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annotate semiconginev2/core/matrix.nim @ 1253:c4f98eb4bb05

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fix: a few things
author sam <sam@basx.dev>
date Fri, 26 Jul 2024 23:39:24 +0700
parents 56781cc0fc7c
children b0f4c8ccd49a
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1 export math
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2
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3 type
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4 # layout is row-first
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5 # having an object instead of directly aliasing the array seems a bit ugly at
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6 # first, but is necessary to be able to work correctly with distinguished
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7 # types (i.e. TMat23 and TMat32 would be an alias for the same type array[6, T]
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8 # which prevents the type system from identifying the correct type at times)
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9 #
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10 # Though, great news is that objects have zero overhead!
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11 TMat2*[T: SomeNumber] = object
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12 data*: array[4, T]
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13 TMat23*[T: SomeNumber] = object
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14 data*: array[6, T]
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15 TMat32*[T: SomeNumber] = object
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16 data*: array[6, T]
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17 TMat3*[T: SomeNumber] = object
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18 data*: array[9, T]
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19 TMat34*[T: SomeNumber] = object
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20 data*: array[12, T]
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21 TMat43*[T: SomeNumber] = object
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22 data*: array[12, T]
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23 TMat4*[T: SomeNumber] = object
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24 data*: array[16, T]
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25 TMat* = TMat2|TMat3|TMat4|TMat23|TMat32|TMat34|TMat43
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26 Mat2* = TMat2[float32]
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27 Mat23* = TMat23[float32]
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28 Mat32* = TMat32[float32]
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29 Mat3* = TMat3[float32]
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30 Mat34* = TMat34[float32]
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31 Mat43* = TMat43[float32]
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32 Mat4* = TMat4[float32]
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33
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34 func MakeUnit2*[T: SomeNumber](): auto {.compiletime.} = TMat2[T](data: [
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35 T(1), T(0),
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36 T(0), T(1),
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37 ])
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38 func MakeUnit3*[T: SomeNumber](): auto {.compiletime.} = TMat3[T](data: [
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39 T(1), T(0), T(0),
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40 T(0), T(1), T(0),
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41 T(0), T(0), T(1),
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42 ])
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43 func MakeUnit4*[T: SomeNumber](): auto {.compiletime.} = TMat4[T](data: [
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44 T(1), T(0), T(0), T(0),
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45 T(0), T(1), T(0), T(0),
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46 T(0), T(0), T(1), T(0),
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47 T(0), T(0), T(0), T(1),
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48 ])
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49
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50 # generates constants: Unit
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51 # Also for Y, Z, R, G, B
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52 # not sure if this is necessary or even a good idea...
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53 macro generateAllMatrixConsts() =
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54 result = newStmtList()
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55 for theType in ["int", "int8", "int16", "int32", "int64", "float", "float32", "float64"]:
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56 var typename = theType[0 .. 0]
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57 if theType[^2].isDigit:
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58 typename = typename & theType[^2]
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59 if theType[^1].isDigit:
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60 typename = typename & theType[^1]
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61 result.add(newConstStmt(
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62 postfix(ident("Unit2" & typename), "*"),
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63 newCall(nnkBracketExpr.newTree(ident("MakeUnit2"), ident(theType)))
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64 ))
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65 result.add(newConstStmt(
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66 postfix(ident("Unit3" & typename), "*"),
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67 newCall(nnkBracketExpr.newTree(ident("MakeUnit3"), ident(theType)))
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68 ))
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69 result.add(newConstStmt(
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70 postfix(ident("Unit4" & typename), "*"),
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71 newCall(nnkBracketExpr.newTree(ident("MakeUnit4"), ident(theType)))
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72 ))
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73
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74 generateAllMatrixConsts()
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75
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76 const Unit2* = MakeUnit2[float32]()
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77 const Unit3* = MakeUnit3[float32]()
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78 const Unit4* = MakeUnit4[float32]()
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79
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80 template RowCount*(m: typedesc): int =
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81 when m is TMat2: 2
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82 elif m is TMat23: 2
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83 elif m is TMat32: 3
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84 elif m is TMat3: 3
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85 elif m is TMat34: 3
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86 elif m is TMat43: 4
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87 elif m is TMat4: 4
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88 template ColumnCount*(m: typedesc): int =
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89 when m is TMat2: 2
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90 elif m is TMat23: 3
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91 elif m is TMat32: 2
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92 elif m is TMat3: 3
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93 elif m is TMat34: 4
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94 elif m is TMat43: 3
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95 elif m is TMat4: 4
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96 template matlen(m: typedesc): int =
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97 when m is TMat2: 4
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98 elif m is TMat23: 6
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99 elif m is TMat32: 6
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100 elif m is TMat3: 9
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101 elif m is TMat34: 12
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102 elif m is TMat43: 12
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103 elif m is TMat4: 16
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104
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105
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106 func toMatString[T: TMat](value: T): string =
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107 var
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108 strvalues: seq[string]
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109 maxwidth = 0
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110
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111 for n in value.data:
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112 let strval = &"{float(n):.4f}"
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113 strvalues.add(strval)
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114 if strval.len > maxwidth:
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115 maxwidth = strval.len
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116
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117 for i in 0 ..< strvalues.len:
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118 let filler = " ".repeat(maxwidth - strvalues[i].len)
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119 if i mod T.ColumnCount == T.ColumnCount - 1:
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120 result &= filler & strvalues[i] & "\n"
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121 else:
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122 if i mod T.ColumnCount == 0:
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123 result &= " "
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124 result &= filler & strvalues[i] & " "
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125
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126 func `$`*(v: TMat2[SomeNumber]): string = toMatString[TMat2[SomeNumber]](v)
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127 func `$`*(v: TMat23[SomeNumber]): string = toMatString[TMat23[SomeNumber]](v)
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128 func `$`*(v: TMat32[SomeNumber]): string = toMatString[TMat32[SomeNumber]](v)
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129 func `$`*(v: TMat3[SomeNumber]): string = toMatString[TMat3[SomeNumber]](v)
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130 func `$`*(v: TMat34[SomeNumber]): string = toMatString[TMat34[SomeNumber]](v)
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131 func `$`*(v: TMat43[SomeNumber]): string = toMatString[TMat43[SomeNumber]](v)
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132 func `$`*(v: TMat4[SomeNumber]): string = toMatString[TMat4[SomeNumber]](v)
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133
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134 func `[]`*[T: TMat](m: T, row, col: int): auto = m.data[col + row * T.ColumnCount]
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135 func `[]=`*[T: TMat, U](m: var T, row, col: int, value: U) = m.data[col + row * T.ColumnCount] = value
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136 func `[]`*[T: TMat](m: T, i: int): auto = m.data[i]
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137 func `[]=`*[T: TMat, U](m: var T, i: int, value: U) = m.data[i] = value
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138
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139 func Row*[T: TMat2](m: T, i: 0..1): auto = TVec2([m[i, 0], m[i, 1]])
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140 func Row*[T: TMat32](m: T, i: 0..2): auto = TVec2([m[i, 0], m[i, 1]])
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141 func Row*[T: TMat23](m: T, i: 0..1): auto = TVec3([m[i, 0], m[i, 1], m[i, 2]])
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142 func Row*[T: TMat3](m: T, i: 0..2): auto = TVec3([m[i, 0], m[i, 1], m[i, 2]])
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143 func Row*[T: TMat43](m: T, i: 0..3): auto = TVec3([m[i, 0], m[i, 1], m[i, 2]])
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144 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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145 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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146
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147 func Col*[T: TMat2](m: T, i: 0..1): auto = TVec2([m[0, i], m[1, i]])
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148 func Col*[T: TMat23](m: T, i: 0..2): auto = TVec2([m[0, i], m[1, i]])
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149 func Col*[T: TMat32](m: T, i: 0..1): auto = TVec3([m[0, i], m[1, i], m[2, i]])
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150 func Col*[T: TMat3](m: T, i: 0..2): auto = TVec3([m[0, i], m[1, i], m[2, i]])
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151 func Col*[T: TMat34](m: T, i: 0..3): auto = TVec3([m[0, i], m[1, i], m[2, i]])
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152 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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153 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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154
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155 proc createMatMatMultiplicationOperator(leftType: typedesc, rightType: typedesc, outType: typedesc): NimNode =
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156 var data = nnkBracket.newTree()
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157 for i in 0 ..< RowCount(leftType):
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158 for j in 0 ..< rightType.ColumnCount:
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159 data.add(newCall(
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160 ident("sum"),
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161 infix(
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162 newCall(newDotExpr(ident("a"), ident("Row")), newLit(i)),
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163 "*",
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164 newCall(newDotExpr(ident("b"), ident("Col")), newLit(j))
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165 )
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166 ))
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167
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168 return newProc(
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169 postfix(nnkAccQuoted.newTree(ident("*")), "*"),
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170 params = [
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171 ident("auto"),
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172 newIdentDefs(ident("a"), ident(leftType.name)),
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173 newIdentDefs(ident("b"), ident(rightType.name))
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174 ],
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175 body = nnkObjConstr.newTree(ident(outType.name), nnkExprColonExpr.newTree(ident("data"), data)),
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176 procType = nnkFuncDef,
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177 )
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178
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179 proc createMatMatAdditionOperator(theType: typedesc): NimNode =
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180 var data = nnkBracket.newTree()
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181 for i in 0 ..< matlen(theType):
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182 data.add(
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183 infix(
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184 nnkBracketExpr.newTree(ident("a"), newLit(i)),
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185 "+",
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186 nnkBracketExpr.newTree(ident("b"), newLit(i)),
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187 ))
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188
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189 return newProc(
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190 postfix(nnkAccQuoted.newTree(ident("+")), "*"),
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191 params = [
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192 ident("auto"),
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193 newIdentDefs(ident("a"), ident(theType.name)),
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194 newIdentDefs(ident("b"), ident(theType.name))
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195 ],
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196 body = nnkObjConstr.newTree(ident(theType.name), nnkExprColonExpr.newTree(ident("data"), data)),
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197 procType = nnkFuncDef,
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198 )
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199
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200 proc createVecMatMultiplicationOperator(matType: typedesc, vecType: typedesc): NimNode =
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201 var data = nnkBracket.newTree()
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202 for i in 0 ..< matType.RowCount:
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203 data.add(newCall(
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204 ident("sum"),
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205 infix(
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206 ident("v"),
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207 "*",
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208 newCall(newDotExpr(ident("m"), ident("Row")), newLit(i))
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209 )
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210 ))
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211
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212 let resultVec = newCall(
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213 nnkBracketExpr.newTree(ident(vecType.name), ident("T")),
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214 data,
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215 )
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216 let name = postfix(nnkAccQuoted.newTree(ident("*")), "*")
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217 let genericParams = nnkGenericParams.newTree(nnkIdentDefs.newTree(ident("T"), ident("SomeNumber"), newEmptyNode()))
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218 let formalParams = nnkFormalParams.newTree(
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219 ident("auto"),
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220 newIdentDefs(ident("m"), nnkBracketExpr.newTree(ident(matType.name), ident("T"))),
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221 newIdentDefs(ident("v"), nnkBracketExpr.newTree(ident(vecType.name), ident("T"))),
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222 )
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223
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224 return nnkFuncDef.newTree(
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225 name,
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226 newEmptyNode(),
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227 genericParams,
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228 formalParams,
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229 newEmptyNode(),
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230 newEmptyNode(),
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231 resultVec
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232 )
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233
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234
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235 proc createMatScalarOperator(matType: typedesc, op: string): NimNode =
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236 result = newStmtList()
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237
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238 var data = nnkBracket.newTree()
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239 for i in 0 ..< matType.RowCount * matType.ColumnCount:
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240 data.add(infix(nnkBracketExpr.newTree(newDotExpr(ident("a"), ident("data")), newLit(i)), op, ident("b")))
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241 result.add(newProc(
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242 postfix(nnkAccQuoted.newTree(ident(op)), "*"),
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243 params = [
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244 ident("auto"),
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245 newIdentDefs(ident("a"), ident(matType.name)),
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246 newIdentDefs(ident("b"), ident("SomeNumber")),
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247 ],
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248 body = nnkObjConstr.newTree(ident(matType.name), nnkExprColonExpr.newTree(ident("data"), data)),
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249 procType = nnkFuncDef,
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250 ))
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251 result.add(newProc(
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252 postfix(nnkAccQuoted.newTree(ident(op)), "*"),
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253 params = [
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254 ident("auto"),
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255 newIdentDefs(ident("b"), ident("SomeNumber")),
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256 newIdentDefs(ident("a"), ident(matType.name)),
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257 ],
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258 body = nnkObjConstr.newTree(ident(matType.name), nnkExprColonExpr.newTree(ident("data"), data)),
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259 procType = nnkFuncDef,
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260 ))
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261 if op == "-":
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262 var data2 = nnkBracket.newTree()
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263 for i in 0 ..< matType.RowCount * matType.ColumnCount:
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264 data2.add(prefix(nnkBracketExpr.newTree(newDotExpr(ident("a"), ident("data")), newLit(i)), op))
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265 result.add(newProc(
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266 postfix(nnkAccQuoted.newTree(ident(op)), "*"),
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267 params = [
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268 ident("auto"),
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269 newIdentDefs(ident("a"), ident(matType.name)),
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270 ],
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271 body = nnkObjConstr.newTree(ident(matType.name), nnkExprColonExpr.newTree(ident("data"), data2)),
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272 procType = nnkFuncDef,
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273 ))
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274
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275 macro createAllMultiplicationOperators() =
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276 result = newStmtList()
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277
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278 for op in ["+", "-", "*", "/"]:
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279 result.add(createMatScalarOperator(TMat2, op))
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280 result.add(createMatScalarOperator(TMat23, op))
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281 result.add(createMatScalarOperator(TMat32, op))
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282 result.add(createMatScalarOperator(TMat3, op))
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283 result.add(createMatScalarOperator(TMat34, op))
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284 result.add(createMatScalarOperator(TMat43, op))
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285 result.add(createMatScalarOperator(TMat4, op))
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286
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287 result.add(createMatMatMultiplicationOperator(TMat2, TMat2, TMat2))
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288 result.add(createMatMatMultiplicationOperator(TMat2, TMat23, TMat23))
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289 result.add(createMatMatMultiplicationOperator(TMat23, TMat32, TMat2))
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290 result.add(createMatMatMultiplicationOperator(TMat23, TMat3, TMat23))
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291 result.add(createMatMatMultiplicationOperator(TMat32, TMat2, TMat32))
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292 result.add(createMatMatMultiplicationOperator(TMat32, TMat23, TMat3))
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293 result.add(createMatMatMultiplicationOperator(TMat3, TMat32, TMat32))
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294 result.add(createMatMatMultiplicationOperator(TMat3, TMat3, TMat3))
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295 result.add(createMatMatMultiplicationOperator(TMat3, TMat34, TMat34))
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296 result.add(createMatMatMultiplicationOperator(TMat43, TMat3, TMat43))
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297 result.add(createMatMatMultiplicationOperator(TMat43, TMat34, TMat4))
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298 result.add(createMatMatMultiplicationOperator(TMat4, TMat43, TMat43))
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299 result.add(createMatMatMultiplicationOperator(TMat4, TMat4, TMat4))
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300
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301 result.add(createMatMatAdditionOperator(TMat2))
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302 result.add(createMatMatAdditionOperator(TMat23))
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303 result.add(createMatMatAdditionOperator(TMat32))
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304 result.add(createMatMatAdditionOperator(TMat3))
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305 result.add(createMatMatAdditionOperator(TMat34))
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306 result.add(createMatMatAdditionOperator(TMat43))
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307 result.add(createMatMatAdditionOperator(TMat4))
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308
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309 result.add(createVecMatMultiplicationOperator(TMat2, TVec2))
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310 result.add(createVecMatMultiplicationOperator(TMat3, TVec3))
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311 result.add(createVecMatMultiplicationOperator(TMat4, TVec4))
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312
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313 createAllMultiplicationOperators()
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314
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315 func `*`*(mat: Mat4, vec: Vec3f): Vec3f =
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316 (mat * vec.ToVec4(1)).ToVec3
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317
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318 func Transposed*[T](m: TMat2[T]): TMat2[T] = TMat2[T](data: [
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319 m[0, 0], m[1, 0],
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320 m[0, 1], m[1, 1],
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321 ])
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322 func Transposed*[T](m: TMat23[T]): TMat32[T] = TMat32[T](data: [
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323 m[0, 0], m[1, 0],
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324 m[0, 1], m[1, 1],
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325 m[0, 2], m[1, 2],
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326 ])
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327 func Transposed*[T](m: TMat32[T]): TMat23[T] = TMat23[T](data: [
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328 m[0, 0], m[1, 0], m[2, 0],
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329 m[0, 1], m[1, 1], m[2, 1],
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330 ])
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331 func Transposed*[T](m: TMat3[T]): TMat3[T] = TMat3[T](data: [
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332 m[0, 0], m[1, 0], m[2, 0],
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333 m[0, 1], m[1, 1], m[2, 1],
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334 m[0, 2], m[1, 2], m[2, 2],
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335 ])
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336 func Transposed*[T](m: TMat43[T]): TMat34[T] = TMat34[T](data: [
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337 m[0, 0], m[1, 0], m[2, 0], m[3, 0],
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338 m[0, 1], m[1, 1], m[2, 1], m[3, 1],
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339 m[0, 2], m[1, 2], m[2, 2], m[3, 2],
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340 ])
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341 func Transposed*[T](m: TMat34[T]): TMat43[T] = TMat43[T](data: [
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342 m[0, 0], m[1, 0], m[2, 0],
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343 m[0, 1], m[1, 1], m[2, 1],
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344 m[0, 2], m[1, 2], m[2, 2],
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345 m[0, 3], m[1, 3], m[2, 3],
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346 ])
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347 func Transposed*[T](m: TMat4[T]): TMat4[T] = TMat4[T](data: [
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348 m[0, 0], m[1, 0], m[2, 0], m[3, 0],
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349 m[0, 1], m[1, 1], m[2, 1], m[3, 1],
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350 m[0, 2], m[1, 2], m[2, 2], m[3, 2],
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351 m[0, 3], m[1, 3], m[2, 3], m[3, 3],
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352 ])
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353
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354 func Translate2d*[T](x, y: T): TMat3[T] = TMat3[T](data: [
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355 T(1), T(0), x,
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356 T(0), T(1), y,
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357 T(0), T(0), T(1),
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358 ])
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359 func Scale2d*[T](sx, sy: T): TMat3[T] = TMat3[T](data: [
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360 sx, T(0), T(0),
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361 T(0), sy, T(0),
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362 T(0), T(0), T(1),
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363 ])
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364 func Rotate2d*[T](angle: T): TMat3[T] = TMat3[T](data: [
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365 cos(angle), -sin(angle), T(0),
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366 sin(angle), cos(angle), T(0),
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367 T(0), T(0), T(1),
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368 ])
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369 func Translate*(x = 0'f32, y = 0'f32, z = 0'f32): TMat4[float32] = Mat4(data: [
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370 1'f32, 0'f32, 0'f32, x,
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371 0'f32, 1'f32, 0'f32, y,
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372 0'f32, 0'f32, 1'f32, z,
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373 0'f32, 0'f32, 0'f32, 1'f32,
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374 ])
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375 func Translate*[T: TVec3](v: T): TMat4[float32] = Translate(v[0], v[1], v[2])
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376 func Scale*(x = 1'f32, y = 1'f32, z = 1'f32): Mat4 = Mat4(data: [
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377 x, 0'f32, 0'f32, 0'f32,
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378 0'f32, y, 0'f32, 0'f32,
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379 0'f32, 0'f32, z, 0'f32,
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380 0'f32, 0'f32, 0'f32, 1'f32,
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381 ])
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382 func Scale*[T: TVec3](v: T): TMat4[float32] = Scale(v[0], v[1], v[2])
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383 func Rotate*(angle: float32, a: Vec3f): Mat4 =
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384 let
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385 cosa = cos(angle)
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386 sina = sin(angle)
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387 x = a[0]
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388 y = a[1]
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389 z = a[2]
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390 Mat4(data: [
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391 x * x * (1 - cosa) + cosa, y * x * (1 - cosa) - z * sina, z * x * (1 - cosa) + y * sina, 0'f32,
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392 x * y * (1 - cosa) + z * sina, y * y * (1 - cosa) + cosa, z * y * (1 - cosa) - x * sina, 0'f32,
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393 x * z * (1 - cosa) - y * sina, y * z * (1 - cosa) + x * sina, z * z * (1 - cosa) + cosa, 0'f32,
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394 0'f32, 0'f32, 0'f32, 1'f32,
840
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395 ])
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396
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397 func asMat3(m: Mat4): auto =
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398 Mat3(data: [
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399 m[0, 0], m[0, 1], m[0, 2],
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400 m[1, 0], m[1, 1], m[1, 2],
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401 m[2, 0], m[2, 1], m[2, 2],
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402 ])
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403
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diff changeset
404
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405 func Inversed*(m: Mat4): Mat4 =
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406 var m3 = m.asMat3.Transposed
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407 m3[0, 0] = 1'f32 / m3[0, 0]
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408 m3[1, 1] = 1'f32 / m3[1, 1]
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409 m3[2, 2] = 1'f32 / m3[2, 2]
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410 let col3 = -(m3 * m.Col(3).xyz)
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411 return Mat4(data: [
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412 m3[0, 0], m3[0, 1], m3[0, 2], col3.x,
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413 m3[1, 0], m3[1, 1], m3[1, 2], col3.y,
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414 m3[2, 0], m3[2, 1], m3[2, 2], col3.z,
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diff changeset
415 0, 0, 0, 1,
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416 ])
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417
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418
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419 # call e.g. TMat32[int]().randomized() to get a random matrix
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420 template makeRandomMatrixInit(mattype: typedesc) =
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421 proc Randomized*[T: SomeInteger](m: mattype[T]): mattype[T] =
901
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422 for i in 0 ..< result.data.len:
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423 result.data[i] = rand(low(typeof(m.data[0])) .. high(typeof(m.data[0])))
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424 proc Randomized*[T: SomeFloat](m: mattype[T]): mattype[T] =
901
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425 for i in 0 ..< result.data.len:
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426 result.data[i] = rand(T(1.0))
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427
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428 makeRandomMatrixInit(TMat2)
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429 makeRandomMatrixInit(TMat23)
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430 makeRandomMatrixInit(TMat32)
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431 makeRandomMatrixInit(TMat3)
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432 makeRandomMatrixInit(TMat34)
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433 makeRandomMatrixInit(TMat43)
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434 makeRandomMatrixInit(TMat4)
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435
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436 func Perspective*(fovy, aspect, zNear, zFar: float32): Mat4 =
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437 let tanHalfFovy = tan(fovy / 2)
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438 return Mat4(data: [
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439 1 / (aspect * tanHalfFovy), 0, 0, 0,
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440 0, 1 / tanHalfFovy, 0, 0,
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441 0, 0, zFar / (zFar - zNear), -(zFar * zNear) / (zFar - zNear),
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442 0, 0, 1, 1,
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443 ])
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444
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445 func Ortho*(left, right, top, bottom, zNear, zFar: float32): Mat4 =
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446 Mat4(data: [
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447 2 / (right - left), 0, 0, -(right + left) / (right - left),
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448 0, 2 / (bottom - top), 0, -(bottom + top) / (bottom - top),
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449 0, 0, 1 / (zFar - zNear), zNear / (zFar - zNear),
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450 0, 0, 0, 1,
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451 ])
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452
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453 # create an orthographic perspective that will map from -1 .. 1 on all axis and keep a 1:1 aspect ratio
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454 # 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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455 func OrthoWindowAspect*(windowAspect: float32): Mat4 =
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456 if windowAspect < 1:
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457 let space = 2 * (1 / windowAspect - 1) / 2
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458 Ortho(-1, 1, -1 - space, 1 + space, 0, 1)
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459 else:
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460 let space = 2 * (windowAspect - 1) / 2
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461 Ortho(-1 - space, 1 + space, -1, 1, 0, 1)
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462
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463 func Position*(mat: Mat4): Vec3f {.deprecated.} =
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464 mat.Col(3).ToVec3
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465
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466 func Scaling*(mat: Mat4): Vec3f {.deprecated.} =
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467 NewVec4f(mat[0, 0], mat[1, 1], mat[2, 2])