3D Vector Class

Feb 26th, 2015
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1. -- ********************************************************************************** --
2. -- **   3D Vector                                                                  ** --
3. -- **                                                                              ** --
4. -- **   Modified version of 2d vector from                                         ** --
5. -- **   https://github.com/vrld/hump/blob/master/vector.lua                        ** --
6. -- **                                                                              ** --
7. -- ********************************************************************************** --
8.
9. vec3 = (function()
10.   local assert = assert
11.   local sqrt, cos, sin, atan2 = math.sqrt, math.cos, math.sin, math.atan2
12.
13.   local vector = {}
14.   vector.__index = vector
15.
16.   local function new(x,y,z)
17.     return setmetatable({x = x or 0, y = y or 0, z = z or 0}, vector)
18.   end
19.   local zero = new(0,0,0)
20.
21.   local function isvector(v)
22.     return type(v) == 'table' and type(v.x) == 'number' and type(v.y) == 'number' and type(v.z) == 'number'
23.   end
24.
25.   function vector:clone()
26.     return new(self.x, self.y, self.z)
27.   end
28.
29.   function vector:unpack()
30.     return self.x, self.y, self.z
31.   end
32.
33.   function vector:__tostring()
34.     return "("..tonumber(self.x)..","..tonumber(self.y)..","..tonumber(self.z)..")"
35.   end
36.
37.   function vector.__unm(a)
38.     return new(-a.x, -a.y, -a.z)
39.   end
40.
42.     assert(isvector(a) and isvector(b), "Add: wrong argument types (<vector> expected)")
43.     return new(a.x+b.x, a.y+b.y, a.z+b.z)
44.   end
45.
46.   function vector.__sub(a,b)
47.     assert(isvector(a) and isvector(b), "Sub: wrong argument types (<vector> expected)")
48.     return new(a.x-b.x, a.y-b.y, a.z-b.z)
49.   end
50.
51.   function vector.__mul(a,b)
52.     if type(a) == "number" then
53.       return new(a*b.x, a*b.y, a*b.z)
54.     elseif type(b) == "number" then
55.       return new(b*a.x, b*a.y, b*a.z)
56.     else
57.       assert(isvector(a) and isvector(b), "Mul: wrong argument types (<vector> or <number> expected)")
58.       return a.x*b.x + a.y*b.y + a.z*b.z
59.     end
60.   end
61.
62.   function vector.__div(a,b)
63.     assert(isvector(a) and type(b) == "number", "wrong argument types (expected <vector> / <number>)")
64.     return new(a.x / b, a.y / b, a.z / b)
65.   end
66.
67.   function vector.__eq(a,b)
68.     return a.x == b.x and a.y == b.y and a.z == b.z
69.   end
70.
71.   function vector.__lt(a,b)
72.     return a.x < b.x and a.y < b.y and a.z < b.z
73.   end
74.
75.   function vector.__le(a,b)
76.     return a.x <= b.x and a.y <= b.y and a.z <= b.z
77.   end
78.
79.   function vector.permul(a,b)
80.     assert(isvector(a) and isvector(b), "permul: wrong argument types (<vector> expected)")
81.     return new(a.x*b.x, a.y*b.y, a.z*b.z)
82.   end
83.
84.   function vector:len2()
85.     return self.x * self.x + self.y * self.y + self.z * self.z
86.   end
87.
88.   function vector:len()
89.     return sqrt(self.x * self.x + self.y * self.y + self.z * self.z)
90.   end
91.
92.   function vector.dist(a, b)
93.     assert(isvector(a) and isvector(b), "dist: wrong argument types (<vector> expected)")
94.     local dx = a.x - b.x
95.     local dy = a.y - b.y
96.     local dz = a.z - b.z
97.     return sqrt(dx * dx + dy * dy + dz * dz)
98.   end
99.
100.   function vector.dist2(a, b)
101.     assert(isvector(a) and isvector(b), "dist: wrong argument types (<vector> expected)")
102.     local dx = a.x - b.x
103.     local dy = a.y - b.y
104.     local dz = a.z - b.z
105.     return (dx * dx + dy * dy + dz * dz)
106.   end
107.
108.   function vector:normalize_inplace()
109.     local l = self:len()
110.     if l > 0 then
111.       self.x, self.y, self.z = self.x / l, self.y / l, self.z / l
112.     end
113.     return self
114.   end
115.
116.   function vector:normalized()
117.     return self:clone():normalize_inplace()
118.   end
119.
120.   function vector:rotate_inplace_z(phi)
121.     local c, s = cos(phi), sin(phi)
122.     self.x, self.y = c * self.x - s * self.y, s * self.x + c * self.y
123.     return self
124.   end
125.   function vector:rotate_inplace_x(phi)
126.     local c, s = cos(phi), sin(phi)
127.     self.y, self.z = c * self.y - s * self.z, s * self.y + c * self.z
128.     return self
129.   end
130.   function vector:rotate_inplace_y(phi)
131.     local c, s = cos(phi), sin(phi)
132.     self.z, self.x = c * self.z - s * self.x, s * self.z + c * self.x
133.     return self
134.   end
135.
136.   function vector:rotated_z(phi)
137.     local c, s = cos(phi), sin(phi)
138.     return new(c * self.x - s * self.y, s * self.x + c * self.y, self.z)
139.   end
140.   function vector:rotated_x(phi)
141.     local c, s = cos(phi), sin(phi)
142.     return new(self.x, c * self.y - s * self.z, s * self.y + c * self.z)
143.   end
144.   function vector:rotated_y(phi)
145.     local c, s = cos(phi), sin(phi)
146.     return new(s * self.z + c * self.x, self.y, c * self.z - s * self.x)
147.   end
148.
149.   function vector:cross(v)
150.     assert(isvector(v), "cross: wrong argument types (<vector> expected)")
151.     return new(self.Y * v.Z - self.Z * v.Y,
152.                self.Z * v.X - self.X * v.Z,
153.                self.X * v.Y - self.Y * v.X)
154.   end
155.
156.   -- ref.: http://blog.signalsondisplay.com/?p=336
157.   function vector:trim_inplace(maxLen)
158.     local s = maxLen * maxLen / self:len2()
159.     s = (s > 1 and 1) or math.sqrt(s)
160.     self.x, self.y, self.z = self.x * s, self.y * s, self.z * s
161.     return self
162.   end
163.
164.   function vector:trimmed(maxLen)
165.     return self:clone():trim_inplace(maxLen)
166.   end
167.
168.
169.   -- the module
170.   return setmetatable({new = new, isvector = isvector, zero = zero},
171.   {__call = function(_, ...) return new(...) end})
172. end)()