summaryrefslogtreecommitdiff
path: root/macros/latex/contrib/tkz/tkz-elements/latex/tkz_elements_functions_maths.lua
blob: 9b4e51d29596fee10477b25e203fb1856cfe5696 (plain)
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
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
-- tkz_elements_functions_maths.lua
-- date 2024/03/25
-- version 2.20c
-- 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.

-- constant
tkzphi      = (1+math.sqrt(5))/2
tkzinvphi   = (math.sqrt(5)-1)/2
tkzsqrtphi  =  math.sqrt(tkzphi)
---------------------------------------------------------------------------
function round(num, idp)
  return topoint(string.format("%." .. (idp or 0) .. "f", num))
end

function tkzround( num, idp )
	local mult = 10 ^ ( idp or 0 )
	return math.floor( num * mult + 0.5 ) / mult
end  

function dot_product (a,b,c)
   return (b-a)..(c-a)
end

function Cramer33(a1,a2,a3,b1,b2,b3,c1,c2,c3)
  return a1*b2*c3+a3*b1*c2+a2*b3*c1-a3*b2*c1-a1*b3*c2-a2*b1*c3
end

function Cramer22(a1,a2,b1,b2)
  return a1*b2-a2*b1
end

function aligned ( m,a,b )
    local z
    z = (b-a)/(m-b)
      if math.abs(z.im) < tkz_epsilon
        then
            return true
        else
            return false
        end
end 

function islinear (z1,z2,z3)
     local dp
    dp = (z2-z1) ^ (z3-z1)
    if math.abs(dp) < tkz_epsilon 
    then 
        return true
    else 
        return false
    end
end

function isortho (z1,z2,z3)
   local dp
   dp = (z2-z1) .. (z3-z1)
   if math.abs(dp) < tkz_epsilon 
    then 
        return true
    else 
        return false
    end
end

function parabola (a,b,c)
   local xa,xb,xc,ya,yb,yc
   xa = a.re
   ya = a.im
   xb = b.re
   yb = b.im
   xc = c.re
   yc = c.im
   D = (xa-xb)*(xa-xc)*(xb-xc)
   A = (xc*(yb-ya) + xb*(ya-yc)+xa*(yc-yb))/D
   B = (xc*xc*(ya-yb)+xb*xb*(yc-ya)+xa*xa*(yb-yc))/D
   C = (xb*xc*(xb-xc)*ya + xc*xa*(xc-xa)*yb +xa*xb*(xa-xb)*yc)/D
   return A,B,C
end

function value (v)
   return scale * v
end

function real (v)
   return v/scale
end

function get_angle (a,b,c)
  return angle_normalize_(get_angle_( a,b,c ))
end 
   
function get_angle_( a,b,c )
	 return point.arg ((c-a)/(b-a))
end

function angle_normalize (a)
return angle_normalize_ (a)
end

function angle_normalize_ (a)
    while a < 0 do
        a = a + 2*math.pi
    end
    while a >= 2*math.pi do
        a = a - 2*math.pi
    end
    return a
end

function barycenter (...)
   return barycenter_ (...)
end

function swap(a,b)
   local t=a
   a=b
   b=t
   return a,b
end
-- real func
function is_integer(x)
    return x == math.round(x)
end

function near_integer(x)
  local i,r  = math.modf  (x)
  if is_zero (r) then 
   return  true
 end
    return false
end

function residue (x)
  dp,ip =  math.modf (x)
  return ip
end

function is_zero (x)
 return math.abs(x) < tkz_epsilon 
end 

function set_zero (x)
  if is_zero (x) then x=0 end
  return x
end

function math.round(num)
  return math.floor(num + 0.5)
end

function checknumber(x)
   if type(x) == 'table' then 
      return x 
   else
     if string.find(x, "e") then
        return string.format("%.12f",x)
      else
          return x
      end
   end
end

function decimal (x)
   if string.find(x, "e") then
      return string.format("%.12f",x)
   else
      return x
   end
end

function format_number(number, dcpl)
  if type(number) == 'table' then return number 
  else
    local format_string = string.format("%%.%df", dcpl)
    return string.format(format_string, number)
  end
end

function get_sign(number)
  local sgn
     if math.abs(number) < tkz_epsilon then
         sgn = ""
     elseif number > 0 then
         sgn = "+"
     else
        sgn = "-"
     end
     return sgn
end

function solve_quadratic(a, b, c)
  local root1, root2,delta ,sqrtdelta
  if (type(a) == "number") and (type(b) == "number") and                (type(c) == "number") 
  then
     delta = b*b - 4*a*c
    if delta < 0 then
       root1, root2 =  solve_cx_quadratic(a, b, c)
      elseif delta == 0 then
         root1 = -b / (2*a)
         root2 = -b / (2*a)
       else
          sqrtdelta = math.sqrt(delta)
           
         root1 = (-b + sqrtdelta) / (2*a)
         root2 = (-b - sqrtdelta) / (2*a)     
       end
  else 
    root1, root2 = solve_cx_quadratic(a, b, c)
  end

   return root1, root2 -- Two real roots
end

function solve_cx_quadratic(a, b, c)
    local d     = b*b - 4*a*c
    local dcx   = point.sqrt(d)  
    local root1 = (- b + dcx) / (2*a)
    local root2 = (- b - dcx) / (2*a)  
    return root1, root2
end

-- function solve_cubic(a, b, c, d)
--     local p       = (3*a*c - b*b)/(3*a*a)
--     local q       = (2*b*b*b - 9*a*b*c + 27*a*a*d)/(27*a*a*a)
--     local delta   = q*q+4*p*p*p/27
--     local offset  = - b / (3*a)
--     if delta > tkz_epsilon then
--          local r = (- q + math.sqrt(delta))/2
--          local s = (- q - math.sqrt(delta))/2
--          if r > 0 then
--              u = r^(1/3)
--          else
--              u = -(-r)^(1/3)
--          end
--          if s > 0 then
--             v = s^(1/3)
--          else
--             v = -(-s)^(1/3)
--          end
--          return u + v + offset
--      end
--      if delta < 0 then
--       local u = 2 * math.sqrt( - p / 3)
--       local v = math.acos(((3*q)/(2*p)) * math.sqrt( -3 / p)) / 3
--       local x1 = u * math.cos(v)  + offset
--       local x2 = u * math.cos(v + 2 * math.pi/3) + offset
--        local x3 = u * math.cos(v - 2 * math.pi/3) + offset
--       return {x1,x2,x3}
--        end
-- if delta == 0 then
--         return {3*q/p+offset,-3*q/(2*p)+offset,-3*q/(2*p)+offset}
--        end
-- end

function display_real (r)
  local format_string,format_string
  if r == nil then  return ""
    else
      if near_integer ( r ) 
         then 
           r = math.round ( r )
           format_string = string.format("%%.%df", 0)
         else
           format_string = string.format("%%.%df", tkz_dc)
      end
   local st = string.format(format_string , r)
   return st
 end
end


function display_imag (r)
  local sgn
  sgn = get_sign (r)
  r = math.abs(r)
  if math.abs(r-1) < tkz_epsilon then
     r = nil
   elseif near_integer ( r ) then
     r = math.abs(math.round(r))
  end
  st = display_real (r)
  return sgn,st
end

function display (z)
  if (type(z) == "number") then return display_real (z)     else
      local real, imag
      real = z.re
      imag = z.im
 if is_zero ( imag ) then
  return display_real (real)
 else
   str = display_real (real)
   sgni,sti = display_imag (imag)
   if str == "0"  then 
     str=""
      sgni = "" end
 local  st = str ..sgni..sti.."i"
  return st
 end
end
end