Eigentlich nur so'n Test, aber ganz lustig und wenn man keine mathematischen, genauen Daten von der Funktion braucht, reichts.
(zum kucken, wie's aussieht und so.)
Code: Alles auswählen
Enumeration
#window
#gadget
#image
EndEnumeration
e.d=Pow(1+1/100000,100000)
Global delta_x.d=1/32,y1.d,y2.d,x1.d,x2.d,x.d
max=256*delta_x
Global Dim f1x.d(514),Dim f2x.d(514)
Global Dim a1x.d(513),Dim a2x.d(513)
Global Dim b1x.d(512),Dim b2x.d(512)
Macro Function(x)
x*x*x-x
EndMacro
x1=-8
For n=0 To 514
x2=x1+delta_x
y1=Function(x1)
y2=Function(x2)
f1x(n)=y1
f2x(n)=y2
x1=x1+delta_x
Next n
For n=0 To 513
a1x(n)=(f2x(n)-f1x(n))/delta_x
a2x(n)=(f2x(n+1)-f1x(n+1))/delta_x
Next n
For n=0 To 512
b1x(n)=(a2x(n)-a1x(n))/delta_x
b2x(n)=(a2x(n+1)-a1x(n+1))/delta_x
Next n
OpenWindow(#window,0,0,512,512,"Grafische Ableitung",#PB_Window_ScreenCentered|#PB_Window_MinimizeGadget)
CreateImage(#image,512,512)
StartDrawing(ImageOutput(#image))
Box(0,0,512,512)
LineXY(0,256,512,256,RGB(255,255,255))
LineXY(256,0,256,512,RGB(255,255,255))
For n=0 To 512
;Funktionsgraph
If (f1x(n)<max And f1x(n)>-max) Or (f1x(n)<max And f2x(n)>max) Or (f1x(n)<-max And f2x(n)>-max) Or (f1x(n)>max And f2x(n)<max) Or (f1x(n)>-max And f2x(n)<-max)
LineXY(n,256-f1x(n)*32,n+1,256-f2x(n)*32,RGB(0,0,255))
EndIf
;Maxima
If (f1x(n)<f1x(n+1) And f1x(n+1)>f1x(n+2)) Or (f1x(n)>f1x(n+1) And f1x(n+1)<f1x(n+2))
DrawingMode(4)
Circle(n+1,256-f1x(n+1)*32,4,RGB(255,0,255))
DrawingMode(0)
EndIf
;Nullstellen
If (Abs(f1x(n))=0 Or (f1x(n)>0 And f2x(n)<0) Or (f1x(n)<0 And f2x(n)>0))
DrawingMode(4)
Circle(n,256,4,RGB(0,255,255))
DrawingMode(0)
EndIf
;1.Ableitung
If (a1x(n)<max And a1x(n)>-max) Or (a1x(n)<max And a2x(n)>max) Or (a1x(n)<-max And a2x(n)>-max) Or (a1x(n)>max And a2x(n)<max) Or (a1x(n)>-max And a2x(n)<-max)
LineXY(n,256-a1x(n)*32,n+1,256-a2x(n)*32,RGB(255,0,0))
EndIf
;2.Ableitung
If (b1x(n)<max And b1x(n)>-max) Or (b1x(n)<max And b2x(n)>max) Or (b1x(n)<-max And b2x(n)>-max) Or (b1x(n)>max And b2x(n)<max) Or (b1x(n)>-max And b2x(n)<-max)
LineXY(n,256-b1x(n)*32,n+1,256-b2x(n)*32,RGB(0,255,0))
EndIf
Next n
DrawText(5,5,"Funktionsgraph",RGB(0,0,255),0)
DrawText(5,21,"1.Ableitung",RGB(255,0,0),0)
DrawText(5,37,"2.Ableitung",RGB(0,255,0),0)
DrawText(5,53,"Maxima",RGB(255,0,255),0)
DrawText(5,69,"Nullstellen",RGB(0,255,255),0)
StopDrawing()
CreateGadgetList(WindowID(#window))
ImageGadget(#gadget,0,0,512,512,ImageID(#image))
Repeat
event=WaitWindowEvent()
Until event=#PB_Event_CloseWindow
