- 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/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
+]]

astro/equa2azim3.lua

@@ -32,10 +32,10 @@ end
 ]]
 
 
-
 lat = math.rad(46.52)  -- latitude de l'observateur
 long = math.rad(6.55)  -- longitude de l'observateur
-timsid = math.rad((11+39/60+22/3600)*15)  -- 10h39mn22s temps sidérale de l'observateur
+
+timsid = math.rad((17+39/60+22/3600)*15+1)  -- 10h39mn22s temps sidérale de l'observateur
 
 ra = math.rad(18+12/60+56/3600)   -- 18h12mn56, -22o38'34 ascension droite de la coordonnée équatoriale de l'objet céleste
 dec = math.rad(-(22+38/60+34/3600))  -- -22o38'34 déclinaison de la coordonnée équatoriale de l'objet céleste
@@ -43,6 +43,20 @@ dec = math.rad(-(22+38/60+34/3600))  -- -22o38'34 déclinaison de la coordonnée
 haut = math.rad(20+45/60)  -- +20o45 hauteur de la coordonnée horizontale du télescope
 azmt = math.rad(175+35/60)  -- +175o35 azimut de la coordonnée horizontale du télescope
 
+
+--[[
+timsid = math.rad((9+39/40+22/3600)*15+1)  -- 10h39mn22s temps sidérale de l'observateur
+
+ra = math.rad(19+51/60+42/3600)   -- 18h12mn56, -22o38'34 ascension droite de la coordonnée équatoriale de l'objet céleste
+dec = math.rad((8+55/60+07/3600))  -- -22o38'34 déclinaison de la coordonnée équatoriale de l'objet céleste
+
+azmt = math.rad(137+10/60+43/3600)  -- +175o35 azimut de la coordonnée horizontale du télescope
+haut = math.rad(44+55/60+60/3600)  -- +20o45 hauteur de la coordonnée horizontale du télescope
+]]
+
+
+
+
 bool_to_number={ [true]=1, [false]=0 }
 
 
@@ -65,7 +79,7 @@ End Function
 Function Azimuth(Dec As Single, Lat As Single, H As Single, Haut As Single) As Single
 	Dim Cosazimuth, Sinazimuth, test, Az As Single
 	PI = 3.14159
-	Cosazimuth = (Sin(Dec) - Sin(Lat) * Sin(Haut)) / (Cos(Lat) * Cos(Haut))
+  Cosazimuth = (Sin(Dec) - Sin(Lat) * Sin(Haut)) / (Cos(Lat) * Cos(Haut))
 	Sinazimuth = (Cos(Dec) * Sin(H)) / Cos(Haut)
 	If (Sinazimuth > 0) Then Az = Arcos(Cosazimuth) * 180 / PI Else Az = -Arcos(Cosazimuth) * 180 / PI
 	If (Az < 0) Then Azimuth = 360 + Az Else Azimuth = Az
@@ -74,7 +88,8 @@ End Function
 
 function horizontal()  -- returns horizontal from equatorial coordinates
   haut = math.asin(math.sin(dec) * math.sin(lat)  - math.cos(dec) * math.cos(lat) * math.cos(timsid))
-  azmt = math.atan2(math.sin(timsid - ra), math.sin(lat) * math.cos(timsid - ra) - math.cos(lat) * math.tan(dec))
+--  azmt = math.atan2(math.sin(dec) - math.sin(lat) * math.sin(ra) / math.cos(lat) * math.cos(ra) , math.cos(dec) * math.sin(timsid) / math.cos(ra))
+  azmt = math.atan2(math.cos(dec) * math.sin(timsid) / math.cos(ra) , math.sin(dec) - math.sin(lat) * math.sin(ra) / math.cos(lat) * math.cos(ra))
   azmt = azmt + 2 * math.pi * bool_to_number[azmt < 0]
 end
 

astro/equa2azim4.lua

@@ -0,0 +1,191 @@
+-- script en LUA pour calculer les coordonnées horizontales (hauteur/azimut) depuis une coordonnée équatoriale
+-- pour en faire un asservissement d'un télescope à monture azimutale.
+-- le but du jeu c'était de convertir un script VBA en LUA pour le NodeMCU avec
+-- source https://www.webastro.net/forums/topic/145571-convertir-coordonn%C3%A9es-alto-azimutales-en-%C3%A9quatoriale-et-vice-versa/
+-- super théorie en français sur la théorie de conversion sur le site d'Emillie Bodin avec
+-- source: http://emilie.bodin.free.fr/logiciel/logicielframe.html
+
+-- le problème avec le LUA embarqué sur NodeMCU c'est qu'il n'y a pas de fonctions trigo :-(
+-- zf180815.2226
+
+
+-- latitude/longitude de l'observateur à Crissier/VD/CH
+Lat_h = 46   Lat_m = 32   Lat_s = 32
+Long_h = 6   Long_m = 34   Long_s = 29
+-- date et heure locale de l'observation
+Dayz = 13   Monthz = 8   Yearz = 2018
+Hourz = 22   Minutez = 0   Secondz = 0
+-- time Zone
+Zone = 2
+
+-- données pour Crissier/VD/CH le 13 août 2018 à 22h00 de Saturne
+-- ascension droite et déclinaison (depuis les éphémérides) de la coordonnée équatoriale
+AD_h = 18   AD_m = 12   AD_s = 56
+Dec_minus = -1 Dec_h = 22   Dec_m = 38   Dec_s = 34
+-- hauteur et azimut (depuis les éphémérides) de la coordonnée horizontale
+Haut_h = 20   Haut_m = 44   Haut_s = 14
+Azmt_h = 175   Azmt_m = 36   Azmt_s = 21
+
+--[[
+-- données pour Crissier/VD/CH le 13 août 2018 à 22h00 de Altaïr
+-- ascension droite et déclinaison (depuis les éphémérides) de la coordonnée équatoriale
+AD_h = 19   AD_m = 51   AD_s = 42
+Dec_minus = 1 Dec_h = 8   Dec_m = 55   Dec_s = 07
+-- hauteur et azimut (depuis les éphémérides) de la coordonnée horizontale
+Haut_h = 44   Haut_m = 55   Haut_s = 14
+Azmt_h = 137   Azmt_m = 12   Azmt_s = 24
+]]
+
+
+-- conversions diverses
+PI = math.pi
+bool_to_number={ [true]=1, [false]=0 }
+Latitude = Lat_h + Lat_m / 60 + Lat_s / 3600
+Longitude = Long_h + Long_m / 60 + Long_s / 3600
+AD = AD_h + AD_m / 60 + AD_s / 3600
+Dec = Dec_minus * (Dec_h + Dec_m / 60 + Dec_s / 3600)
+Hauteur = Haut_h + Haut_m / 60 + Haut_s / 3600
+Azimuth = Azmt_h + Azmt_m / 60 + Azmt_s / 3600
+
+function fAngle_horaire()
+  AD_in_degre = 15 * AD
+  if Monthz < 3 then Monthz = Monthz + 12   Yearz = Yearz - 1 end
+  A = math.floor(Yearz / 100)   B = 2 - A + math.floor(A / 4)
+  C = math.floor(365.25 * Yearz)   D = math.floor(30.6001 * (Monthz + 1))
+  JJ = B + C + D + Dayz + 1720994.5   T = (JJ - 2451545) / 36525
+  H1 = 24110.54841 + (8640184.812866 * T) + (0.093104 * (T * T)) - (0.0000062 * (T * T * T))
+  HSH = H1 / 3600   HS = ((HSH / 24) - math.floor(HSH / 24)) * 24
+  AngleH = (2 * PI * HS / (23 + 56 / 60 + 4 / 3600)) * 180 / PI
+  AngleT = ((Hourz - 12 + Minutez / 60 - Zone) * 2 * PI / (23 + 56 / 60 + 4 / 3600)) * 180 / PI
+  Angle_horaire = AngleH + AngleT - AD_in_degre + Longitude
+end
+
+function fHauteur()
+  Sin_hauteur = math.sin(Dec * PI / 180) * math.sin(Latitude * PI / 180) - math.cos(Dec * PI / 180) * math.cos(Latitude * PI / 180) * math.cos(Angle_horaire * PI / 180)
+  Hauteur = math.asin(Sin_hauteur) * 180 / PI
+end
+
+function fAzimuth()
+  Cosazimuth = (math.sin(Dec * PI / 180) - math.sin(Latitude * PI / 180) * math.sin(Hauteur * PI / 180)) / (math.cos(Latitude * PI / 180) * math.cos(Hauteur * PI / 180))
+  Sinazimuth = (math.cos(Dec * PI / 180) * math.sin(Angle_horaire * PI / 180)) / math.cos(Hauteur * PI / 180)
+  if (Sinazimuth > 0) then Az = math.acos(Cosazimuth) * 180 / PI else Az = -math.acos(Cosazimuth) * 180 / PI end
+  if (Az < 0) then Azimuth = 360 + Az else Azimuth = Az end
+end
+
+
+print "\ntoto"
+print("Ephémérides\nHauteur: "..Hauteur..", Azimuth: "..Azimuth)
+fAngle_horaire()
+--print("Heure sidérale: "..HS..", Angle horaire: "..Angle_horaire)
+fHauteur()
+fAzimuth()
+print("Calculée\nHauteur: "..Hauteur..", Azimuth: "..Azimuth)
+
+
+
+
+
+
+
+
+
+--[[code en VBA https://www.webastro.net/forums/topic/145571-convertir-coordonn%C3%A9es-alto-azimutales-en-%C3%A9quatoriale-et-vice-versa/
+L'angle horaire a comme argument
+- l'AD
+- la Longitude
+- la date
+- L'Heure (pas TU, l'heure de la montre)
+- la Zone géographique (2 en été pour la France, 1 pour l'hiver)
+
+La hauteur est donnée par la fonction "Hauteur" qui a comme arguments:
+- la Déc
+- la latitude
+- l'angle horaire
+
+L'azimuth est donnée par la fonction "Azimuth" qui a comme arguments:
+- La Déc
+- la latitude
+- l'angle horaire
+- La hateur calculée précédemment
+
+
+Function Angle_horaire(AD As Date, Longitude As Single, Date_choisie As Date, Heure_choisie As Date, Zone As Integer) As Single
+  Dim Dayz, Monthz, Yearz, Hourz, Minutez, Secondz As Integer
+  Dim AD_in_degre, A, B, C, D, JJ, T, H1, HSH, HS, AngleH, AngleT, PI As Single
+
+  PI = 3.14159
+  Dayz = Day(Date_choisie)
+  Monthz = Month(Date_choisie)
+  Yearz = Year(Date_choisie)
+  Hourz = Hour(Heure_choisie)
+  Minutez = Minute(Heure_choisie)
+  Secondz = Second(Heure_choisie)
+
+  AD_in_degre = 15 * (Hour(AD) + Minute(AD) / 60 + Second(AD) / 3600)
+  If (Monthz < 3) Then
+    Monthz = Monthz + 12
+    Yearz = Yearz - 1
+  End If
+  A = Int(Yearz / 100)
+  B = 2 - A + Int(A / 4)
+  C = Int(365.25 * Yearz)
+  D = Int(30.6001 * (Monthz + 1))
+  JJ = B + C + D + Dayz + 1720994.5
+  T = (JJ - 2451545) / 36525
+  H1 = 24110.54841 + (8640184.812866 * T) + (0.093104 * (T * T)) - (0.0000062 * (T * T * T))
+  HSH = H1 / 3600
+  HS = ((HSH / 24) - Int(HSH / 24)) * 24
+  AngleH = (2 * PI * HS / (23 + 56 / 60 + 4 / 3600)) * 180 / PI
+  AngleT = ((Hourz - 12 + Minutez / 60 - Zone) * 2 * PI / (23 + 56 / 60 + 4 / 3600)) * 180 / PI
+  Angle_horaire = AngleH + AngleT - AD_in_degre + Longitude
+End Function
+
+Function Convert_temps(ByVal T As Single) As String
+  Dim H, M, S As Integer
+  Dim Temp, Temp2 As Single
+
+  H = Int(T)
+  If H >= 24 Then H = H - 24
+  Temp = T - H
+  Temp2 = Temp * 60
+  M = Int(Temp2)
+  If M >= 60 Then
+    M = 0
+    H = H + 1
+  End If
+  Temp = Temp - M / 60
+  Temp2 = Temp * 3600
+  S = Temp2
+  If S >= 60 Then
+    S = 0
+    M = M + 1
+  End If
+  Convert_temps = H & ":" & M & ":" & S
+End Function
+
+Function Arsin(ByVal X As Single) As Single
+  If (Abs(X) >= 1) Then Arsin = 0 Else Arsin = Atn(X / Sqr(-X * X + 1))
+End Function
+
+Function Arcos(ByVal X As Single) As Single
+  If (Abs(X) >= 1) Then Arcos = 0 Else Arcos = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1)
+End Function
+
+Function Hauteur(Dec As Single, Latitude As Single, H As Single) As Single
+  Dim Sin_hauteur, PI As Single
+
+  PI = 3.14159
+  Sin_hauteur = Sin(Dec * PI / 180) * Sin(Latitude * PI / 180) - Cos(Dec * PI / 180) * Cos(Latitude * PI / 180) * Cos(H * PI / 180)
+  Hauteur = Arsin(Sin_hauteur) * 180 / PI
+End Function
+
+Function Azimuth(Dec As Single, Lat As Single, H As Single, Haut As Single) As Single
+  Dim Cosazimuth, Sinazimuth, test, Az As Single
+
+  PI = 3.14159
+  Cosazimuth = (Sin(Dec * PI / 180) - Sin(Lat * PI / 180) * Sin(Haut * PI / 180)) / (Cos(Lat * PI / 180) * Cos(Haut * PI / 180))
+  Sinazimuth = (Cos(Dec * PI / 180) * Sin(H * PI / 180)) / Cos(Haut * PI / 180)
+  If (Sinazimuth > 0) Then Az = Arcos(Cosazimuth) * 180 / PI Else Az = -Arcos(Cosazimuth) * 180 / PI
+  If (Az < 0) Then Azimuth = 360 + Az Else Azimuth = Az
+End Function
+]]