;Drawing hypercube (4D cube, tesseract) projection using cylinders as ribs and spheres as vertexes by Matt Merkulov
;Control keys: 1-6 - rotate tesseract in one of 6 4D rotational surfaces
Graphics3D 640,480,32
p=CreatePivot()
PositionEntity CreateCamera(p), 0,0,-5
RotateEntity CreateLight(), 45,45,0
; Filling a file of tops. Thus if number of each top to present in
; Binary calculation everyone of bats will define(determine) corresponding(meeting)
; Coordinate: if bats it is switched off, the coordinate is equal-1, differently - +1
Dim v#(15,4)
For n1=0 To 15
For n2=0 To 3
v#(n1, n2)=Sgn(n1 And(1 Shl n2))*2-1
Next
; Creation of the spheres representing tops
v(n1,4)=CreateSphere(10)
ScaleEntity v(n1,4), .2, .2, .2
Next
; Filling a file of planes of rotation(every possible variants of pairs axes)
Dim r(5,1)
For n1=0 To 2
For n2=n1+1 To 3
r(n, 0)=n1
r(n, 1)=n2
n=n+1
Next
Next
; A file of addresses of cylinders - edges
Dim e(15,3)
; An auxiliary vector
Dim d#(2)
; Preliminary calculations
ang#=1
sina#=Sin(ang#)
cosa#=Cos(ang#)
Repeat
; Turn of a body(and is more exact-tops) around of planes by pressing keys 1-6
For n3=0 To 5
If KeyDown(n3+2) Then
n1=r(n3,0)
n2=r(n3,1)
For n=0 To 15
c1#=v(n, n1)*cosa#-v(n, n2)*sina#
c2#=v(n, n1)*sina#+ v(n, n2)*cosa#
v(n, n1)=c1#
v(n, n2)=c2#
Next
End If
Next
; Creation of edges. A cycle on all tops
For n1=0 To 15
For n=0 To 3
; Definition of adjacent top by inclusion one bat(that is changes
; One of coordinates). Thus occurs(happens) otsecheni duplicating edges: number
; The first coordinate there should be less the second.
n2=n1 Or(1 Shl n)
If n1 <> n2 Then
; Creation of the cylinder-edge(if it is not created yet)
If e(n1, n)=0 Then e(n1, n)=CreateCylinder(8, False)
a=e(n1, n)
; Calculation of the center of an edge and installation of the cylinder in the center
For n3=0 To 2
d#(n3)=.5*(v(n1, n3) +v(n2, n3))
Next
PositionEntity a, d#(0), d#(1), d#(2)
; Calculations of a vector of an edge and alignment of the cylinder on it(him,them)
dd#=0
For n3=0 To 2
d#(n3)=v(n1, n3)-v(n2, n3)
dd#=dd#+ d#(n3)*d#(n3)
Next
AlignToVector a, d#(0), d#(1), d#(2), 2
; Scaling the cylinder on length of an edge
ScaleEntity a, .1, .5*Sqr(dd#),.1
End If
Next
Next
For n3=0 To 2
If KeyDown(n3+8) Then
TurnEntity p, ang#*(n3=0), ang#*(n3=1), ang#*(n3=2)
End If
Next
; Installation of spheres
For n=0 To 15
PositionEntity v(n, 4), v(n, 0), v(n, 1), v(n, 2)
Next
RenderWorld
Flip
Until KeyHit(1) |
