1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
|
vector = {}
function vector.new(a, b, c)
if type(a) == "table" then
assert(a.x and a.y and a.z, "Invalid vector passed to vector.new()")
return {x=a.x, y=a.y, z=a.z}
elseif a then
assert(b and c, "Invalid arguments for vector.new()")
return {x=a, y=b, z=c}
end
return {x=0, y=0, z=0}
end
function vector.equals(a, b)
return a.x == b.x and
a.y == b.y and
a.z == b.z
end
function vector.length(v)
return math.hypot(v.x, math.hypot(v.y, v.z))
end
function vector.normalize(v)
local len = vector.length(v)
if len == 0 then
return {x=0, y=0, z=0}
else
return vector.divide(v, len)
end
end
function vector.floor(v)
return {
x = math.floor(v.x),
y = math.floor(v.y),
z = math.floor(v.z)
}
end
function vector.round(v)
return {
x = math.floor(v.x + 0.5),
y = math.floor(v.y + 0.5),
z = math.floor(v.z + 0.5)
}
end
function vector.apply(v, func)
return {
x = func(v.x),
y = func(v.y),
z = func(v.z)
}
end
function vector.distance(a, b)
local x = a.x - b.x
local y = a.y - b.y
local z = a.z - b.z
return math.hypot(x, math.hypot(y, z))
end
function vector.direction(pos1, pos2)
return vector.normalize({
x = pos2.x - pos1.x,
y = pos2.y - pos1.y,
z = pos2.z - pos1.z
})
end
function vector.angle(a, b)
local dotp = a.x * b.x + a.y * b.y + a.z * b.z
local cpx = a.y * b.z - a.z * b.y
local cpy = a.z * b.x - a.x * b.z
local cpz = a.x * b.y - a.y * b.x
local crossplen = math.sqrt(cpx ^ 2 + cpy ^ 2 + cpz ^ 2)
return math.atan2(crossplen, dotp)
end
function vector.dot(a, b)
return a.x * b.x + a.y * b.y + a.z * b.z
end
function vector.cross(a, b)
return {
x = a.y * b.z - a.z * b.y,
y = a.z * b.x - a.x * b.z,
z = a.x * b.y - a.y * b.x
}
end
function vector.add(a, b)
if type(b) == "table" then
return {x = a.x + b.x,
y = a.y + b.y,
z = a.z + b.z}
else
return {x = a.x + b,
y = a.y + b,
z = a.z + b}
end
end
function vector.subtract(a, b)
if type(b) == "table" then
return {x = a.x - b.x,
y = a.y - b.y,
z = a.z - b.z}
else
return {x = a.x - b,
y = a.y - b,
z = a.z - b}
end
end
function vector.multiply(a, b)
if type(b) == "table" then
return {x = a.x * b.x,
y = a.y * b.y,
z = a.z * b.z}
else
return {x = a.x * b,
y = a.y * b,
z = a.z * b}
end
end
function vector.divide(a, b)
if type(b) == "table" then
return {x = a.x / b.x,
y = a.y / b.y,
z = a.z / b.z}
else
return {x = a.x / b,
y = a.y / b,
z = a.z / b}
end
end
function vector.sort(a, b)
return {x = math.min(a.x, b.x), y = math.min(a.y, b.y), z = math.min(a.z, b.z)},
{x = math.max(a.x, b.x), y = math.max(a.y, b.y), z = math.max(a.z, b.z)}
end
|
