Graphics3D 640,480,32,2
SetBuffer BackBuffer()
frametimer= CreateTimer(30)


light=CreateLight(2)
LightColor light,50,50,50
RotateEntity light,0,0,0
PositionEntity light,0,5,-2


Global dummy=CreatePivot()
Global cam=CreateCamera(dummy)
CameraClsColor cam,12,12,100
PositionEntity cam,0,0,-10
PointEntity cam,dummy

CameraZoom cam,4


Type lineType
Field mesh
Field alpha#
Field destroy
End Type
Global l.lineType






angle#=0
achsenneigung#=0


While Not KeyHit(1)


   
If KeyDown(30)  Then TurnEntity dummy,0,1,0
If KeyDown(32)  Then TurnEntity dummy,0,-1,0

   
If KeyDown(200)   Then achsenneigung = achsenneigung+0.05
If KeyDown(208) Then achsenneigung = achsenneigung-0.05


;------------------------------------------------

angle = (angle+5) Mod 360   ; Rotationswinkel


vec1X# = 1     ;Erster Vektor der rotiert wird
vec1Y# = 1
vec1Z# = 0
TFormNormal vec1X,vec1Y,vec1Z,0,0
vec1X = TFormedX#()
vec1Y = TFormedY#()
vec1Z = TFormedZ#()


vec2X# = 1      ; Rotationsachse
vec2Y# = achsenneigung
vec2Z# = 0
TFormNormal vec2X,vec2Y,vec2Z,0,0
vec2X = TFormedX#()
vec2Y = TFormedY#()
vec2Z = TFormedZ#()




crossX# = vec1Y*vec2Z - vec2Y*vec1Z  ; Kreuzprodukt vec1 + Achse
crossY# = vec1Z*vec2X - vec2Z*vec1X
crossZ# = vec1X*vec2Y - vec2X*vec1Y




vec1X = vec1X*Cos#(angle) + vec2X*(vec2X*vec1X)*(1-Cos#(angle)) + crossX*Sin#(angle) ; Axis/Angle Rotation
vec1Y = vec1Y*Cos#(angle) + vec2Y*(vec2Y*vec1Y)*(1-Cos#(angle)) + crossY*Sin#(angle)
vec1Z = vec1Z*Cos#(angle) + vec2Z*(vec2Z*vec1Z)*(1-Cos#(angle)) + crossZ*Sin#(angle)
TFormNormal vec1X,vec1Y,vec1Z,0,0
vec1X = TFormedX#()
vec1Y = TFormedY#()
vec1Z = TFormedZ#()



;------------------------------------------------------------------------------------


vec3X# = 0.5    ; Zweiter Vektor der rotiert wird
vec3Y# = -1
vec3Z# = 0
TFormNormal vec3X,vec3Y,vec3Z,0,0
vec3X = TFormedX#()
vec3Y = TFormedY#()
vec3Z = TFormedZ#()


cross2X# = vec3Y*vec2Z - vec2Y*vec3Z   ; Kreuzprodukt vec3 + Achse
cross2Y# = vec3Z*vec2X - vec2Z*vec3X
cross2Z# = vec3X*vec2Y - vec2X*vec3Y




vec3X = vec3X*Cos#(angle) + vec2X*(vec2X*vec3X)*(1-Cos#(angle)) + cross2X*Sin#(angle)   ; Axis/Angle Rotation
vec3Y = vec3Y*Cos#(angle) + vec2Y*(vec2Y*vec3Y)*(1-Cos#(angle)) + cross2Y*Sin#(angle)
vec3Z = vec3Z*Cos#(angle) + vec2Z*(vec2Z*vec3Z)*(1-Cos#(angle)) + cross2Z*Sin#(angle)
TFormNormal vec3X,vec3Y,vec3Z,0,0
vec3X = TFormedX#()
vec3Y = TFormedY#()
vec3Z = TFormedZ#()





dot1to2# = (vec1X*vec2X) + (vec1Y*vec2Y) + (vec1Z*vec2Z)   ; Dotproduct vec1 + Achse

dot3to2# = (vec3X*vec2X) + (vec3Y*vec2Y) + (vec3Z*vec2Z)   ; Dotproduct vec3 + Achse

dot3to1# = (vec3X*vec1X) + (vec3Y*vec1Y) + (vec3Z*vec1Z)   ; Dotproduct vec3 + vec1






l.lineType = New lineType                           ; Zeichne Vektoren
l\mesh = createLine(0,0,0,vec1X,vec1Y,vec1Z,255,0,0)
l\destroy = 20
l\alpha = 1

l.lineType = New lineType
l\mesh = createLine(0,0,0,vec2X,vec2Y,vec2Z,255,255,0)
l\destroy = 20
l\alpha = 1


l.lineType = New lineType
l\mesh = createLine(0,0,0,vec3X,vec3Y,vec3Z,0,255,0)
l\destroy = 20
l\alpha = 1


For l.lineType = Each lineType

   l\alpha = l\alpha - 0.05
   EntityAlpha l\mesh,l\alpha
   l\destroy = l\destroy - 1
   If l\destroy = 0 Then
      FreeEntity l\mesh
      Delete l
   EndIf
   
Next



   CameraClsMode(cam,1,1)
   WireFrame(0)
   RenderWorld()


   CameraClsMode(cam,0,0)
   WireFrame(1)
   RenderWorld()
   
   
   
   
   
Text 10,10, "Winkel vec1 (rot)  -> Achse (gelb)"
Text 10,25, "Winkel vec3 (grün) -> Achse (gelb)"
Text 10,40, "Winkel vec3 (grün) -> vec1 (rot)"

Text 300,10, ACos(dot1to2)
Text 300,25, ACos(dot3to2)
Text 300,40, ACos(dot3to1)   

Text 250,400, " Kamerasteuerung a,d"
Text 250,415, " Achse kippen Pfeiltasten"
   



   WaitTimer frametimer
   
   Flip 0
   
   
Wend   



;------------------------------------------------------------------

Function createLine(x1#,y1#,z1#, x2#,y2#,z2#, r,b,g, mesh=0)
   
   If mesh = 0 Then
      mesh=CreateMesh()
      EntityFX(mesh,16)
      surf=CreateSurface(mesh)   
      verts = 0   
   
      AddVertex surf,x1#,y1#,z1#,0,0
   Else
      surf = GetSurface(mesh,1)
      verts = CountVertices(surf)-1
   End If
   
   AddVertex surf,(x1#+x2#)/2,(y1#+y2#)/2,(z1#+z2#)/2,0,0

   AddVertex surf,x2#,y2#,z2#,1,0
   
   AddTriangle surf,verts,verts+2,verts+1
   
   EntityColor mesh,r,b,g

   
   Return mesh
End Function