option explicit
option default FLOAT
cpu 48
' 3D wire frame graphics demo using quarternions to rotate the coordinates
cls
dim q1(4),v(4),vout(4),M_PI=3.14159265359,i%,x1,y1,z1,x2,y2,z2
' define the coordinates of a cube with the z-axis towards the viewer
dim cube(3,7)=(-100,-100,100,0, -100,100,100,0, 100,-100,100,0, 100,100,100,0, -100,-100,-100,0, -100,100,-100,0, 100,-100,-100,0, 100,100,-100,0 ) 'coordinates of the cube
' define the coordinate pairs that make up the edges of the cube
DIM cubelocation(2)=(mm.hres/2,MM.VRES/2,-500) 'actual location of the centre of the cube in space
' define the coordinate pairs that make up the edges of the cube
dim cubelines%(1,11)=(0,1, 0,2, 1,3, 2,3, 4,5, 4,6, 5,7, 6,7, 0,4, 1,5, 2,6, 3,7)
'define the projection plane
DIM viewplane = -200
dim lines%(3,11),oldlines%(3,11) 'storage for the coordinates for lines drawn
for i%=0 to 7 'convert coordinates to normalised form
x1=cube(0,i%): y1=cube(1,i%): z1=cube(2,i%)
create_vector(x1,y1,z1,v())
cube(0,i%)=v(2): cube(1,i%)=v(3): cube(2,i%)=v(4): cube(3,i%)=v(0)
next i%
'create a quarternion to rotate 2 degrees about x axis
'play with the x,y,z vector which is the sxis of rotation
create_normalised_quaternion(2,1,0,0,q1())
do
for i%=0 to 11 'project the coordinates onto the viewplane
z1=cube(2,cubelines%(0,i%))*cube(3,cubelines%(0,i%))+cubelocation(2)
x1=(cube(0,cubelines%(0,i%))*cube(3,cubelines%(0,i%))*viewplane/z1 +cubelocation(0))
y1=(cube(1,cubelines%(0,i%))*cube(3,cubelines%(0,i%))*viewplane/z1 +cubelocation(1))
z2=cube(2,cubelines%(1,i%))*cube(3,cubelines%(1,i%))+cubelocation(2)
x2=(cube(0,cubelines%(1,i%))*cube(3,cubelines%(1,i%))*viewplane/z2 +cubelocation(0))
y2=(cube(1,cubelines%(1,i%))*cube(3,cubelines%(1,i%))*viewplane/z2 +cubelocation(1))
lines%(0,i%)=x1 :lines%(1,i%)=y1 :lines%(2,i%)=x2 :lines%(3,i%)=y2
next i%
for i%=0 to 7 'rotate coordinates
v(2)=cube(0,i%): v(3)=cube(1,i%): v(4)=cube(2,i%): v(0)=cube(3,i%): v(1)=0
rotate_vector(vout(),v(),q1())
cube(0,i%)=vout(2): cube(1,i%)=vout(3): cube(2,i%)=vout(4): cube(3,i%)=vout(0)
next i%
for i%=0 to 11 'delete the old lines
line oldlines%(0,i%),oldlines%(1,i%),oldlines%(2,i%),oldlines%(3,i%),1,rgb(black)
next i%
for i%=0 to 11 'draw the new lines
line lines%(0,i%),lines%(1,i%),lines%(2,i%),lines%(3,i%),1,rgb(white)
oldlines%(0,i%)=lines%(0,i%):oldlines%(1,i%)=lines%(1,i%):oldlines%(2,i%)=lines%(2,i%):oldlines%(3,i%)=lines%(3,i%)
next i%
loop
end

'
sub create_normalised_quaternion(theta,x,y,z,q())
local radians = theta/180.0*M_PI
local sineterm= sin(radians!/2)
q(1)=cos(radians/2)
q(2)=x* sineterm
q(3)=y* sineterm
q(4)=z* sineterm
q(0)=sqr(q!(1)*q(1) + q(2)*q(2) + q(3)*q(3) + q(4)*q(4)) 'calculate the magnitude
q(1)=q(1)/q(0) 'create a normalised quaternion
q(2)=q(2)/q(0)
q(3)=q(3)/q(0)
q(4)=q(4)/q(0)
q(0)=1
end sub
'
sub invert_quaternion(n(),q())
n(0)=q(0)
n(1)=q(1)
n(2)=-q(2)
n(3)=-q(3)
n(4)=-q(4)
end sub
'
sub multiply_quaternion(n(),q1(),q2())
local a1=q1(1),a2=q2(1),b1=q1(2),b2=q2(2),c1=q1(3),c2=q2(3),d1=q1(4),d2=q2(4)
n(1)=a1*a2-b1*b2-c1*c2-d1*d2
n(2)=a1*b2+b1*a2+c1*d2-d1*c2
n(3)=a1*c2-b1*d2+c1*a2+d1*b2
n(4)=a1*d2+b1*c2-c1*b2+d1*a2
n(0)=q1(0)*q2(0)
end sub
'
sub create_vector(x,y,z,v())
v(0)=sqr(x*x + y*y + z*z)
v(1)=0
v(2)=x/v(0)
v(3)=y/v(0)
v(4)=z/v(0)
end sub

sub rotate_vector(vnew(),v(),q())
local n(4),iq(4)
multiply_quaternion(n(),q(),v())
invert_quaternion(iq(),q())
multiply_quaternion(vnew(),n(),iq())
end sub

OPTION LCDPANEL ILI9341, L, 4, 5, 6
OPTION TOUCH 7, 2