option nolet
!+++++++++++++++++++++++++++++
! coordinates of the window
!+++++++++++++++++++++++++++++
! x values window
xmin = -5
xmax = 5
! y values window
ymin = -5
ymax = 5
set window xmin,xmax,ymin,ymax
!+++++++++++++++++++++++++++++
!
!+++++++++++++++++++++++++++++++++
! info programma,title,author,time
!+++++++++++++++++++++++++++++++++
set color "blue"
plot text,at xmin +.5,ymax -.5:"vector field 3d ,version 1.0"
plot text,at xmin+.5,ymax - .75:"peter.vlasschaert@gmail.com,07/04/2020"
set color "black"
!+++++++++++++++++++++++++++++++++++++++++++
! general parameter , compass needles
!+++++++++++++++++++++++++++++++++++++++++++
w =0.1   !( dimension compass needle )
!+++++++++++++++++++++++++++++++++++++++++++
! general parameter , differential equations
!+++++++++++++++++++++++++++++++++++++++++++
a=2
b=-1
c=1
d=4
!+++++++++++++++++++++++++++++++++++++++++++
xm =3 ! x-range
xstep = .25
ym =2 ! y-yrange
ystep = .25
zm =3 ! z-range
zstep = 2
!++++++++++++++++++++++++++++++++++++++++++
for z=-zm to zm step  zstep
 for x=-xm to xm step  xstep
  for y=-ym to ym step ystep
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! system three differential equations ,'example:see parameters above'
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  dx = a*x+b*y*x
  dy = c*x+d*y-z
  dz = 2*z
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
   ds=sqr(dx^2+dy^2+dz^2)
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
   call cor2to3(x,y,z,xs,ys) 
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! compass needle are tangent to curve,(dy/ds)/(dx/ds) = dy/dx
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 if ds>0 then plot xs-w*dx/ds,ys-w*dy/ds;xs+w*dx/ds,ys+w*dy/ds
    next y
  next x
next z
!  z=0,rectangle, 'black'
call cor2to3(xm+3,ym+3,0,xs,ys)
plot -xs,0;xs,0
plot 0,-ys;0,ys
plot -xs,ys;xs,-ys
plot -xs,-ys;xs,-ys
plot xs,-ys;xs,ys
plot xs,-ys;-xs,ys
plot xs,ys;xs,-ys
plot xs,ys;-xs,-ys
plot xs,ys;-xs,ys
plot -xs,-ys;-xs,ys
set color "red"
!+++++++++++++++++++++++++++++
! conversion 3d to 2d
!++++++++++++++++++++++++++++++
! axis z,1e) + axis ,2e) - axis
plot 0,0;0,zm+2
PLOT TEXT, AT 0.25,zm+1:"z axis"
plot 0,0;0,-zm-2
set color "green"
! axis x,1e) + axis ,2e) - axis
plot 0,0;-xm/2-2,-xm/2-2
PLOT TEXT, AT -xm/2-2,-xm/2-2:"x axis"
plot 0,0;+xm/2+2,+xm/2+2
set color "blue"
! axis y,1e) + axis ,2e) - axis
plot 0,0;ym+2,0
PLOT TEXT, AT ym+2,0+0.1:"y axis"
plot 0,0;-ym-2,0
! origin of graphics
! number for simple color 1-16
set color 13
PLOT TEXT, AT 0,0+0.1:"(0,0,0)"
end

!++++++++++++++++++++++++++++++++++++++++++++++++
!3d to 2d:world coordinates to screen coordinates
!++++++++++++++++++++++++++++++++++++++++++++++++

sub cor2to3(x1,y1,z1,xs,ys)
xs=y1-x1/2
ys=z1-x1/2
end sub