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! Drawing "spirograph" curves - epitrochoids, cycolids, roulettes
!
! Copyright (C) 2007 Arjen Markus
! Copyright (C) 2008 Andrew Ross
! Copyright (C) 2008-2016 Alan W. Irwin
!
! 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
!
! N.B. the pl_test_flt parameter used in this code is only
! provided by the plplot module to allow convenient developer
! testing of either kind(1.0) or kind(1.0d0) floating-point
! precision regardless of the floating-point precision of the
! PLplot C libraries. We do not guarantee the value of this test
! parameter so it should not be used by users, and instead user
! code should replace the pl_test_flt parameter by whatever
! kind(1.0) or kind(1.0d0) precision is most convenient for them.
! For further details on floating-point precision issues please
! consult README_precision in this directory.
!
!
! --------------------------------------------------------------------------
! main
!
! Generates two kinds of plots:
! - construction of a cycloid (animated)
! - series of epitrochoids and hypotrochoids
! --------------------------------------------------------------------------
program x27f
use plplot
implicit none
integer i, j, fill
real(kind=pl_test_flt) params(4,9)
! R, r, p, N
! R and r should be integers to give correct termination of the
integer :: plparseopts_rc
! 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).
data ( ( params(i,j) ,i=1,4) ,j=1,9 ) / &
21.0_pl_test_flt, 7.0_pl_test_flt, 7.0_pl_test_flt, 3.0_pl_test_flt, &
21.0_pl_test_flt, 7.0_pl_test_flt, 10.0_pl_test_flt, 3.0_pl_test_flt, &
21.0_pl_test_flt, -7.0_pl_test_flt, 10.0_pl_test_flt, 3.0_pl_test_flt, &
20.0_pl_test_flt, 3.0_pl_test_flt, 7.0_pl_test_flt, 20.0_pl_test_flt, &
20.0_pl_test_flt, 3.0_pl_test_flt, 10.0_pl_test_flt, 20.0_pl_test_flt, &
20.0_pl_test_flt, -3.0_pl_test_flt, 10.0_pl_test_flt, 20.0_pl_test_flt, &
20.0_pl_test_flt, 13.0_pl_test_flt, 7.0_pl_test_flt, 20.0_pl_test_flt, &
20.0_pl_test_flt, 13.0_pl_test_flt, 20.0_pl_test_flt, 20.0_pl_test_flt, &
20.0_pl_test_flt,-13.0_pl_test_flt, 20.0_pl_test_flt, 20.0_pl_test_flt/
! plplot initialization
! Parse and process command line arguments
plparseopts_rc = plparseopts(PL_PARSE_FULL)
if(plparseopts_rc .ne. 0) stop "plparseopts error"
! Initialize plplot
call plinit()
! Illustrate the construction of a cycloid
call cycloid()
! Loop over the various curves
! First an overview, then all curves one by one
call plssub(3, 3)
fill = 0
do i = 1,9
call pladv(0)
call plvpor( 0.0_pl_test_flt, 1.0_pl_test_flt, 0.0_pl_test_flt, 1.0_pl_test_flt )
call spiro( params(1,i), fill )
end do
call pladv(0)
call plssub(1, 1)
do i = 1,9
call pladv(0)
call plvpor( 0.0_pl_test_flt, 1.0_pl_test_flt, 0.0_pl_test_flt, 1.0_pl_test_flt )
call spiro( params(1,i), fill )
end do
! fill the curves.
fill = 1
call pladv(0)
call plssub(1, 1)
do i = 1,9
call pladv(0)
call plvpor( 0.0_pl_test_flt, 1.0_pl_test_flt, 0.0_pl_test_flt, 1.0_pl_test_flt )
call spiro( params(1,i), fill )
end do
! Finally, an example to test out plarc capabilities
call arcs()
call plend()
contains
! --------------------------------------------------------------------------
! Calculate greatest common divisor following pseudo-code for the
! Euclidian algorithm at http://en.wikipedia.org/wiki/Euclidean_algorithm
integer function gcd (a, b)
use plplot
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 function gcd
! ===============================================================
subroutine cycloid
! TODO
end subroutine cycloid
! ===============================================================
subroutine spiro( params, fill )
use plplot, double_PI => PL_PI
implicit none
real(kind=pl_test_flt), parameter :: PI = double_PI
real(kind=pl_test_flt) params(*)
integer NPNT
parameter ( NPNT = 2000 )
integer n
real(kind=pl_test_flt) xcoord(NPNT+1)
real(kind=pl_test_flt) ycoord(NPNT+1)
integer windings
integer steps
integer i
integer fill
real(kind=pl_test_flt) phi
real(kind=pl_test_flt) phiw
real(kind=pl_test_flt) dphi
real(kind=pl_test_flt) xmin
real(kind=pl_test_flt) xmax
real(kind=pl_test_flt) xrange_adjust
real(kind=pl_test_flt) ymin
real(kind=pl_test_flt) ymax
real(kind=pl_test_flt) yrange_adjust
! Fill the coordinates
! Proper termination of the angle loop very near the beginning
! point, see
! http://mathforum.org/mathimages/index.php/Hypotrochoid.
windings = int(abs(params(2))/gcd(int(params(1)), int(params(2))))
steps = NPNT/windings
dphi = 2.0_pl_test_flt*PI/real(steps,kind=pl_test_flt)
n = windings*steps+1
! Initialize variables to prevent compiler warnings
xmin = 0.0
xmax = 0.0
ymin = 0.0
ymax = 0.0
do i = 1,n
phi = real(i-1,kind=pl_test_flt) * 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)
end do
xrange_adjust = 0.15_pl_test_flt * (xmax - xmin)
xmin = xmin - xrange_adjust
xmax = xmax + xrange_adjust
yrange_adjust = 0.15_pl_test_flt * (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(xcoord(1:n), ycoord(1:n) )
else
call plline(xcoord(1:n), ycoord(1:n) )
endif
end subroutine spiro
! ===============================================================
subroutine arcs( )
use plplot, double_PI => PL_PI
implicit none
real(kind=pl_test_flt), parameter :: PI = double_PI
integer NSEG
parameter ( NSEG = 8 )
integer i;
real (kind=pl_test_flt) theta, dtheta
real (kind=pl_test_flt) a, b
theta = 0.0_pl_test_flt
dtheta = 360.0_pl_test_flt / real(NSEG,kind=pl_test_flt)
call plenv( -10.0_pl_test_flt, 10.0_pl_test_flt, -10.0_pl_test_flt, 10.0_pl_test_flt, 1, 0 )
! Plot segments of circle in different colors
do i = 0, NSEG-1
call plcol0( mod(i,2) + 1 )
call plarc(0.0_pl_test_flt, 0.0_pl_test_flt, 8.0_pl_test_flt, 8.0_pl_test_flt, theta, &
theta + dtheta, 0.0_pl_test_flt, .false.)
theta = theta + dtheta
enddo
! Draw several filled ellipses inside the circle at different
! angles.
a = 3.0_pl_test_flt
b = a * tan( (dtheta/180.0_pl_test_flt*PI)/2.0_pl_test_flt )
theta = dtheta/2.0_pl_test_flt
do i = 0, NSEG-1
call plcol0( 2 - mod(i,2) )
call plarc( a*cos(theta/180.0_pl_test_flt*PI), &
a*sin(theta/180.0_pl_test_flt*PI), &
a, b, 0.0_pl_test_flt, 360.0_pl_test_flt, theta, .true.)
theta = theta + dtheta;
enddo
end subroutine arcs
end program x27f
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