*[T](m: TMat2[T]): TMat2[T] = TMat2[T](data: [
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328 m[0, 0], m[1, 0],
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329 m[0, 1], m[1, 1],
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330 ])
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331 func Transposed*[T](m: TMat23[T]): TMat32[T] = TMat32[T](data: [
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332 m[0, 0], m[1, 0],
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333 m[0, 1], m[1, 1],
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334 m[0, 2], m[1, 2],
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335 ])
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336 func Transposed*[T](m: TMat32[T]): TMat23[T] = TMat23[T](data: [
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337 m[0, 0], m[1, 0], m[2, 0],
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338 m[0, 1], m[1, 1], m[2, 1],
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339 ])
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340 func Transposed*[T](m: TMat3[T]): TMat3[T] = TMat3[T](data: [
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341 m[0, 0], m[1, 0], m[2, 0],
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342 m[0, 1], m[1, 1], m[2, 1],
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343 m[0, 2], m[1, 2], m[2, 2],
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344 ])
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345 func Transposed*[T](m: TMat43[T]): TMat34[T] = TMat34[T](data: [
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346 m[0, 0], m[1, 0], m[2, 0], m[3, 0],
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347 m[0, 1], m[1, 1], m[2, 1], m[3, 1],
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348 m[0, 2], m[1, 2], m[2, 2], m[3, 2],
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349 ])
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350 func Transposed*[T](m: TMat34[T]): TMat43[T] = TMat43[T](data: [
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351 m[0, 0], m[1, 0], m[2, 0],
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352 m[0, 1], m[1, 1], m[2, 1],
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353 m[0, 2], m[1, 2], m[2, 2],
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354 m[0, 3], m[1, 3], m[2, 3],
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355 ])
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356 func Transposed*[T](m: TMat4[T]): TMat4[T] = TMat4[T](data: [
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357 m[0, 0], m[1, 0], m[2, 0], m[3, 0],
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358 m[0, 1], m[1, 1], m[2, 1], m[3, 1],
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359 m[0, 2], m[1, 2], m[2, 2], m[3, 2],
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360 m[0, 3], m[1, 3], m[2, 3], m[3, 3],
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361 ])
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362
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363 func Translate2d*[T](x, y: T): TMat3[T] = TMat3[T](data: [
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364 T(1), T(0), x,
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365 T(0), T(1), y,
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366 T(0), T(0), T(1),
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367 ])
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368 func Scale2d*[T](sx, sy: T): TMat3[T] = TMat3[T](data: [
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369 sx, T(0), T(0),
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370 T(0), sy, T(0),
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371 T(0), T(0), T(1),
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372 ])
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373 func Rotate2d*[T](angle: T): TMat3[T] = TMat3[T](data: [
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374 cos(angle), -sin(angle), T(0),
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375 sin(angle), cos(angle), T(0),
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376 T(0), T(0), T(1),
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377 ])
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378 func Translate*(x = 0'f32, y = 0'f32, z = 0'f32): TMat4[float32] = Mat4(data: [
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379 1'f32, 0'f32, 0'f32, x,
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380 0'f32, 1'f32, 0'f32, y,
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381 0'f32, 0'f32, 1'f32, z,
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382 0'f32, 0'f32, 0'f32, 1'f32,
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383 ])
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384 func Translate*[T: TVec3](v: T): TMat4[float32] = Translate(v[0], v[1], v[2])
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385 func Scale*(x = 1'f32, y = 1'f32, z = 1'f32): Mat4 = Mat4(data: [
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386 x, 0'f32, 0'f32, 0'f32,
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387 0'f32, y, 0'f32, 0'f32,
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diff changeset
388 0'f32, 0'f32, z, 0'f32,
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389 0'f32, 0'f32, 0'f32, 1'f32,
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390 ])
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391 func Scale*[T: TVec3](v: T): TMat4[float32] = Scale(v[0], v[1], v[2])
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392 func Rotate*(angle: float32, a: Vec3f): Mat4 =
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393 let
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394 cosa = cos(angle)
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395 sina = sin(angle)
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396 x = a[0]
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397 y = a[1]
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398 z = a[2]
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399 Mat4(data: [
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400 x * x * (1 - cosa) + cosa, y * x * (1 - cosa) - z * sina, z * x * (1 - cosa) + y * sina, 0'f32,
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401 x * y * (1 - cosa) + z * sina, y * y * (1 - cosa) + cosa, z * y * (1 - cosa) - x * sina, 0'f32,
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402 x * z * (1 - cosa) - y * sina, y * z * (1 - cosa) + x * sina, z * z * (1 - cosa) + cosa, 0'f32,
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403 0'f32, 0'f32, 0'f32, 1'f32,
840
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404 ])
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405
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Sam <sam@basx.dev>
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406 func asMat3(m: Mat4): auto =
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diff changeset
407 Mat3(data: [
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diff changeset
408 m[0, 0], m[0, 1], m[0, 2],
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Sam <sam@basx.dev>
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diff changeset
409 m[1, 0], m[1, 1], m[1, 2],
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diff changeset
410 m[2, 0], m[2, 1], m[2, 2],
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diff changeset
411 ])
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parents:
diff changeset
412
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Sam <sam@basx.dev>
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diff changeset
413
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414 func Inversed*(m: Mat4): Mat4 =
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415 var m3 = m.asMat3.Transposed
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416 m3[0, 0] = 1'f32 / m3[0, 0]
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417 m3[1, 1] = 1'f32 / m3[1, 1]
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418 m3[2, 2] = 1'f32 / m3[2, 2]
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419 let col3 = -(m3 * m.Col(3).xyz)
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420 return Mat4(data: [
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421 m3[0, 0], m3[0, 1], m3[0, 2], col3.x,
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422 m3[1, 0], m3[1, 1], m3[1, 2], col3.y,
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423 m3[2, 0], m3[2, 1], m3[2, 2], col3.z,
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diff changeset
424 0, 0, 0, 1,
840
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425 ])
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diff changeset
426
44ec744fbedc did: package restructuring according to nimble recommendation for libraries
Sam <sam@basx.dev>
parents:
diff changeset
427
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Sam <sam@basx.dev>
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diff changeset
428 # call e.g. TMat32[int]().randomized() to get a random matrix
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429 template makeRandomInit(mattype: typedesc) =
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430 proc Randomized*[T: SomeInteger](m: mattype[T]): mattype[T] =
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431 for i in 0 ..< result.data.len:
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432 result.data[i] = rand(low(typeof(m.data[0])) .. high(typeof(m.data[0])))
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433 proc Randomized*[T: SomeFloat](m: mattype[T]): mattype[T] =
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434 for i in 0 ..< result.data.len:
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435 result.data[i] = rand(T(1.0))
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436
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437 makeRandomInit(TMat2)
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438 makeRandomInit(TMat23)
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439 makeRandomInit(TMat32)
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440 makeRandomInit(TMat3)
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441 makeRandomInit(TMat34)
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442 makeRandomInit(TMat43)
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443 makeRandomInit(TMat4)
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444
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445 func Perspective*(fovy, aspect, zNear, zFar: float32): Mat4 =
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446 let tanHalfFovy = tan(fovy / 2)
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447 return Mat4(data: [
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448 1 / (aspect * tanHalfFovy), 0, 0, 0,
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449 0, 1 / tanHalfFovy, 0, 0,
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450 0, 0, zFar / (zFar - zNear), -(zFar * zNear) / (zFar - zNear),
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451 0, 0, 1, 1,
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452 ])
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453
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454 func Ortho*(left, right, top, bottom, zNear, zFar: float32): Mat4 =
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455 Mat4(data: [
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456 2 / (right - left), 0, 0, -(right + left) / (right - left),
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457 0, 2 / (bottom - top), 0, -(bottom + top) / (bottom - top),
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458 0, 0, 1 / (zFar - zNear), zNear / (zFar - zNear),
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459 0, 0, 0, 1,
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460 ])
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461
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462 # create an orthographic perspective that will map from -1 .. 1 on all axis and keep a 1:1 aspect ratio
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463 # the smaller dimension (width or height) will always be 1 and the larger dimension will be larger, to keep the ratio
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464 func OrthoWindowAspect*(windowAspect: float32): Mat4 =
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465 if windowAspect < 1:
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466 let space = 2 * (1 / windowAspect - 1) / 2
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467 Ortho(-1, 1, -1 - space, 1 + space, 0, 1)
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468 else:
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469 let space = 2 * (windowAspect - 1) / 2
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470 Ortho(-1 - space, 1 + space, -1, 1, 0, 1)
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471
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472 func Position*(mat: Mat4): Vec3f {.deprecated.} =
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473 mat.Col(3).ToVec3
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474
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475 func Scaling*(mat: Mat4): Vec3f {.deprecated.} =
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476 NewVec4f(mat[0, 0], mat[1, 1], mat[2, 2])