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comparison src/zamikongine/math/vector.nim @ 480:14e5151f68d1

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did: introduce scene graph, meshs and generic vertex buffers
author Sam <sam@basx.dev>
date Mon, 09 Jan 2023 11:04:19 +0700
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children c472abfcee57
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479:16842d15319a 480:14e5151f68d1
1 import std/random
2 import std/math
3 import std/strutils
4 import std/macros
5 import std/typetraits
6 import std/tables
7
8
9 type
10 Vec2*[T: SomeNumber] = array[2, T]
11 Vec3*[T: SomeNumber] = array[3, T]
12 Vec4*[T: SomeNumber] = array[4, T]
13 Vec* = Vec2|Vec3|Vec4
14
15 # define some often used constants
16 func ConstOne2[T: SomeNumber](): auto {.compiletime.} = Vec2[T]([T(1), T(1)])
17 func ConstOne3[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(1), T(1), T(1)])
18 func ConstOne4[T: SomeNumber](): auto {.compiletime.} = Vec4[T]([T(1), T(1), T(1), T(1)])
19 func ConstX[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(1), T(0), T(0)])
20 func ConstY[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(0), T(1), T(0)])
21 func ConstZ[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(0), T(0), T(1)])
22 func ConstR[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(1), T(0), T(0)])
23 func ConstG[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(0), T(1), T(0)])
24 func ConstB[T: SomeNumber](): auto {.compiletime.} = Vec3[T]([T(0), T(0), T(1)])
25
26 # generates constants: Xf, Xf32, Xf64, Xi, Xi8, Xi16, Xi32, Xi64
27 # Also for Y, Z, R, G, B and One
28 # not sure if this is necessary or even a good idea...
29 macro generateAllConsts() =
30 result = newStmtList()
31 for component in ["X", "Y", "Z", "R", "G", "B", "One2", "One3", "One4"]:
32 for theType in ["int", "int8", "int16", "int32", "int64", "float", "float32", "float64"]:
33 var typename = theType[0 .. 0]
34 if theType[^2].isDigit:
35 typename = typename & theType[^2]
36 if theType[^1].isDigit:
37 typename = typename & theType[^1]
38 result.add(
39 newConstStmt(
40 postfix(ident(component & typename), "*"),
41 newCall(nnkBracketExpr.newTree(ident("Const" & component), ident(theType)))
42 )
43 )
44
45 generateAllConsts()
46
47 const X* = ConstX[float]()
48 const Y* = ConstY[float]()
49 const Z* = ConstZ[float]()
50 const One2* = ConstOne2[float]()
51 const One3* = ConstOne3[float]()
52 const One4* = ConstOne4[float]()
53
54 func newVec2*[T](x, y: T): auto = Vec2([x, y])
55 func newVec3*[T](x, y, z: T): auto = Vec3([x, y, z])
56 func newVec4*[T](x, y, z, w: T): auto = Vec4([x, y, z, w])
57
58 func to*[T](v: Vec2): auto = Vec2([T(v[0]), T(v[1])])
59 func to*[T](v: Vec3): auto = Vec3([T(v[0]), T(v[1]), T(v[2])])
60 func to*[T](v: Vec4): auto = Vec4([T(v[0]), T(v[1]), T(v[2]), T(v[3])])
61
62 func toString[T](value: T): string =
63 var items: seq[string]
64 for item in value:
65 items.add($item)
66 $T & "(" & join(items, " ") & ")"
67
68 func `$`*(v: Vec2[SomeNumber]): string = toString[Vec2[SomeNumber]](v)
69 func `$`*(v: Vec3[SomeNumber]): string = toString[Vec3[SomeNumber]](v)
70 func `$`*(v: Vec4[SomeNumber]): string = toString[Vec4[SomeNumber]](v)
71
72 func length*(vec: Vec2[SomeFloat]): auto = sqrt(vec[0] * vec[0] + vec[1] * vec[1])
73 func length*(vec: Vec2[SomeInteger]): auto = sqrt(float(vec[0] * vec[0] + vec[1] * vec[1]))
74 func length*(vec: Vec3[SomeFloat]): auto = sqrt(vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2])
75 func length*(vec: Vec3[SomeInteger]): auto = sqrt(float(vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2]))
76 func length*(vec: Vec4[SomeFloat]): auto = sqrt(vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2] + vec[3] * vec[3])
77 func length*(vec: Vec4[SomeInteger]): auto = sqrt(float(vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2] + vec[3] * vec[3]))
78
79 func normalized*[T](vec: Vec2[T]): auto =
80 let l = vec.length
81 when T is SomeFloat:
82 Vec2[T]([vec[0] / l, vec[1] / l])
83 else:
84 Vec2[float]([float(vec[0]) / l, float(vec[1]) / l])
85 func normalized*[T](vec: Vec3[T]): auto =
86 let l = vec.length
87 when T is SomeFloat:
88 Vec3[T]([vec[0] / l, vec[1] / l, vec[2] / l])
89 else:
90 Vec3[float]([float(vec[0]) / l, float(vec[1]) / l, float(vec[2]) / l])
91 func normalized*[T](vec: Vec4[T]): auto =
92 let l = vec.length
93 when T is SomeFloat:
94 Vec4[T]([vec[0] / l, vec[1] / l, vec[2] / l, vec[3] / l])
95 else:
96 Vec4[float]([float(vec[0]) / l, float(vec[1]) / l, float(vec[2]) / l, float(vec[3]) / l])
97
98 # scalar operations
99 func `+`*(a: Vec2, b: SomeNumber): auto = Vec2([a[0] + b, a[1] + b])
100 func `+`*(a: Vec3, b: SomeNumber): auto = Vec3([a[0] + b, a[1] + b, a[2] + b])
101 func `+`*(a: Vec4, b: SomeNumber): auto = Vec4([a[0] + b, a[1] + b, a[2] + b, a[3] + b])
102 func `-`*(a: Vec2, b: SomeNumber): auto = Vec2([a[0] - b, a[1] - b])
103 func `-`*(a: Vec3, b: SomeNumber): auto = Vec3([a[0] - b, a[1] - b, a[2] - b])
104 func `-`*(a: Vec4, b: SomeNumber): auto = Vec4([a[0] - b, a[1] - b, a[2] - b, a[3] - b])
105 func `*`*(a: Vec2, b: SomeNumber): auto = Vec2([a[0] * b, a[1] * b])
106 func `*`*(a: Vec3, b: SomeNumber): auto = Vec3([a[0] * b, a[1] * b, a[2] * b])
107 func `*`*(a: Vec4, b: SomeNumber): auto = Vec4([a[0] * b, a[1] * b, a[2] * b, a[3] * b])
108 func `/`*[T: SomeInteger](a: Vec2[T], b: SomeInteger): auto = Vec2([a[0] div b, a[1] div b])
109 func `/`*[T: SomeFloat](a: Vec2[T], b: SomeFloat): auto = Vec2([a[0] / b, a[1] / b])
110 func `/`*[T: SomeInteger](a: Vec3[T], b: SomeInteger): auto = Vec3([a[0] div b, a[1] div b, a[2] div b])
111 func `/`*[T: SomeFloat](a: Vec3[T], b: SomeFloat): auto = Vec3([a[0] / b, a[1] / b, a[2] / b])
112 func `/`*[T: SomeInteger](a: Vec4[T], b: SomeInteger): auto = Vec4([a[0] div b, a[1] div b, a[2] div b, a[3] div b])
113 func `/`*[T: SomeFloat](a: Vec4[T], b: SomeFloat): auto = Vec4([a[0] / b, a[1] / b, a[2] / b, a[3] / b])
114
115 func `+`*(a: SomeNumber, b: Vec2): auto = Vec2([a + b[0], a + b[1]])
116 func `+`*(a: SomeNumber, b: Vec3): auto = Vec3([a + b[0], a + b[1], a + b[2]])
117 func `+`*(a: SomeNumber, b: Vec4): auto = Vec4([a + b[0], a + b[1], a + b[2], a + b[3]])
118 func `-`*(a: SomeNumber, b: Vec2): auto = Vec2([a - b[0], a - b[1]])
119 func `-`*(a: SomeNumber, b: Vec3): auto = Vec3([a - b[0], a - b[1], a - b[2]])
120 func `-`*(a: SomeNumber, b: Vec4): auto = Vec4([a - b[0], a - b[1], a - b[2], a - b[3]])
121 func `*`*(a: SomeNumber, b: Vec2): auto = Vec2([a * b[0], a * b[1]])
122 func `*`*(a: SomeNumber, b: Vec3): auto = Vec3([a * b[0], a * b[1], a * b[2]])
123 func `*`*(a: SomeNumber, b: Vec4): auto = Vec4([a * b[0], a * b[1], a * b[2], a * b[3]])
124 func `/`*[T: SomeInteger](a: SomeInteger, b: Vec2[T]): auto = Vec2([a div b[0], a div b[1]])
125 func `/`*[T: SomeFloat](a: SomeFloat, b: Vec2[T]): auto = Vec2([a / b[0], a / b[1]])
126 func `/`*[T: SomeInteger](a: SomeInteger, b: Vec3[T]): auto = Vec3([a div b[0], a div b[1], a div b[2]])
127 func `/`*[T: SomeFloat](a: SomeFloat, b: Vec3[T]): auto = Vec3([a / b[0], a / b[1], a / b[2]])
128 func `/`*[T: SomeInteger](a: SomeInteger, b: Vec4[T]): auto = Vec4([a div b[0], a div b[1], a div b[2], a div b[3]])
129 func `/`*[T: SomeFloat](a: SomeFloat, b: Vec4[T]): auto = Vec4([a / b[0], a / b[1], a / b[2], a / b[3]])
130
131 # compontent-wise operations
132 func `+`*(a, b: Vec2): auto = Vec2([a[0] + b[0], a[1] + b[1]])
133 func `+`*(a, b: Vec3): auto = Vec3([a[0] + b[0], a[1] + b[1], a[2] + b[2]])
134 func `+`*(a, b: Vec4): auto = Vec4([a[0] + b[0], a[1] + b[1], a[2] + b[2], a[3] + b[3]])
135 func `-`*(a: Vec2): auto = Vec2([-a[0], -a[1]])
136 func `-`*(a: Vec3): auto = Vec3([-a[0], -a[1], -a[2]])
137 func `-`*(a: Vec4): auto = Vec4([-a[0], -a[1], -a[2], -a[3]])
138 func `-`*(a, b: Vec2): auto = Vec2([a[0] - b[0], a[1] - b[1]])
139 func `-`*(a, b: Vec3): auto = Vec3([a[0] - b[0], a[1] - b[1], a[2] - b[2]])
140 func `-`*(a, b: Vec4): auto = Vec4([a[0] - b[0], a[1] - b[1], a[2] - b[2], a[3] - b[3]])
141 func `*`*(a, b: Vec2): auto = Vec2([a[0] * b[0], a[1] * b[1]])
142 func `*`*(a, b: Vec3): auto = Vec3([a[0] * b[0], a[1] * b[1], a[2] * b[2]])
143 func `*`*(a, b: Vec4): auto = Vec4([a[0] * b[0], a[1] * b[1], a[2] * b[2], a[3] * b[3]])
144 func `/`*[T: SomeInteger](a, b: Vec2[T]): auto = Vec2([a[0] div b[0], a[1] div b[1]])
145 func `/`*[T: SomeFloat](a, b: Vec2[T]): auto = Vec2([a[0] / b[0], a[1] / b[1]])
146 func `/`*[T: SomeInteger](a, b: Vec3[T]): auto = Vec3([a[0] div b[0], a[1] div b[1], a[2] div b[2]])
147 func `/`*[T: SomeFloat](a, b: Vec3[T]): auto = Vec3([a[0] / b[0], a[1] / b[1], a[2] / b[2]])
148 func `/`*[T: SomeInteger](a, b: Vec4[T]): auto = Vec4([a[0] div b[0], a[1] div b[1], a[2] div b[2], a[3] div b[3]])
149 func `/`*[T: SomeFloat](a, b: Vec4[T]): auto = Vec4([a[0] / b[0], a[1] / b[1], a[2] / b[2], a[3] / b[3]])
150
151 # special operations
152 func dot*(a, b: Vec2): auto = a[0] * b[0] + a[1] * b[1]
153 func dot*(a, b: Vec3): auto = a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
154 func dot*(a, b: Vec4): auto = a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3]
155 func cross*(a, b: Vec3): auto = Vec3([
156 a[1] * b[2] - a[2] * b[1],
157 a[2] * b[0] - a[0] * b[2],
158 a[0] * b[1] - a[1] * b[0],
159 ])
160
161
162 # macro to allow creation of new vectors by specifying vector components as attributes
163 # e.g. myVec.xxy will return a new Vec3 that contains the components x, x an y of the original vector
164 # (instead of x, y, z for a simple copy)
165 proc vectorAttributeAccessor(accessor: string): NimNode =
166 const ACCESSOR_INDICES = {
167 'x': 0,
168 'y': 1,
169 'z': 2,
170 'w': 3,
171 'r': 0,
172 'g': 1,
173 'b': 2,
174 'a': 3,
175 }.toTable
176 var ret: NimNode
177 let accessorvalue = accessor
178
179 if accessorvalue.len == 0:
180 raise newException(Exception, "empty attribute")
181 elif accessorvalue.len == 1:
182 ret = nnkBracket.newTree(ident("value"), newLit(ACCESSOR_INDICES[accessorvalue[0]]))
183 if accessorvalue.len > 1:
184 var attrs = nnkBracket.newTree()
185 for attrname in accessorvalue:
186 attrs.add(nnkBracketExpr.newTree(ident("value"), newLit(ACCESSOR_INDICES[attrname])))
187 ret = nnkCall.newTree(ident("Vec" & $accessorvalue.len), attrs)
188
189 newProc(
190 name=nnkPostfix.newTree(ident("*"), ident(accessor)),
191 params=[ident("auto"), nnkIdentDefs.newTree(ident("value"), ident("Vec"), newEmptyNode())],
192 body=newStmtList(ret),
193 procType = nnkFuncDef,
194 )
195
196 macro createVectorAttribAccessorFuncs() =
197 const COORD_ATTRS = ["x", "y", "z", "w"]
198 const COLOR_ATTRS = ["r", "g", "b", "a"]
199 result = nnkStmtList.newTree()
200 for attlist in [COORD_ATTRS, COLOR_ATTRS]:
201 for i in attlist:
202 result.add(vectorAttributeAccessor(i))
203 for j in attlist:
204 result.add(vectorAttributeAccessor(i & j))
205 for k in attlist:
206 result.add(vectorAttributeAccessor(i & j & k))
207 for l in attlist:
208 result.add(vectorAttributeAccessor(i & j & k & l))
209
210 createVectorAttribAccessorFuncs()
211
212 # call e.g. Vec2[int]().randomized() to get a random matrix
213 template makeRandomInit(mattype: typedesc) =
214 proc randomized*[T: SomeInteger](m: mattype[T]): mattype[T] =
215 for i in 0 ..< result.len:
216 result[i] = rand(low(typeof(m[0])) .. high(typeof(m[0])))
217 proc randomized*[T: SomeFloat](m: mattype[T]): mattype[T] =
218 for i in 0 ..< result.len:
219 result[i] = rand(1.0)
220
221 makeRandomInit(Vec2)
222 makeRandomInit(Vec3)
223 makeRandomInit(Vec4)