--[[ $Id: x09.lua 9533 2009-02-16 22:18:37Z smekal $
Contour plot demo.
Copyright (C) 2008 Werner Smekal
This file is part of PLplot.
PLplot is free software you can redistribute it and/or modify
it under the terms of the GNU General Library Public License as published
by the Free Software Foundation either version 2 of the License, or
(at your option) any later version.
PLplot is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Library General Public License for more details.
You should have received a copy of the GNU Library General Public License
along with PLplot if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
--]]
-- initialise Lua bindings for PLplot examples.
dofile("plplot_examples.lua")
XPTS = 35 -- Data points in x
YPTS = 46 -- Data points in y
XSPA = 2/(XPTS-1)
YSPA = 2/(YPTS-1)
-- polar plot data
PERIMETERPTS = 100
RPTS = 40
THETAPTS = 40
-- potential plot data
PPERIMETERPTS = 100
PRPTS = 40
PTHETAPTS = 64
PNLEVEL = 20
clevel = { -1, -0.8, -0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8, 1}
-- Transformation function
tr = { XSPA, 0, -1, 0, YSPA, -1 }
function mypltr(x, y)
tx = tr[1] * x + tr[2] * y + tr[3]
ty = tr[4] * x + tr[5] * y + tr[6]
return tx, ty
end
--polar contour plot example.
function polar()
px = {}
py = {}
lev = {}
pl.env(-1, 1, -1, 1, 0, -2)
pl.col0(1)
--Perimeter
for i=1, PERIMETERPTS do
t = (2*math.pi/(PERIMETERPTS-1))*(i-1)
px[i] = math.cos(t)
py[i] = math.sin(t)
end
pl.line(px, py)
--create data to be contoured.
cgrid2["xg"] = {}
cgrid2["yg"] = {}
cgrid2["nx"] = RPTS
cgrid2["ny"] = THETAPTS
z = {}
for i = 1, RPTS do
r = (i-1)/(RPTS-1)
cgrid2["xg"][i] = {}
cgrid2["yg"][i] = {}
z[i] = {}
for j = 1, THETAPTS do
theta = (2*math.pi/(THETAPTS-1))*(j-1)
cgrid2["xg"][i][j] = r*math.cos(theta)
cgrid2["yg"][i][j] = r*math.sin(theta)
z[i][j] = r
end
end
for i = 1, 10 do
lev[i] = 0.05 + 0.10*(i-1)
end
pl.col0(2)
pl.cont(z, 1, RPTS, 1, THETAPTS, lev, "pltr2", cgrid2)
pl.col0(1)
pl.lab("", "", "Polar Contour Plot")
end
----------------------------------------------------------------------------
-- f2mnmx
--
-- Returns min & max of input 2d array.
----------------------------------------------------------------------------
function f2mnmx(f, nx, ny)
fmax = f[1][1]
fmin = fmax
for i=1, nx do
for j=1, ny do
fmax = math.max(fmax, f[i][j])
fmin = math.min(fmin, f[i][j])
end
end
return fmin, fmax
end
--shielded potential contour plot example.
function potential()
clevelneg = {}
clevelpos = {}
px = {}
py = {}
--create data to be contoured.
cgrid2["xg"] = {}
cgrid2["yg"] = {}
cgrid2["nx"] = PRPTS
cgrid2["ny"] = PTHETAPTS
z = {}
for i = 1, PRPTS do
r = 0.5 + (i-1)
cgrid2["xg"][i] = {}
cgrid2["yg"][i] = {}
for j = 1, PTHETAPTS do
theta = 2*math.pi/(PTHETAPTS-1)*(j-0.5)
cgrid2["xg"][i][j] = r*math.cos(theta)
cgrid2["yg"][i][j] = r*math.sin(theta)
end
end
rmax = PRPTS-0.5
xmin, xmax = f2mnmx(cgrid2["xg"], PRPTS, PTHETAPTS)
ymin, ymax = f2mnmx(cgrid2["yg"], PRPTS, PTHETAPTS)
x0 = (xmin + xmax)/2
y0 = (ymin + ymax)/2
-- Expanded limits
peps = 0.05
xpmin = xmin - math.abs(xmin)*peps
xpmax = xmax + math.abs(xmax)*peps
ypmin = ymin - math.abs(ymin)*peps
ypmax = ymax + math.abs(ymax)*peps
-- Potential inside a conducting cylinder (or sphere) by method of images.
-- Charge 1 is placed at (d1, d1), with image charge at (d2, d2).
-- Charge 2 is placed at (d1, -d1), with image charge at (d2, -d2).
-- Also put in smoothing term at small distances.
eps = 2
q1 = 1
d1 = rmax/4
q1i = - q1*rmax/d1
d1i = rmax^2/d1
q2 = -1
d2 = rmax/4
q2i = - q2*rmax/d2
d2i = rmax^2/d2
for i = 1, PRPTS do
z[i] = {}
for j = 1, PTHETAPTS do
div1 = math.sqrt((cgrid2.xg[i][j]-d1)^2 + (cgrid2.yg[i][j]-d1)^2 + eps^2)
div1i = math.sqrt((cgrid2.xg[i][j]-d1i)^2 + (cgrid2.yg[i][j]-d1i)^2 + eps^2)
div2 = math.sqrt((cgrid2.xg[i][j]-d2)^2 + (cgrid2.yg[i][j]+d2)^2 + eps^2)
div2i = math.sqrt((cgrid2.xg[i][j]-d2i)^2 + (cgrid2.yg[i][j]+d2i)^2 + eps^2)
z[i][j] = q1/div1 + q1i/div1i + q2/div2 + q2i/div2i
end
end
zmin, zmax = f2mnmx(z, PRPTS, PTHETAPTS)
-- Positive and negative contour levels.
dz = (zmax-zmin)/PNLEVEL
nlevelneg = 1
nlevelpos = 1
for i = 1, PNLEVEL do
clevel = zmin + (i-0.5)*dz
if clevel <= 0 then
clevelneg[nlevelneg] = clevel
nlevelneg = nlevelneg + 1
else
clevelpos[nlevelpos] = clevel
nlevelpos = nlevelpos + 1
end
end
-- Colours!
ncollin = 11
ncolbox = 1
ncollab = 2
-- Finally start plotting this page!
pl.adv(0)
pl.col0(ncolbox)
pl.vpas(0.1, 0.9, 0.1, 0.9, 1)
pl.wind(xpmin, xpmax, ypmin, ypmax)
pl.box("", 0, 0, "", 0, 0)
pl.col0(ncollin)
if nlevelneg>1 then
-- Negative contours
pl.lsty(2)
pl.cont(z, 1, PRPTS, 1, PTHETAPTS, clevelneg, "pltr2", cgrid2)
end
if nlevelpos>1 then
-- Positive contours
pl.lsty(1)
pl.cont(z, 1, PRPTS, 1, PTHETAPTS, clevelpos, "pltr2", cgrid2)
end
-- Draw outer boundary
for i = 1, PPERIMETERPTS do
t = (2*math.pi/(PPERIMETERPTS-1))*(i-1)
px[i] = x0 + rmax*math.cos(t)
py[i] = y0 + rmax*math.sin(t)
end
pl.col0(ncolbox)
pl.line(px, py)
pl.col0(ncollab)
pl.lab("", "", "Shielded potential of charges in a conducting sphere")
end
----------------------------------------------------------------------------
-- main
--
-- Does several contour plots using different coordinate mappings.
----------------------------------------------------------------------------
mark = { 1500 }
space = { 1500 }
-- Parse and process command line arguments
pl.parseopts(arg, pl.PL_PARSE_FULL)
-- Initialize plplot
pl.init()
-- Set up function arrays
z = {}
w = {}
for i = 1, XPTS do
xx = (i-1 - math.floor(XPTS/2)) / math.floor(XPTS/2)
z[i] = {}
w[i] = {}
for j = 1, YPTS do
yy = (j-1 - math.floor(YPTS/2)) / math.floor(YPTS/2) - 1
z[i][j] = xx^2 - yy^2
w[i][j] = 2 * xx * yy
end
end
-- Set up grids
cgrid1 = {}
cgrid1["xg"] = {}
cgrid1["yg"] = {}
cgrid1["nx"] = XPTS
cgrid1["ny"] = YPTS
cgrid2 = {}
cgrid2["xg"] = {}
cgrid2["yg"] = {}
cgrid2["nx"] = XPTS
cgrid2["ny"] = YPTS
for i = 1, XPTS do
cgrid2["xg"][i] = {}
cgrid2["yg"][i] = {}
for j = 1, YPTS do
xx, yy = mypltr(i-1, j-1)
argx = xx * math.pi/2
argy = yy * math.pi/2
distort = 0.4
cgrid1["xg"][i] = xx + distort * math.cos(argx)
cgrid1["yg"][j] = yy - distort * math.cos(argy)
cgrid2["xg"][i][j] = xx + distort * math.cos(argx) * math.cos(argy)
cgrid2["yg"][i][j] = yy - distort * math.cos(argx) * math.cos(argy)
end
end
-- Plot using identity transform
pl.setcontlabelformat(4, 3)
pl.setcontlabelparam(0.006, 0.3, 0.1, 1)
pl.env(-1, 1, -1, 1, 0, 0)
pl.col0(2)
pl.cont(z, 1, XPTS, 1, YPTS, clevel, "mypltr")
pl.styl(mark, space)
pl.col0(3)
pl.cont(w, 1, XPTS, 1, YPTS, clevel, "mypltr")
pl.styl({}, {})
pl.col0(1)
pl.lab("X Coordinate", "Y Coordinate", "Streamlines of flow")
pl.setcontlabelparam(0.006, 0.3, 0.1, 0)
-- Plot using 1d coordinate transform
pl.env(-1, 1, -1, 1, 0, 0)
pl.col0(2)
pl.cont(z, 1, XPTS, 1, YPTS, clevel, "pltr1", cgrid1)
pl.styl(mark, space)
pl.col0(3)
pl.cont(w, 1, XPTS, 1, YPTS, clevel, "pltr1", cgrid1)
pl.styl({}, {})
pl.col0(1)
pl.lab("X Coordinate", "Y Coordinate", "Streamlines of flow")
-- Plot using 2d coordinate transform
pl.env(-1, 1, -1, 1, 0, 0)
pl.col0(2)
pl.cont(z, 1, XPTS, 1, YPTS, clevel, "pltr2", cgrid2)
pl.styl(mark, space)
pl.col0(3)
pl.cont(w, 1, XPTS, 1, YPTS, clevel, "pltr2", cgrid2)
pl.styl({}, {})
pl.col0(1)
pl.lab("X Coordinate", "Y Coordinate", "Streamlines of flow")
pl.setcontlabelparam(0.006, 0.3, 0.1, 0)
polar()
pl.setcontlabelparam(0.006, 0.3, 0.1, 0)
potential()
-- Clean up
pl.plend()