-- Vector plot example

-- Gareth Rees  wgr2@cam.ac.uk
-- 11 March 2007

-- This example generates and then plots the flow field around a sphere
-- in a uniformly flowing incompressible irrotational fluid


include "vectorplot"

mod(a,b)=a-b*trunc(a/b)

-- make uniform grid array of xp and yp values
xp[i]=(trunc((i-1)/40)-19.5)*0.1 dim[1601]
yp[i]=(mod(i-1,40)-19.5)*0.1 dim[1601]

-- field due to dipole at (0,0)
xd:=xp:
yd:=yp:
rd:=sqrt(xd*xd+yd*yd):
xp2:=(2-3*yd*yd/rd/rd)/4/pi/rd^3:
yp2:=3*xd*yd/4/pi/rd^5:

-- add field due to steady flow
xp2:=xp2-1/2/pi:

-- specify extent of plot

Xmin=-2; Xmax=2; Ymin=-2; Ymax=2

-- Make a background image from rd[]
Zmin=.04; Zmax=2.7
rimg[i,j] = 2.8-rd[(i-1)*40+j] dim[40,40]
image rimg

-- Plot vector field using the include file
Tracecolor:=1:
plotline A


-- show the sphere on the plot too
Tracecolor:=2:
B[i]={cos(i),sin(i)} dim[360]
plotline B