Mercurial > games > semicongine
annotate semiconginev2/core/matrix.nim @ 1257:e9b8d87b9883
fix: super stupid bug in perspective matrix X(
author | sam <sam@basx.dev> |
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date | Sun, 28 Jul 2024 18:55:46 +0700 |
parents | 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 |
1254 | 26 TSquareMat = TMat2|TMat3|TMat4 |
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27 Mat2* = TMat2[float32] |
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28 Mat23* = TMat23[float32] |
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29 Mat32* = TMat32[float32] |
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30 Mat3* = TMat3[float32] |
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31 Mat34* = TMat34[float32] |
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32 Mat43* = TMat43[float32] |
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33 Mat4* = TMat4[float32] |
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34 |
1136 | 35 func MakeUnit2*[T: SomeNumber](): auto {.compiletime.} = TMat2[T](data: [ |
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36 T(1), T(0), |
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37 T(0), T(1), |
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38 ]) |
1136 | 39 func MakeUnit3*[T: SomeNumber](): auto {.compiletime.} = TMat3[T](data: [ |
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40 T(1), T(0), T(0), |
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41 T(0), T(1), T(0), |
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42 T(0), T(0), T(1), |
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43 ]) |
1136 | 44 func MakeUnit4*[T: SomeNumber](): auto {.compiletime.} = TMat4[T](data: [ |
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45 T(1), T(0), T(0), T(0), |
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46 T(0), T(1), T(0), T(0), |
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47 T(0), T(0), T(1), T(0), |
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48 T(0), T(0), T(0), T(1), |
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49 ]) |
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50 |
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51 # generates constants: Unit |
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52 # Also for Y, Z, R, G, B |
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53 # not sure if this is necessary or even a good idea... |
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54 macro generateAllMatrixConsts() = |
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55 result = newStmtList() |
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56 for theType in ["int", "int8", "int16", "int32", "int64", "float", "float32", "float64"]: |
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57 var typename = theType[0 .. 0] |
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58 if theType[^2].isDigit: |
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59 typename = typename & theType[^2] |
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60 if theType[^1].isDigit: |
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61 typename = typename & theType[^1] |
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62 result.add(newConstStmt( |
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63 postfix(ident("Unit2" & typename), "*"), |
1136 | 64 newCall(nnkBracketExpr.newTree(ident("MakeUnit2"), ident(theType))) |
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65 )) |
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66 result.add(newConstStmt( |
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67 postfix(ident("Unit3" & typename), "*"), |
1136 | 68 newCall(nnkBracketExpr.newTree(ident("MakeUnit3"), ident(theType))) |
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69 )) |
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70 result.add(newConstStmt( |
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71 postfix(ident("Unit4" & typename), "*"), |
1136 | 72 newCall(nnkBracketExpr.newTree(ident("MakeUnit4"), ident(theType))) |
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73 )) |
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74 |
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75 generateAllMatrixConsts() |
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76 |
1136 | 77 const Unit2* = MakeUnit2[float32]() |
78 const Unit3* = MakeUnit3[float32]() | |
79 const Unit4* = MakeUnit4[float32]() | |
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80 |
1136 | 81 template RowCount*(m: typedesc): int = |
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82 when m is TMat2: 2 |
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83 elif m is TMat23: 2 |
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84 elif m is TMat32: 3 |
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85 elif m is TMat3: 3 |
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86 elif m is TMat34: 3 |
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87 elif m is TMat43: 4 |
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88 elif m is TMat4: 4 |
1136 | 89 template ColumnCount*(m: typedesc): int = |
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90 when m is TMat2: 2 |
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91 elif m is TMat23: 3 |
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92 elif m is TMat32: 2 |
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93 elif m is TMat3: 3 |
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94 elif m is TMat34: 4 |
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95 elif m is TMat43: 3 |
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96 elif m is TMat4: 4 |
1136 | 97 template matlen(m: typedesc): int = |
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98 when m is TMat2: 4 |
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99 elif m is TMat23: 6 |
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100 elif m is TMat32: 6 |
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101 elif m is TMat3: 9 |
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102 elif m is TMat34: 12 |
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103 elif m is TMat43: 12 |
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104 elif m is TMat4: 16 |
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105 |
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106 |
1253 | 107 func toMatString[T: TMat](value: T): string = |
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108 var |
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109 strvalues: seq[string] |
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110 maxwidth = 0 |
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111 |
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112 for n in value.data: |
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113 let strval = &"{float(n):.4f}" |
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114 strvalues.add(strval) |
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115 if strval.len > maxwidth: |
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116 maxwidth = strval.len |
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117 |
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118 for i in 0 ..< strvalues.len: |
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119 let filler = " ".repeat(maxwidth - strvalues[i].len) |
1136 | 120 if i mod T.ColumnCount == T.ColumnCount - 1: |
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121 result &= filler & strvalues[i] & "\n" |
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122 else: |
1136 | 123 if i mod T.ColumnCount == 0: |
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124 result &= " " |
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125 result &= filler & strvalues[i] & " " |
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126 |
1253 | 127 func `$`*(v: TMat2[SomeNumber]): string = toMatString[TMat2[SomeNumber]](v) |
128 func `$`*(v: TMat23[SomeNumber]): string = toMatString[TMat23[SomeNumber]](v) | |
129 func `$`*(v: TMat32[SomeNumber]): string = toMatString[TMat32[SomeNumber]](v) | |
130 func `$`*(v: TMat3[SomeNumber]): string = toMatString[TMat3[SomeNumber]](v) | |
131 func `$`*(v: TMat34[SomeNumber]): string = toMatString[TMat34[SomeNumber]](v) | |
132 func `$`*(v: TMat43[SomeNumber]): string = toMatString[TMat43[SomeNumber]](v) | |
133 func `$`*(v: TMat4[SomeNumber]): string = toMatString[TMat4[SomeNumber]](v) | |
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134 |
1136 | 135 func `[]`*[T: TMat](m: T, row, col: int): auto = m.data[col + row * T.ColumnCount] |
136 func `[]=`*[T: TMat, U](m: var T, row, col: int, value: U) = m.data[col + row * T.ColumnCount] = value | |
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137 func `[]`*[T: TMat](m: T, i: int): auto = m.data[i] |
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138 func `[]=`*[T: TMat, U](m: var T, i: int, value: U) = m.data[i] = value |
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139 |
1136 | 140 func Row*[T: TMat2](m: T, i: 0..1): auto = TVec2([m[i, 0], m[i, 1]]) |
141 func Row*[T: TMat32](m: T, i: 0..2): auto = TVec2([m[i, 0], m[i, 1]]) | |
142 func Row*[T: TMat23](m: T, i: 0..1): auto = TVec3([m[i, 0], m[i, 1], m[i, 2]]) | |
143 func Row*[T: TMat3](m: T, i: 0..2): auto = TVec3([m[i, 0], m[i, 1], m[i, 2]]) | |
144 func Row*[T: TMat43](m: T, i: 0..3): auto = TVec3([m[i, 0], m[i, 1], m[i, 2]]) | |
145 func Row*[T: TMat34](m: T, i: 0..2): auto = TVec4([m[i, 0], m[i, 1], m[i, 2], m[i, 3]]) | |
146 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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147 |
1136 | 148 func Col*[T: TMat2](m: T, i: 0..1): auto = TVec2([m[0, i], m[1, i]]) |
149 func Col*[T: TMat23](m: T, i: 0..2): auto = TVec2([m[0, i], m[1, i]]) | |
150 func Col*[T: TMat32](m: T, i: 0..1): auto = TVec3([m[0, i], m[1, i], m[2, i]]) | |
151 func Col*[T: TMat3](m: T, i: 0..2): auto = TVec3([m[0, i], m[1, i], m[2, i]]) | |
152 func Col*[T: TMat34](m: T, i: 0..3): auto = TVec3([m[0, i], m[1, i], m[2, i]]) | |
153 func Col*[T: TMat43](m: T, i: 0..2): auto = TVec4([m[0, i], m[1, i], m[2, i], m[3, i]]) | |
154 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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155 |
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156 proc createMatMatMultiplicationOperator(leftType: typedesc, rightType: typedesc, outType: typedesc): NimNode = |
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157 var data = nnkBracket.newTree() |
1136 | 158 for i in 0 ..< RowCount(leftType): |
159 for j in 0 ..< rightType.ColumnCount: | |
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160 data.add(newCall( |
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161 ident("sum"), |
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162 infix( |
1136 | 163 newCall(newDotExpr(ident("a"), ident("Row")), newLit(i)), |
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164 "*", |
1136 | 165 newCall(newDotExpr(ident("b"), ident("Col")), newLit(j)) |
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166 ) |
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167 )) |
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168 |
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169 return newProc( |
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170 postfix(nnkAccQuoted.newTree(ident("*")), "*"), |
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171 params = [ |
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172 ident("auto"), |
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173 newIdentDefs(ident("a"), ident(leftType.name)), |
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174 newIdentDefs(ident("b"), ident(rightType.name)) |
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175 ], |
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176 body = nnkObjConstr.newTree(ident(outType.name), nnkExprColonExpr.newTree(ident("data"), data)), |
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177 procType = nnkFuncDef, |
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178 ) |
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179 |
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180 proc createMatMatAdditionOperator(theType: typedesc): NimNode = |
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181 var data = nnkBracket.newTree() |
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182 for i in 0 ..< matlen(theType): |
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183 data.add( |
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184 infix( |
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185 nnkBracketExpr.newTree(ident("a"), newLit(i)), |
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186 "+", |
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187 nnkBracketExpr.newTree(ident("b"), newLit(i)), |
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188 )) |
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189 |
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190 return newProc( |
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191 postfix(nnkAccQuoted.newTree(ident("+")), "*"), |
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192 params = [ |
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193 ident("auto"), |
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194 newIdentDefs(ident("a"), ident(theType.name)), |
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195 newIdentDefs(ident("b"), ident(theType.name)) |
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196 ], |
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197 body = nnkObjConstr.newTree(ident(theType.name), nnkExprColonExpr.newTree(ident("data"), data)), |
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198 procType = nnkFuncDef, |
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199 ) |
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200 |
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201 proc createVecMatMultiplicationOperator(matType: typedesc, vecType: typedesc): NimNode = |
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202 var data = nnkBracket.newTree() |
1136 | 203 for i in 0 ..< matType.RowCount: |
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204 data.add(newCall( |
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205 ident("sum"), |
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206 infix( |
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207 ident("v"), |
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208 "*", |
1136 | 209 newCall(newDotExpr(ident("m"), ident("Row")), newLit(i)) |
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210 ) |
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211 )) |
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212 |
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213 let resultVec = newCall( |
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214 nnkBracketExpr.newTree(ident(vecType.name), ident("T")), |
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215 data, |
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216 ) |
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217 let name = postfix(nnkAccQuoted.newTree(ident("*")), "*") |
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218 let genericParams = nnkGenericParams.newTree(nnkIdentDefs.newTree(ident("T"), ident("SomeNumber"), newEmptyNode())) |
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219 let formalParams = nnkFormalParams.newTree( |
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220 ident("auto"), |
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221 newIdentDefs(ident("m"), nnkBracketExpr.newTree(ident(matType.name), ident("T"))), |
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222 newIdentDefs(ident("v"), nnkBracketExpr.newTree(ident(vecType.name), ident("T"))), |
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223 ) |
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224 |
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225 return nnkFuncDef.newTree( |
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226 name, |
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227 newEmptyNode(), |
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228 genericParams, |
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229 formalParams, |
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230 newEmptyNode(), |
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231 newEmptyNode(), |
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232 resultVec |
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233 ) |
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234 |
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235 |
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236 proc createMatScalarOperator(matType: typedesc, op: string): NimNode = |
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237 result = newStmtList() |
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238 |
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239 var data = nnkBracket.newTree() |
1136 | 240 for i in 0 ..< matType.RowCount * matType.ColumnCount: |
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241 data.add(infix(nnkBracketExpr.newTree(newDotExpr(ident("a"), ident("data")), newLit(i)), op, ident("b"))) |
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242 result.add(newProc( |
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243 postfix(nnkAccQuoted.newTree(ident(op)), "*"), |
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244 params = [ |
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245 ident("auto"), |
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246 newIdentDefs(ident("a"), ident(matType.name)), |
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247 newIdentDefs(ident("b"), ident("SomeNumber")), |
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248 ], |
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249 body = nnkObjConstr.newTree(ident(matType.name), nnkExprColonExpr.newTree(ident("data"), data)), |
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250 procType = nnkFuncDef, |
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251 )) |
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252 result.add(newProc( |
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253 postfix(nnkAccQuoted.newTree(ident(op)), "*"), |
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254 params = [ |
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255 ident("auto"), |
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256 newIdentDefs(ident("b"), ident("SomeNumber")), |
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257 newIdentDefs(ident("a"), ident(matType.name)), |
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258 ], |
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259 body = nnkObjConstr.newTree(ident(matType.name), nnkExprColonExpr.newTree(ident("data"), data)), |
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260 procType = nnkFuncDef, |
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261 )) |
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262 if op == "-": |
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263 var data2 = nnkBracket.newTree() |
1136 | 264 for i in 0 ..< matType.RowCount * matType.ColumnCount: |
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265 data2.add(prefix(nnkBracketExpr.newTree(newDotExpr(ident("a"), ident("data")), newLit(i)), op)) |
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266 result.add(newProc( |
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267 postfix(nnkAccQuoted.newTree(ident(op)), "*"), |
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268 params = [ |
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269 ident("auto"), |
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270 newIdentDefs(ident("a"), ident(matType.name)), |
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271 ], |
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272 body = nnkObjConstr.newTree(ident(matType.name), nnkExprColonExpr.newTree(ident("data"), data2)), |
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273 procType = nnkFuncDef, |
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274 )) |
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275 |
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276 macro createAllMultiplicationOperators() = |
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277 result = newStmtList() |
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278 |
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279 for op in ["+", "-", "*", "/"]: |
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280 result.add(createMatScalarOperator(TMat2, op)) |
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281 result.add(createMatScalarOperator(TMat23, op)) |
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282 result.add(createMatScalarOperator(TMat32, op)) |
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283 result.add(createMatScalarOperator(TMat3, op)) |
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284 result.add(createMatScalarOperator(TMat34, op)) |
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285 result.add(createMatScalarOperator(TMat43, op)) |
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286 result.add(createMatScalarOperator(TMat4, op)) |
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287 |
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288 result.add(createMatMatMultiplicationOperator(TMat2, TMat2, TMat2)) |
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289 result.add(createMatMatMultiplicationOperator(TMat2, TMat23, TMat23)) |
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290 result.add(createMatMatMultiplicationOperator(TMat23, TMat32, TMat2)) |
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291 result.add(createMatMatMultiplicationOperator(TMat23, TMat3, TMat23)) |
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292 result.add(createMatMatMultiplicationOperator(TMat32, TMat2, TMat32)) |
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293 result.add(createMatMatMultiplicationOperator(TMat32, TMat23, TMat3)) |
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294 result.add(createMatMatMultiplicationOperator(TMat3, TMat32, TMat32)) |
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295 result.add(createMatMatMultiplicationOperator(TMat3, TMat3, TMat3)) |
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296 result.add(createMatMatMultiplicationOperator(TMat3, TMat34, TMat34)) |
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297 result.add(createMatMatMultiplicationOperator(TMat43, TMat3, TMat43)) |
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298 result.add(createMatMatMultiplicationOperator(TMat43, TMat34, TMat4)) |
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299 result.add(createMatMatMultiplicationOperator(TMat4, TMat43, TMat43)) |
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300 result.add(createMatMatMultiplicationOperator(TMat4, TMat4, TMat4)) |
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301 |
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302 result.add(createMatMatAdditionOperator(TMat2)) |
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303 result.add(createMatMatAdditionOperator(TMat23)) |
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304 result.add(createMatMatAdditionOperator(TMat32)) |
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305 result.add(createMatMatAdditionOperator(TMat3)) |
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306 result.add(createMatMatAdditionOperator(TMat34)) |
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307 result.add(createMatMatAdditionOperator(TMat43)) |
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308 result.add(createMatMatAdditionOperator(TMat4)) |
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309 |
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310 result.add(createVecMatMultiplicationOperator(TMat2, TVec2)) |
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311 result.add(createVecMatMultiplicationOperator(TMat3, TVec3)) |
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312 result.add(createVecMatMultiplicationOperator(TMat4, TVec4)) |
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313 |
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314 createAllMultiplicationOperators() |
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315 |
1254 | 316 proc `+=`*[T1: TSquareMat, T2: TSquareMat|SomeNumber](a: var T1, b: T2) = |
317 a = a + b | |
318 | |
319 proc `-=`*[T1: TSquareMat, T2: TSquareMat|SomeNumber](a: var T1, b: T2) = | |
320 a = a + b | |
321 | |
322 proc `*=`*[T1: TSquareMat, T2: TSquareMat|SomeNumber](a: var T1, b: T2) = | |
323 a = a * b | |
324 | |
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325 func `*`*(mat: Mat4, vec: Vec3f): Vec3f = |
1136 | 326 (mat * vec.ToVec4(1)).ToVec3 |
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327 |
1136 | 328 func Transposed*[T](m: TMat2[T]): TMat2[T] = TMat2[T](data: [ |
840
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329 m[0, 0], m[1, 0], |
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330 m[0, 1], m[1, 1], |
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331 ]) |
1136 | 332 func Transposed*[T](m: TMat23[T]): TMat32[T] = TMat32[T](data: [ |
840
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333 m[0, 0], m[1, 0], |
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334 m[0, 1], m[1, 1], |
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335 m[0, 2], m[1, 2], |
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336 ]) |
1136 | 337 func Transposed*[T](m: TMat32[T]): TMat23[T] = TMat23[T](data: [ |
840
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338 m[0, 0], m[1, 0], m[2, 0], |
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339 m[0, 1], m[1, 1], m[2, 1], |
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340 ]) |
1136 | 341 func Transposed*[T](m: TMat3[T]): TMat3[T] = TMat3[T](data: [ |
840
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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 ]) |
1136 | 346 func Transposed*[T](m: TMat43[T]): TMat34[T] = TMat34[T](data: [ |
840
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347 m[0, 0], m[1, 0], m[2, 0], m[3, 0], |
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348 m[0, 1], m[1, 1], m[2, 1], m[3, 1], |
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349 m[0, 2], m[1, 2], m[2, 2], m[3, 2], |
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350 ]) |
1136 | 351 func Transposed*[T](m: TMat34[T]): TMat43[T] = TMat43[T](data: [ |
840
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352 m[0, 0], m[1, 0], m[2, 0], |
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353 m[0, 1], m[1, 1], m[2, 1], |
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354 m[0, 2], m[1, 2], m[2, 2], |
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355 m[0, 3], m[1, 3], m[2, 3], |
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356 ]) |
1136 | 357 func Transposed*[T](m: TMat4[T]): TMat4[T] = TMat4[T](data: [ |
840
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358 m[0, 0], m[1, 0], m[2, 0], m[3, 0], |
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359 m[0, 1], m[1, 1], m[2, 1], m[3, 1], |
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360 m[0, 2], m[1, 2], m[2, 2], m[3, 2], |
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361 m[0, 3], m[1, 3], m[2, 3], m[3, 3], |
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362 ]) |
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363 |
1136 | 364 func Translate2d*[T](x, y: T): TMat3[T] = TMat3[T](data: [ |
840
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365 T(1), T(0), x, |
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366 T(0), T(1), y, |
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367 T(0), T(0), T(1), |
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368 ]) |
1136 | 369 func Scale2d*[T](sx, sy: T): TMat3[T] = TMat3[T](data: [ |
840
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370 sx, T(0), T(0), |
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371 T(0), sy, T(0), |
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372 T(0), T(0), T(1), |
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373 ]) |
1136 | 374 func Rotate2d*[T](angle: T): TMat3[T] = TMat3[T](data: [ |
840
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375 cos(angle), -sin(angle), T(0), |
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376 sin(angle), cos(angle), T(0), |
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377 T(0), T(0), T(1), |
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378 ]) |
1136 | 379 func Translate*(x = 0'f32, y = 0'f32, z = 0'f32): TMat4[float32] = Mat4(data: [ |
840
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380 1'f32, 0'f32, 0'f32, x, |
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381 0'f32, 1'f32, 0'f32, y, |
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382 0'f32, 0'f32, 1'f32, z, |
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383 0'f32, 0'f32, 0'f32, 1'f32, |
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384 ]) |
1136 | 385 func Translate*[T: TVec3](v: T): TMat4[float32] = Translate(v[0], v[1], v[2]) |
386 func Scale*(x = 1'f32, y = 1'f32, z = 1'f32): Mat4 = Mat4(data: [ | |
901
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387 x, 0'f32, 0'f32, 0'f32, |
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388 0'f32, y, 0'f32, 0'f32, |
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389 0'f32, 0'f32, z, 0'f32, |
840
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390 0'f32, 0'f32, 0'f32, 1'f32, |
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391 ]) |
1136 | 392 func Scale*[T: TVec3](v: T): TMat4[float32] = Scale(v[0], v[1], v[2]) |
393 func Rotate*(angle: float32, a: Vec3f): Mat4 = | |
840
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394 let |
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395 cosa = cos(angle) |
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396 sina = sin(angle) |
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397 x = a[0] |
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398 y = a[1] |
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399 z = a[2] |
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400 Mat4(data: [ |
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401 x * x * (1 - cosa) + cosa, y * x * (1 - cosa) - z * sina, z * x * (1 - cosa) + y * sina, 0'f32, |
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402 x * y * (1 - cosa) + z * sina, y * y * (1 - cosa) + cosa, z * y * (1 - cosa) - x * sina, 0'f32, |
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403 x * z * (1 - cosa) - y * sina, y * z * (1 - cosa) + x * sina, z * z * (1 - cosa) + cosa, 0'f32, |
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404 0'f32, 0'f32, 0'f32, 1'f32, |
840
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405 ]) |
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406 |
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407 func asMat3(m: Mat4): auto = |
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408 Mat3(data: [ |
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409 m[0, 0], m[0, 1], m[0, 2], |
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410 m[1, 0], m[1, 1], m[1, 2], |
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411 m[2, 0], m[2, 1], m[2, 2], |
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412 ]) |
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413 |
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414 |
1136 | 415 func Inversed*(m: Mat4): Mat4 = |
416 var m3 = m.asMat3.Transposed | |
840
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417 m3[0, 0] = 1'f32 / m3[0, 0] |
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418 m3[1, 1] = 1'f32 / m3[1, 1] |
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419 m3[2, 2] = 1'f32 / m3[2, 2] |
1136 | 420 let col3 = -(m3 * m.Col(3).xyz) |
840
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421 return Mat4(data: [ |
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422 m3[0, 0], m3[0, 1], m3[0, 2], col3.x, |
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423 m3[1, 0], m3[1, 1], m3[1, 2], col3.y, |
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424 m3[2, 0], m3[2, 1], m3[2, 2], col3.z, |
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425 0, 0, 0, 1, |
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426 ]) |
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427 |
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428 |
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429 # call e.g. TMat32[int]().randomized() to get a random matrix |
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430 template makeRandomMatrixInit(mattype: typedesc) = |
1136 | 431 proc Randomized*[T: SomeInteger](m: mattype[T]): mattype[T] = |
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432 for i in 0 ..< result.data.len: |
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433 result.data[i] = rand(low(typeof(m.data[0])) .. high(typeof(m.data[0]))) |
1136 | 434 proc Randomized*[T: SomeFloat](m: mattype[T]): mattype[T] = |
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435 for i in 0 ..< result.data.len: |
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436 result.data[i] = rand(T(1.0)) |
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437 |
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438 makeRandomMatrixInit(TMat2) |
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439 makeRandomMatrixInit(TMat23) |
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440 makeRandomMatrixInit(TMat32) |
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441 makeRandomMatrixInit(TMat3) |
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442 makeRandomMatrixInit(TMat34) |
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443 makeRandomMatrixInit(TMat43) |
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444 makeRandomMatrixInit(TMat4) |
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445 |
1136 | 446 func Perspective*(fovy, aspect, zNear, zFar: float32): Mat4 = |
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447 let tanHalfFovy = 1 / tan(fovy / 2) |
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448 return Mat4(data: [ |
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449 tanHalfFovy / aspect, 0, 0, 0, |
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450 0, tanHalfFovy, 0, 0, |
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451 0, 0, zFar / (zFar - zNear), -(zFar * zNear) / (zFar - zNear), |
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452 0, 0, 1, 0, |
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453 ]) |
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454 |
1136 | 455 func Ortho*(left, right, top, bottom, zNear, zFar: float32): Mat4 = |
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456 Mat4(data: [ |
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457 2 / (right - left), 0, 0, -(right + left) / (right - left), |
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458 0, 2 / (bottom - top), 0, -(bottom + top) / (bottom - top), |
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459 0, 0, 1 / (zFar - zNear), zNear / (zFar - zNear), |
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460 0, 0, 0, 1, |
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461 ]) |
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462 |
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463 # create an orthographic perspective that will map from -1 .. 1 on all axis and keep a 1:1 aspect ratio |
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464 # the smaller dimension (width or height) will always be 1 and the larger dimension will be larger, to keep the ratio |
1136 | 465 func OrthoWindowAspect*(windowAspect: float32): Mat4 = |
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466 if windowAspect < 1: |
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467 let space = 2 * (1 / windowAspect - 1) / 2 |
1136 | 468 Ortho(-1, 1, -1 - space, 1 + space, 0, 1) |
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469 else: |
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470 let space = 2 * (windowAspect - 1) / 2 |
1136 | 471 Ortho(-1 - space, 1 + space, -1, 1, 0, 1) |
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472 |
1136 | 473 func Position*(mat: Mat4): Vec3f {.deprecated.} = |
474 mat.Col(3).ToVec3 | |
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475 |
1136 | 476 func Scaling*(mat: Mat4): Vec3f {.deprecated.} = |
477 NewVec4f(mat[0, 0], mat[1, 1], mat[2, 2]) |