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# $Id: xw27.py 11859 2011-08-05 08:38:34Z andrewross $
#
# Copyright (C) 2007 Arjen Markus
# Copyright (C) 2008 Andrew Ross
# Drawing "spirograph" curves - epitrochoids, cycolids, roulettes
# This file is part of PLplot.
#
# PLplot is free software; you can redistribute it and/or modify
# it under the terms of the GNU Library General 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
#
from plplot_py_demos import *
import types
# main
#
# Generates two kinds of plots:
# - construction of a cycloid (animated)
# - series of epitrochoids and hypotrochoids
def main():
# R, r, p, N
# R and r should be integers to give correct termination of the
# angle loop using gcd.
# N.B. N is just a place holder since it is no longer used
# (because we now have proper termination of the angle loop).
params = [ [21.0, 7.0, 7.0, 3.0], # Deltoid
[21.0, 7.0, 10.0, 3.0],
[21.0, -7.0, 10.0, 3.0],
[20.0, 3.0, 7.0, 20.0],
[20.0, 3.0, 10.0, 20.0],
[20.0, -3.0, 10.0, 20.0],
[20.0, 13.0, 7.0, 20.0],
[20.0, 13.0, 20.0, 20.0],
[20.0,-13.0, 20.0, 20.0] ]
# Illustrate the construction of a cycloid
# TODO
#cycloid()
# Loop over the various curves
# First an overview, then all curves one by one
plssub(3, 3) # Three by three window
for i in range(9) :
pladv(0)
plvpor( 0.0, 1.0, 0.0, 1.0 )
spiro( params[i], 0 )
pladv(0)
plssub(1, 1) # One window per curve
for i in range(9):
pladv(0)
plvpor( 0.0, 1.0, 0.0, 1.0 )
spiro( params[i], 0 )
# Fill the curves.
pladv(0)
plssub(1, 1) # One window per curve
for i in range(9):
pladv(0)
plvpor( 0.0, 1.0, 0.0, 1.0 )
spiro( params[i], 1 )
arcs()
def gcd(a, b):
if not (type(a) is types.IntType and type(b) is types.IntType):
raise RuntimeError, "gcd arguments must be integers"
a = abs(a);
b = abs(b);
while(b != 0):
t = b
b = a % b
a = t
return a
def spiro(params, fill):
# Fill the coordinates
NPNT = 2000
# Proper termination of the angle loop very near the beginning
# point, see
# http://mathforum.org/mathimages/index.php/Hypotrochoid.
windings = int(abs(params[1])/gcd(int(params[0]), int(params[1])))
steps = int(NPNT/windings)
dphi = 2.0*pi/float(steps)
phi = arange(windings*steps+1)*dphi
phiw = (params[0]-params[1])/params[1]*phi
xcoord = (params[0]-params[1])*cos(phi) + params[2]*cos(phiw)
ycoord = (params[0]-params[1])*sin(phi) - params[2]*sin(phiw)
xmin = min(xcoord)
xmax = max(xcoord)
ymin = min(ycoord)
ymax = max(ycoord)
xrange_adjust = 0.15 * (xmax - xmin)
xmin -= xrange_adjust
xmax += xrange_adjust
yrange_adjust = 0.15 * (ymax - ymin)
ymin -= yrange_adjust
ymax += yrange_adjust
plwind( xmin, xmax, ymin, ymax )
plcol0(1)
if fill:
plfill( xcoord, ycoord )
else:
plline( xcoord, ycoord )
def arcs() :
NSEG = 8
theta = 0.0
dtheta = 360.0 / NSEG
plenv( -10.0, 10.0, -10.0, 10.0, 1, 0 )
# Plot segments of circle in different colors
for i in range (NSEG) :
plcol0( i%2 + 1 )
plarc(0.0, 0.0, 8.0, 8.0, theta, theta + dtheta, 0.0, 0)
theta = theta + dtheta
# Draw several filled ellipses inside the circle at different
# angles.
a = 3.0
b = a * tan( (dtheta/180.0*pi)/2.0 )
theta = dtheta/2.0
for i in range(NSEG):
plcol0( 2 - i%2 )
plarc( a*cos(theta/180.0*pi), a*sin(theta/180.0*pi), a, b, 0.0, 360.0, theta, 1)
theta = theta + dtheta
main()
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