# $Id: singulr.dem,v 1.6 2003/10/28 05:35:54 sfeam Exp $ # # Demo that plots some surfaces with singularities. # Author: Carsten Steger # # (x,y,x^2y^2,2xy) is the graph of w=z^2 in 4space. # Therefore (x^2y^2,2xy,x,y) is the graph of w=sqrt(z) in 4space. # Coordinates 1, 2, and 3 give the real part of either function, # whereas coordinates 1, 2, and 4 give the imaginary part. # The same holds for the cube function w=z^3. The graphs are given by # (x,y,x^33xy^2,3x^2yy^3) and (x^33xy^2,3x^2yy^3,x,y). # And so on... set parametric set hidden3d set isosamples 21 set autoscale set view 60,30 set urange [3:3] set vrange [3:3] set title "Real part of complex square root function" splot u**2v**2,2*u*v,u 
set view 60,210 set title "Real part of complex square root function (different view)" replot 
set view 60,120 set urange [3:3] set vrange [3:3] set title "Imaginary part of complex square root function" splot u**2v**2,2*u*v,v 
set view 60,300 set title "Imaginary part of complex square root function (different view)" replot 
set view 60,30 set urange [3:3] set vrange [3:3] set title "Real part of complex cube root function" splot u**33*u*v**2,3*u**2*vv**3,u 
set view 60,210 set title "Real part of complex cube root function (different view)" replot 
set view 60,30 set urange [3:3] set vrange [3:3] set title "Imaginary part of complex cube root function" splot u**33*u*v**2,3*u**2*vv**3,v 
set view 60,210 set title "Imaginary part of complex cube root function (different view)" replot 
set view 60,30 set isosamples 31 set urange [1:1] set vrange [1:1] set title "Real part of complex 4th root function" splot u**46*u**2*v**2+v**4,4*u**3*v4*u*v**3,u 
set view 60,210 set title "Real part of complex 4th root function (different view)" replot 
set view 60,120 set urange [1:1] set vrange [1:1] set title "Imaginary part of complex 4th root function" splot u**46*u**2*v**2+v**4,4*u**3*v4*u*v**3,v 
set view 60,300 set title "Imaginary part of complex 4th root function (different view)" replot 
set isosamples 21 set view 60,20 set urange [3:3] set vrange [3:3] set title "Enneper's surface" splot uu**3/3+u*v**2,vv**3/3+v*u**2,u**2v**2 
set view 60,110 set title "Enneper's surface (different view)" replot 
set isosamples 31,11 set view 60,30 set title "Moebius strip" set urange [0:2*pi] set vrange [0.25:0.25] splot (2v*sin(u/2))*sin(u),(2v*sin(u/2))*cos(u),v*cos(u/2) 
set view 60,210 set title "Moebius strip (view from opposite side)" replot 
unset key set xrange [10:10] set yrange [10:10] set zrange [3:3] set urange [0:2*pi] set vrange [0:2*pi] set isosamples 39,60 set view 60,120 set title "Klein bottle" splot (2*sin(u)*cos(v/2)sin(2*u)*sin(v/2)+8)*cos(v), \ (2*sin(u)*cos(v/2)sin(2*u)*sin(v/2)+8)*sin(v), \ 2*sin(u)*sin(v/2)+sin(2*u)*cos(v/2) 
set urange [0:2*pi] set vrange [0:4*pi/3] set isosamples 39,40 set view 60,20 set title "Klein bottle with look at the 'inside'" replot 
set style data lines set xrange [12:12] set yrange [12:12] set zrange [*:*] unset hidden3d set ticslevel 0. set view 50,15 #HBB: ,1,1.7 set title "Klein bottle, glassblowers' version (lookthrough)" splot "klein.dat" 
set hidden3d set view 70,305 set title "Klein bottle, glassblowers' version (solid)" splot "klein.dat" 
