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