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c
c Drawing "spirograph" curves - epitrochoids, cycolids, roulettes
c
c Copyright (C) 2007 Arjen Markus
c
c This file is part of PLplot.
c
c PLplot is free software; you can redistribute it and/or modify
c it under the terms of the GNU Library General Public License as published
c by the Free Software Foundation; either version 2 of the License, or
c (at your option) any later version.
c
c PLplot is distributed in the hope that it will be useful,
c but WITHOUT ANY WARRANTY; without even the implied warranty of
c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
c GNU Library General Public License for more details.
c
c You should have received a copy of the GNU Library General Public License
c along with PLplot; if not, write to the Free Software
c Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
c
c
c --------------------------------------------------------------------------
c main
c
c Generates two kinds of plots:
c - construction of a cycloid (animated)
c - series of epitrochoids and hypotrochoids
c --------------------------------------------------------------------------
program x27f
implicit none
include 'plplot_parameters.h'
integer i, j, fill
real*8 params(4,9)
c R, r, p, N
c R and r should be integers to give correct termination of the
c angle loop using gcd.
c N.B. N is just a place holder since it is no longer used
c (because we now have proper termination of the angle loop).
data ( ( params(i,j) ,i=1,4) ,j=1,9 ) /
& 21.0d0, 7.0d0, 7.0d0, 3.0d0,
& 21.0d0, 7.0d0, 10.0d0, 3.0d0,
& 21.0d0, -7.0d0, 10.0d0, 3.0d0,
& 20.0d0, 3.0d0, 7.0d0, 20.0d0,
& 20.0d0, 3.0d0, 10.0d0, 20.0d0,
& 20.0d0, -3.0d0, 10.0d0, 20.0d0,
& 20.0d0, 13.0d0, 7.0d0, 20.0d0,
& 20.0d0, 13.0d0, 20.0d0, 20.0d0,
& 20.0d0,-13.0d0, 20.0d0, 20.0d0/
c plplot initialization
c Parse and process command line arguments
call plparseopts(PL_PARSE_FULL)
c Initialize plplot
call plinit()
c Illustrate the construction of a cycloid
call cycloid()
c Loop over the various curves
c First an overview, then all curves one by one
call plssub(3, 3)
fill = 0
do 110 i = 1,9
call pladv(0)
call plvpor( 0.0d0, 1.0d0, 0.0d0, 1.0d0 )
call spiro( params(1,i), fill )
110 continue
call pladv(0)
call plssub(1, 1)
do 120 i = 1,9
call pladv(0)
call plvpor( 0.0d0, 1.0d0, 0.0d0, 1.0d0 )
call spiro( params(1,i), fill )
120 continue
c fill the curves.
fill = 1
call pladv(0)
call plssub(1, 1)
do 130 i = 1,9
call pladv(0)
call plvpor( 0.0d0, 1.0d0, 0.0d0, 1.0d0 )
call spiro( params(1,i), fill )
130 continue
c Finally, an example to test out plarc capabilities
call arcs()
call plend()
end
c --------------------------------------------------------------------------
c Calculate greatest common divisor following pseudo-code for the
c Euclidian algorithm at http://en.wikipedia.org/wiki/Euclidean_algorithm
integer function gcd (a, b)
implicit none
integer a, b, t
a = abs(a)
b = abs(b)
do while ( b .ne. 0 )
t = b
b = mod (a, b)
a = t
enddo
gcd = a
end
c ===============================================================
subroutine cycloid
c TODO
end
c ===============================================================
subroutine spiro( params, fill )
implicit none
include 'plplot_parameters.h'
real*8 params(*)
integer NPNT
parameter ( NPNT = 2000 )
real*8 xcoord(NPNT+1)
real*8 ycoord(NPNT+1)
integer windings
integer steps
integer i
integer fill
real*8 phi
real*8 phiw
real*8 dphi
real*8 xmin
real*8 xmax
real*8 xrange_adjust
real*8 ymin
real*8 ymax
real*8 yrange_adjust
integer gcd
c Fill the coordinates
c Proper termination of the angle loop very near the beginning
c point, see
c http://mathforum.org/mathimages/index.php/Hypotrochoid.
windings = int(abs(params(2))/gcd(int(params(1)), int(params(2))))
steps = NPNT/windings
dphi = 2.d0*PI/dble(steps)
do 110 i = 1,windings*steps+1
phi = dble(i-1) * dphi
phiw = (params(1)-params(2))/params(2)*phi
xcoord(i) = (params(1)-params(2))*cos(phi)+params(3)*cos(phiw)
ycoord(i) = (params(1)-params(2))*sin(phi)-params(3)*sin(phiw)
if (i.eq.1) then
xmin = xcoord(1)
xmax = xcoord(1)
ymin = ycoord(1)
ymax = ycoord(1)
endif
if ( xmin > xcoord(i) ) xmin = xcoord(i)
if ( xmax < xcoord(i) ) xmax = xcoord(i)
if ( ymin > ycoord(i) ) ymin = ycoord(i)
if ( ymax < ycoord(i) ) ymax = ycoord(i)
110 continue
xrange_adjust = 0.15d0 * (xmax - xmin)
xmin = xmin - xrange_adjust
xmax = xmax + xrange_adjust
yrange_adjust = 0.15d0 * (ymax - ymin)
ymin = ymin - yrange_adjust
ymax = ymax + yrange_adjust
call plwind( xmin, xmax, ymin, ymax )
call plcol0(1)
if (fill.eq.1) then
call plfill( 1+steps*windings, xcoord, ycoord )
else
call plline( 1+steps*windings, xcoord, ycoord )
endif
end
c ===============================================================
subroutine arcs()
implicit none
include 'plplot_parameters.h'
integer NSEG
parameter ( NSEG = 8 )
integer i;
real*8 theta, dtheta
real*8 a, b
theta = 0.0d0
dtheta = 360.0d0 / dble(NSEG)
call plenv( -10.0d0, 10.0d0, -10.0d0, 10.0d0, 1, 0 )
c Plot segments of circle in different colors
do i = 0, NSEG-1
call plcol0( mod(i,2) + 1 )
call plarc(0.0d0, 0.0d0, 8.0d0, 8.0d0, theta, theta + dtheta,
1 0.0d0, 0)
theta = theta + dtheta
enddo
c Draw several filled ellipses inside the circle at different
c angles.
a = 3.0d0
b = a * tan( (dtheta/180.0d0*pi)/2.0d0 )
theta = dtheta/2.0d0
do i = 0, NSEG-1
call plcol0( 2 - mod(i,2) )
call plarc( a*cos(theta/180.0d0*pi), a*sin(theta/180.0d0*pi),
1 a, b, 0.0d0, 360.0d0, theta, .true.)
theta = theta + dtheta;
enddo
end
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