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
|
-- tkz_elements_vectors.lua
-- date 2024/02/04
-- version 2.00c
-- Copyright 2024 Alain Matthes
-- This work may be distributed and/or modified under the
-- conditions of the LaTeX Project Public License, either version 1.3
-- of this license or (at your option) any later version.
-- The latest version of this license is in
-- http://www.latex-project.org/lppl.txt
-- and version 1.3 or later is part of all distributions of LaTeX
-- version 2005/12/01 or later.
-- This work has the LPPL maintenance status “maintained”.
-- The Current Maintainer of this work is Alain Matthes.
-- ----------------------------------------------------------------------------
vector = {}
function vector: new(za, zb)
local type = 'vector'
local slope = angle_normalize_(point.arg(zb-za))
local norm = point.mod(zb-za)
local o = {t = za,
h = zb,
norm = norm,
slope = slope,
type = type }
setmetatable(o, self)
self.__index = self
return o
end
function vector.__add(v1,v2)
return v1 : add (v2)
end
function vector.__sub(v1,v2)
local v = v2 : scale(-1)
return v1 : add (v)
end
function vector.__unm(v)
return v : scale(-1)
end
function vector.__mul(r,v)
return v : scale(r)
end
function vector: normalize ()
local z = self.h-self.t
local d = point.abs(z)
local nz = point(z.re/d,z.im/d)
return vector : new (self.t,nz + self.t)
end
function vector: add (ve)
return vector :new (self.t,self.h+ve.h-ve.t)
end
function vector: orthogonal (d)
local z
if d == nil then
return vector : new (self.t, rotation_(self.t,math.pi/2,self.h))
else
z = self.t+ point (d*math.cos(self.slope),d*math.sin(self.slope))
return vector : new (self.t, rotation_(self.t,math.pi/2,z))
end
end
function vector: scale (d)
local l,z
l = self.norm
z = self.t+ point (d*l*math.cos(self.slope),d*l*math.sin(self.slope))
return vector : new (self.t,z )
end
function vector: at (zc)
return vector :new (zc,zc+self.h-self.t)
end
return vector
|