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\n") +print("\ntest_trigo1.lua zf180820.2209 \n") -- chargement des routines trigonométriques dofile("trigo3.lua") -for i = 0, 2*pi, 2*pi/100 do +for i = 0, 2*math.pi, 2*math.pi/32 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)) +-- b=math.tan(a) +-- print("arctangente: "..a..", "..b..", "..math.atan(b)..", "..zatan(b)..", "..math.atan(b)/zatan(b)) +-- print("sinus: "..a..", "..math.sin(a)..", "..zsin(a)..", "..math.sin(a)/zsin(a)) +-- print("cosinus: "..a..", "..math.cos(a)..", "..zcos(a)..", "..math.cos(a)/zcos(a)) +-- print("tangente: "..a..", "..math.tan(a)..", "..ztan(a)..", "..math.tan(a)/ztan(a)) +-- b=math.sin(a) +-- print("arcsinus: "..a..", "..b..", "..math.asin(b)..", "..zasin(b)..", "..math.asin(b)/zasin(b)) + b=math.cos(a) + print("arccosinus: "..a..", "..b..", "..math.acos(b)..", "..zacos(b)..", "..math.acos(b)/zacos(b)) end + +print("\n") +x=-0.70710678118655 +print(math.acos(x)) +print(zatan(math.sqrt(1-x*x)/x)) +print(math.sqrt(1-x*x)/x) diff --git a/Trigo/trigo3.lua b/Trigo/trigo3.lua index 3ad9d58..691ce4f 100644 --- a/Trigo/trigo3.lua +++ b/Trigo/trigo3.lua @@ -1,20 +1,26 @@ --- 3e Essais de faire des fonctions trigos qui manque dans NodeMCU +-- 3e Essais de faire des fonctions trigos qui manquent 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 +print("\ntrigo3.lua zf180820.2205 \n") + +Gros problème encore avec les atan négatives et du coup avec les acos, zf180820.2252 + 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 + local y=1 + if x>math.pi*2 then x=x%(math.pi*2) end + if x>math.pi then y=-1 x=x-math.pi end + if x>math.pi/2 then x=math.pi-x end + local p=x local f=1 local r=p + for j=2,10,2 do p=-p * x * x f=f*j*(j+1) r=r+p/f end + return(y*r) end function zcos(x) + if x>math.pi*2 then x=x%(math.pi*2) end + if x>math.pi then x=math.pi-x end return zsin(math.pi/2-x) end @@ -22,19 +28,22 @@ function ztan(x) return zsin(x)/zcos(x) end +function zasin(x) + return zatan(x/math.sqrt(1-x*x)) +end + +function zacos(x) + return zatan(math.sqrt(1-x*x)/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 + if x<0 then y=-1 x=y*x end + if x<1 then z=zzatan(x) else z=math.pi/2-zatan(1/x) end return y*z end @@ -45,24 +54,6 @@ 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)