option nolet
!+++++++++++++++++++++++++++++
! coordinates of the window  +
!+++++++++++++++++++++++++++++
! x values window
xmax = 7
xmin = -xmax
! y values window
ymax = 7
ymin = -ymax
set window xmin,xmax,ymin,ymax
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
!+ correction 'total': dx=dx0=f1(x,y,z) -> dy=dy0=f2(x,y,z)-> dz=dz0=f3(x,y,z) +
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! info programma,title,author,time                                             +
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
set color "blue"
plot text,at xmin +.5,ymax -.5:"vector field 3d with trajectory,version 1.0b"
plot text,at xmin+.5,ymax - .75:"peter.vlasschaert@gmail.com,17/10/2020"
set color "black"
!+++++++++++++++++++++++++++++++++++++++++++
! general parameter , compass needles
!+++++++++++++++++++++++++++++++++++++++++++
w =0.05   !( dimension compass needle )
!+++++++++++++++++++++++++++++++++++++++++++
! general parameter , differential equations
!+++++++++++++++++++++++++++++++++++++++++++
a=2
b=1
c=-3
d=4
n=45
!+++++++++++++++++++++++++++++++++++++++++++
xma =4.5 ! x-range
xmi = -xma
di =(xma-xmi)/n 
yma =4.5 ! y-yrange
ymi = -yma
dj =(yma-ymi)/n
zm =4.5 ! z-range
zstep = 1
!++++++++++++++++++++++++++++++++++++++++++
for z=-zm to zm step  zstep
 for i=1 to n
     x=xmi+i*di
  for j = 1 to n
     y=ymi+j*dj
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! 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)
  ma=dx/ds
  mb=dy/ds
  mc=dz/ds
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
   call cor2to3(x,y,z,xs,ys)
   call cor2to3(ma,mb,mc,nx,ny)
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
! compass needle are tangent to curve,(dy/ds)/(dx/ds) = dy/dx
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 if ds>0 then plot xs-w*nx,ys-w*ny;xs+w*nx,ys+w*ny
    next j
  next i
next z
plot ! disconnect
!  z=0,rectangle, 'black'
call cor2to3(xma+3,yma+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;-xma/2-2,-xma/2-2
PLOT TEXT, AT +xma/2+2,+xma/2+2.1:"x axis"
plot 0,0;+xma/2+2,+xma/2+2
set color "blue"
! axis y,1e) + axis ,2e) - axis
plot 0,0;ym+2,0
PLOT TEXT, AT yma+2,0+0.2:"y axis"
plot 0,0;-yma-2,0
! origin of graphics
! number for simple color 1-16
set color 13
PLOT TEXT, AT 0,0+0.1:"(0,0,0)"
!******************************************
! see :https://www.truebasic.com/node/1075
plot ! Stop connecting points
!******************************************
! trajectory file 3d to 2d
nn=10
x0=3  ! initial values trajectory
y0=3
z0=2
set color 4 

for i=1 to nn step 0.05

  dx0 = a*x0+b*y0*x0
  dy0 = c*x0+d*y0-z0
  dz0 = 2*z0
 ds0=sqr(dx0^2+dy0^2+dz0^2)
m1=dx0/ds0
m2=dy0/ds0
m3=dz0/ds0
x1=10*(x0+w*m1)/10! notation correction
y1=10*(y0+w*m2)/10! notation correction
z1=10*(z0+w*m3)/10! notation correction
call cor2to3(x0,y0,z0,xx0s,yy0s)
call cor2to3(x1,y1,z1,xxs,yys)
call cor2to3(m1,m2,m3,mx,my)
plot xx0s+w*mx,yy0s+w*my;xxs+w*mx,yys+w*my
x0=x1
y0=y1
z0=z1
next i
end

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

sub cor2to3(x11,y11,z11,xas,yas)
xas=y11-x11/2
yas=z11-x11/2
end sub