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
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
|
-- tkz_elements_lines.lua
-- date 2023/10/20
-- version 1.00b
-- Copyright 2023 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.
-- -------------------------------------------------------------------------
-- Lines
-- -------------------------------------------------------------------------
line = {}
function line: new(za, zb)
local type = 'line'
local mid = (za+zb)/2
local north_pa = rotation_ (za,math.pi/2,zb)
local south_pa = rotation_ (za,-math.pi/2,zb)
local north_pb = rotation_ (zb,-math.pi/2,za)
local south_pb = rotation_ (zb,math.pi/2,za)
local west = rotation_ (za,math.pi/2,north_pa)
local east = rotation_ (zb,math.pi/2,south_pb)
local slope = point.arg(zb-za)
local length = point.mod(zb-za)
local new_line = {pa = za, pb = zb,
north_pa = north_pa,south_pa = south_pa,west = west,east = east,
north_pb = north_pb,south_pb = south_pb,
slope = slope,mid = mid,type = type,length = length}
setmetatable(new_line, {__index = line})
return new_line
end
-------------------
-- Result -> point
-------------------
function line: set_projection (...)
local tp = table.pack(...)
local i
local t = {}
for i=1,tp.n do
table.insert( t , projection_ (self.pa,self.pb , tp[i]) )
end
return table.unpack ( t )
end
function line: symmetry_axial ( pt )
return symmetry_axial_ ( self.pa,self.pb,pt )
end
function line: set_symmetry_axial (...)
local tp = table.pack(...)
local i
local t = {}
for i=1,tp.n do
table.insert( t , symmetry_axial_ (self.pa,self.pb , tp[i]) )
end
return table.unpack ( t )
end
-- k_div ig "gold" or "phi" then
function line: barycenter (ka,kb)
return barycenter_({self.pa,ka},{self.pb,kb})
end
function line: point (t) -- t=o A t=1 B t = AM / AB
return barycenter_({self.pa,1-t},{self.pb,(t)})
end
function line: midpoint ()
return (self.pa+self.pb)/2
end
function line: harmonic_int (pt)
return div_harmonic_int_(self.pa,self.pb,pt)
end
function line: harmonic_ext (pt)
return div_harmonic_ext_(self.pa,self.pb,pt)
end
function line: harmonic_both (k)
return div_harmonic_both_(self.pa,self.pb,k)
end
function line: gold_ratio()
return self.pa + (self.pb-self.pa)*tkzinvphi
end
-------------------
-- Result -> line
-------------------
function line: ll_from ( pt )
return line : new (pt,pt+self.pb-self.pa)
end
function line: ortho_from ( pt )
return line : new (pt,pt+(self.pb-self.pa)*point(0,1))
end
function line: projection ( pt )
return projection_ ( self.pa,self.pb,pt )
end
function line: mediator ()
local m
m = midpoint_ (self.pa,self.pb)
return line : new (m,rotation_ (m,math.pi/2,self.pb))
end
-------------------
-- Result -> circle
-------------------
function line: circle ()
return circle : new (self.pa,self.pb)
end
function line: circle_swap ()
return circle : new (self.pb,self.pa)
end
-------------------
-- Result -> real
-------------------
function line: distance (pt)
return point.mod(projection(self,pt)-pt)
end
-------------------
-- Result -> boolean
-------------------
function line: in_out (pt)
local sc,epsilon
epsilon = 10^(-12)
sc = math.abs ((pt-self.pa)^(pt-self.pb))
if sc <= epsilon
then
return true
else
return false
end
end
function line: slope ()
return slope_(self.pa,self.pb)
end
----------------------
-- Result -> triangle
----------------------
function line: equilateral ()
return triangle : new (self.pa,self.pb,rotation_ (self.pa,math.pi/3,self.pb))
end
function line: isosceles (phi)
local pta,ptb
pta = rotation_ (self.pa,phi,self.pb)
ptb = rotation_ (self.pb,-phi,self.pa)
return triangle : new (self.pa,self.pb, intersection_ll_ (self.pa,pta,self.pb,ptb ))
end
function line: gold ()
local pt
pt = rotation_ (self.pa,math.pi/2,self.pb)
return triangle : new (self.pa,self.pb, self.pa + (pt-self.pa) * tkzinvphi)
end
function line: euclide ()
return triangle : new (self.pa,self.pb, rotation_ (self.pa,math.pi/5,self.pb))
end
function line: golden ()
local pt
pt = rotation_ (self.pa,2*math.pi/5,self.pb)
return triangle : new (self.pa,self.pb, self.pa + (pt-self.pa) * tkzphi)
end
------------------------------
-- Result -> couple of points
------------------------------
function line: square ()
return rotation_ (self.pb,-math.pi/2,self.pa), rotation_ (self.pa,math.pi/2,self.pb)
end
return line
|