- totalement réécrit la fonction arctangente dans le module trigo pour nodeMCU

- réécrit aussi equa2azim, cela a l'air de bien fonctionner maintenant

Trigo/Lua, tables de trigonométrie.gsheet

@@ -0,0 +1 @@
+{"url": "https://docs.google.com/open?id=1p7vD3c2epzUz_xE9CP6CEJbpspGn2hzpBLVqSr5hP1c", "doc_id": "1p7vD3c2epzUz_xE9CP6CEJbpspGn2hzpBLVqSr5hP1c", "email": "christian.zufferey@gmail.com"}

Trigo/sincos.csv

@@ -0,0 +1,102 @@
+Angle [rad],Sinus,Cosinus
+0,0,1
+0.06283185307,0.06279051953,0.9980267284
+0.1256637061,0.1253332336,0.9921147013
+0.1884955592,0.1873813146,0.9822872507
+0.2513274123,0.2486898872,0.9685831611
+0.3141592654,0.3090169944,0.9510565163
+0.3769911184,0.3681245527,0.9297764859
+0.4398229715,0.4257792916,0.9048270525
+0.5026548246,0.4817536741,0.87630668
+0.5654866776,0.535826795,0.8443279255
+0.6283185307,0.5877852523,0.8090169944
+0.6911503838,0.6374239897,0.7705132428
+0.7539822369,0.6845471059,0.7289686274
+0.8168140899,0.7289686274,0.6845471059
+0.879645943,0.7705132428,0.6374239897
+0.9424777961,0.8090169944,0.5877852523
+1.005309649,0.8443279255,0.535826795
+1.068141502,0.87630668,0.4817536741
+1.130973355,0.9048270525,0.4257792916
+1.193805208,0.9297764859,0.3681245527
+1.256637061,0.9510565163,0.3090169944
+1.319468915,0.9685831611,0.2486898872
+1.382300768,0.9822872507,0.1873813146
+1.445132621,0.9921147013,0.1253332336
+1.507964474,0.9980267284,0.06279051953
+1.570796327,1,0
+1.63362818,0.9980267284,-0.06279051953
+1.696460033,0.9921147013,-0.1253332336
+1.759291886,0.9822872507,-0.1873813146
+1.822123739,0.9685831611,-0.2486898872
+1.884955592,0.9510565163,-0.3090169944
+1.947787445,0.9297764859,-0.3681245527
+2.010619298,0.9048270525,-0.4257792916
+2.073451151,0.87630668,-0.4817536741
+2.136283004,0.8443279255,-0.535826795
+2.199114858,0.8090169944,-0.5877852523
+2.261946711,0.7705132428,-0.6374239897
+2.324778564,0.7289686274,-0.6845471059
+2.387610417,0.6845471059,-0.7289686274
+2.45044227,0.6374239897,-0.7705132428
+2.513274123,0.5877852523,-0.8090169944
+2.576105976,0.535826795,-0.8443279255
+2.638937829,0.4817536741,-0.87630668
+2.701769682,0.4257792916,-0.9048270525
+2.764601535,0.3681245527,-0.9297764859
+2.827433388,0.3090169944,-0.9510565163
+2.890265241,0.2486898872,-0.9685831611
+2.953097094,0.1873813146,-0.9822872507
+3.015928947,0.1253332336,-0.9921147013
+3.078760801,0.06279051953,-0.9980267284
+3.141592654,0,-1
+3.204424507,-0.06279051953,-0.9980267284
+3.26725636,-0.1253332336,-0.9921147013
+3.330088213,-0.1873813146,-0.9822872507
+3.392920066,-0.2486898872,-0.9685831611
+3.455751919,-0.3090169944,-0.9510565163
+3.518583772,-0.3681245527,-0.9297764859
+3.581415625,-0.4257792916,-0.9048270525
+3.644247478,-0.4817536741,-0.87630668
+3.707079331,-0.535826795,-0.8443279255
+3.769911184,-0.5877852523,-0.8090169944
+3.832743037,-0.6374239897,-0.7705132428
+3.89557489,-0.6845471059,-0.7289686274
+3.958406744,-0.7289686274,-0.6845471059
+4.021238597,-0.7705132428,-0.6374239897
+4.08407045,-0.8090169944,-0.5877852523
+4.146902303,-0.8443279255,-0.535826795
+4.209734156,-0.87630668,-0.4817536741
+4.272566009,-0.9048270525,-0.4257792916
+4.335397862,-0.9297764859,-0.3681245527
+4.398229715,-0.9510565163,-0.3090169944
+4.461061568,-0.9685831611,-0.2486898872
+4.523893421,-0.9822872507,-0.1873813146
+4.586725274,-0.9921147013,-0.1253332336
+4.649557127,-0.9980267284,-0.06279051953
+4.71238898,-1,0
+4.775220833,-0.9980267284,0.06279051953
+4.838052687,-0.9921147013,0.1253332336
+4.90088454,-0.9822872507,0.1873813146
+4.963716393,-0.9685831611,0.2486898872
+5.026548246,-0.9510565163,0.3090169944
+5.089380099,-0.9297764859,0.3681245527
+5.152211952,-0.9048270525,0.4257792916
+5.215043805,-0.87630668,0.4817536741
+5.277875658,-0.8443279255,0.535826795
+5.340707511,-0.8090169944,0.5877852523
+5.403539364,-0.7705132428,0.6374239897
+5.466371217,-0.7289686274,0.6845471059
+5.52920307,-0.6845471059,0.7289686274
+5.592034923,-0.6374239897,0.7705132428
+5.654866776,-0.5877852523,0.8090169944
+5.71769863,-0.535826795,0.8443279255
+5.780530483,-0.4817536741,0.87630668
+5.843362336,-0.4257792916,0.9048270525
+5.906194189,-0.3681245527,0.9297764859
+5.969026042,-0.3090169944,0.9510565163
+6.031857895,-0.2486898872,0.9685831611
+6.094689748,-0.1873813146,0.9822872507
+6.157521601,-0.1253332336,0.9921147013
+6.220353454,-0.06279051953,0.9980267284
+6.283185307,0,1

Trigo/test_trigo1.lua

@@ -0,0 +1,12 @@
+-- tests des routines trigonométriques pour NodeMCU
+print("\ntest_trigo1.lua   zf180819.1731   \n")
+
+-- chargement des routines trigonométriques
+dofile("trigo3.lua")
+
+for i = 0, 2*pi, 2*pi/100 do
+  a=i
+  --print("tangente: "..a..", "..math.tan(a)..", "..ztan(a))
+  b=math.tan(a)
+  print("arctangente: "..b..", "..math.atan(b)..", "..zatan(b)..", "..math.atan(b)/zatan(b))
+end

Trigo/trigo1.lua

@@ -0,0 +1,49 @@
+-- Essais de fire des fonctions trigos qui manque dans NodeMCU
+-- ATTENTION: arcsin ne fonctionne pas pour les valeur proche de 1 !
+-- source: https://www.esp8266.com/viewtopic.php?p=64415#
+print("\ntrigo1.lua   zf180726.1136   \n")
+
+function sin(x)
+   local p=-x*x*x
+   local f=6
+   local r=x+p/f
+   for j=1,60 do
+      p=-p*x*x
+      f=f*2*(j+1)*(j+j+3)
+      r=r+p/f
+   end
+   return r
+end
+
+function cos(x)
+   return sin(math.pi/2-x)
+end
+
+function tan(x)
+   return sin(x)/cos(x)
+end
+
+function arcsin(x)
+   local suma=x
+   for i=1,60 do
+      suma = suma + (dfi(2*i-1)/dfp(2*i))*(math.pow(x,2*i+1)/(2*i+1))
+      print("Suma: "..suma)
+   end
+   return suma
+end
+
+function dfp(x)
+   local par=1
+   for i=2,x,2 do
+      par = par * i
+   end
+   return par
+end
+
+function dfi(x)
+   local impar=1
+   for i=1,x,2 do
+      impar = impar * i
+   end
+   return impar
+end

Trigo/trigo2.lua

@@ -0,0 +1,90 @@
+-- 2e Essais de faire des fonctions trigos qui manque dans NodeMCU
+-- source pour sin&cos: https://www.esp8266.com/viewtopic.php?p=64415#
+-- source pour arcsin&arctan: http://www.electronicwings.com/nodemcu/magnetometer-hmc5883l-interfacing-with-nodemcu
+print("\ntrigo2.lua   zf180726.1149   \n")
+
+
+
+function sin(x)
+   local p=-x*x*x
+   local f=6
+   local r=x+p/f
+   for j=1,60 do
+      p=-p*x*x
+      f=f*2*(j+1)*(j+j+3)
+      r=r+p/f
+   end
+   return r
+end
+
+function cos(x)
+   return sin(math.pi/2-x)
+end
+
+function tan(x)
+   return sin(x)/cos(x)
+end
+
+
+
+
+pi = 3.14159265358979323846
+
+
+function arcsin(value)
+    local val = value
+    local sum = value 
+    if(value == nil) then
+        return 0
+    end
+-- as per equation it needs infinite iterations to reach upto 100% accuracy
+-- but due to technical limitations we are using
+-- only 10000 iterations to acquire reliable accuracy
+    for i = 1,10000, 2 do
+        val = (val*(value*value)*(i*i)) / ((i+1)*(i+2))
+        sum = sum + val;
+    end
+    return sum
+end
+
+function arctan(value)
+    if(value == nil) then
+        return 0
+    end
+    local _value = value/math.sqrt((value*value)+1)
+    return arcsin(_value)
+end
+
+function atan2(y, x)
+    if(x == nil or y == nil) then
+        return 0
+    end
+
+    if(x > 0) then
+        return arctan(y/x)
+    end
+    if(x < 0 and 0 <= y) then
+        return arctan(y/x) + pi
+    end
+    if(x < 0 and y < 0) then
+        return arctan(y/x) - pi
+    end
+    if(x == 0 and y > 0) then
+        return pi/2
+    end
+    if(x == 0 and y < 0) then
+        return -pi/2
+    end
+    if(x == 0 and y == 0) then
+        return 0
+    end
+    return 0
+end
+
+print("On voit que l'arc sinus est précis au 1/2% prêt !")
+print("sin(3.14/2): "..sin(3.14/2))
+print("pi/(arcsin(1)*2): "..pi/(arcsin(1)*2))
+
+
+
+

Trigo/trigo3.lua

@@ -0,0 +1,117 @@
+-- 3e Essais de faire des fonctions trigos qui manque dans NodeMCU
+-- source pour arctan,arcsin et arccos: http://mathonweb.com/help_ebook/html/algorithms.htm
+-- source pour sin&cos: https://www.esp8266.com/viewtopic.php?p=64415#
+-- source pour arcsin&arctan: http://www.electronicwings.com/nodemcu/magnetometer-hmc5883l-interfacing-with-nodemcu
+print("\ntrigo3.lua   zf180819.1745   \n")
+
+pi = 3.14159265358979323846
+
+function zsin(x)
+   local p=-x*x*x   local f=6   local r=x+p/f
+   for j=1,60 do
+      p=-p*x*x   f=f*2*(j+1)*(j+j+3)   r=r+p/f
+   end
+   return r
+end
+
+function zcos(x)
+   return zsin(math.pi/2-x)
+end
+
+function ztan(x)
+   return zsin(x)/zcos(x)
+end
+
+
+
+
+function zatan(x)
+  local y=1  local z
+  if x<0 then
+    y=-1  x=y*x
+  end
+  if x<1 then
+    z=zzatan(x)
+  else
+    z=pi/2-zatan(1/x)
+  end
+  return y*z
+end
+
+function zzatan(x)
+  return x-x^3/3+x^5/5-x^7/7
+end
+
+
+
+
+--[[
+--print("On voit que l'arc sinus est précis au 1/2% prêt !")
+a=0.9
+print("théorique tan("..a.."): "..math.tan(a))
+print("calculée  tan("..a.."): "..ztan(a))
+b=math.tan(a)
+print("théorique atan("..b.."): "..math.atan(b))
+print("calculée  atan("..b.."): "..zatan(b)..", "..pi/2-zatan(1/b))
+--print("pi/(arcsin(1)*2): "..pi/(arcsin(1)*2))
+]]
+
+
+--[[
+print("On voit que l'arc sinus est précis au 1/2% prêt !")
+print("sin(3.14/2): "..sin(3.14/2))
+print("pi/(arcsin(1)*2): "..pi/(arcsin(1)*2))
+]]
+
+
+--[[
+function arcsin(value)
+    local val = value
+    local sum = value
+    if(value == nil) then
+        return 0
+    end
+-- as per equation it needs infinite iterations to reach upto 100% accuracy
+-- but due to technical limitations we are using
+-- only 10000 iterations to acquire reliable accuracy
+    for i = 1,10000, 2 do
+        val = (val*(value*value)*(i*i)) / ((i+1)*(i+2))
+        sum = sum + val;
+    end
+    return sum
+end
+
+function arctan(value)
+    if(value == nil) then
+        return 0
+    end
+    local _value = value/math.sqrt((value*value)+1)
+    return arcsin(_value)
+end
+
+function atan2(y, x)
+    if(x == nil or y == nil) then
+        return 0
+    end
+
+    if(x > 0) then
+        return arctan(y/x)
+    end
+    if(x < 0 and 0 <= y) then
+        return arctan(y/x) + pi
+    end
+    if(x < 0 and y < 0) then
+        return arctan(y/x) - pi
+    end
+    if(x == 0 and y > 0) then
+        return pi/2
+    end
+    if(x == 0 and y < 0) then
+        return -pi/2
+    end
+    if(x == 0 and y == 0) then
+        return 0
+    end
+    return 0
+end
+]]