# $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^2-y^2,2xy) is the graph of w=z^2 in 4-space. # Therefore (x^2-y^2,2xy,x,y) is the graph of w=sqrt(z) in 4-space. # 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^3-3xy^2,3x^2y-y^3) and (x^3-3xy^2,3x^2y-y^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**2-v**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**2-v**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**3-3*u*v**2,3*u**2*v-v**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**3-3*u*v**2,3*u**2*v-v**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**4-6*u**2*v**2+v**4,4*u**3*v-4*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**4-6*u**2*v**2+v**4,4*u**3*v-4*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 u-u**3/3+u*v**2,v-v**3/3+v*u**2,u**2-v**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 (2-v*sin(u/2))*sin(u),(2-v*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 (look-through)" splot "klein.dat" |
set hidden3d set view 70,305 set title "Klein bottle, glassblowers' version (solid)" splot "klein.dat" |
reset |