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--[[
Drawing "spirograph" curves - epitrochoids, cycolids, roulettes
Copyright (C) 2009 Werner Smekal
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
--]]
-- initialise Lua bindings for PLplot examples.
dofile("plplot_examples.lua")
--------------------------------------------------------------------------
-- Calculate greatest common divisor following pseudo-code for the
-- Euclidian algorithm at http://en.wikipedia.org/wiki/Euclidean_algorithm
function gcd (a, b)
a = math.floor(math.abs(a))
b = math.floor(math.abs(b))
while b~=0 do
t = b
b = a % b
a = t
end
return a
end
function cycloid()
-- TODO
end
function spiro( params, fill )
NPNT = 2000
xcoord = {}
ycoord = {}
-- Fill the coordinates
-- Proper termination of the angle loop very near the beginning
-- point, see
-- http://mathforum.org/mathimages/index.php/Hypotrochoid.
windings = math.floor(math.abs(params[2])/gcd(params[1], params[2]))
steps = math.floor(NPNT/windings)
dphi = 2*math.pi/steps
for i = 1, windings*steps+1 do
phi = (i-1) * dphi
phiw = (params[1]-params[2])/params[2]*phi
xcoord[i] = (params[1]-params[2])*math.cos(phi) + params[3]*math.cos(phiw)
ycoord[i] = (params[1]-params[2])*math.sin(phi) - params[3]*math.sin(phiw)
if i == 1 then
xmin = xcoord[i]
xmax = xcoord[i]
ymin = ycoord[i]
ymax = ycoord[i]
end
if xmin>xcoord[i] then xmin = xcoord[i] end
if xmax<xcoord[i] then xmax = xcoord[i] end
if ymin>ycoord[i] then ymin = ycoord[i] end
if ymax<ycoord[i] then ymax = ycoord[i] end
end
xrange_adjust = 0.15*(xmax-xmin)
xmin = xmin - xrange_adjust
xmax = xmax + xrange_adjust
yrange_adjust = 0.15*(ymax-ymin)
ymin = ymin - yrange_adjust
ymax = ymax + yrange_adjust
pl.wind(xmin, xmax, ymin, ymax)
pl.col0(1)
if fill == 1 then
pl.fill(xcoord, ycoord)
else
pl.line(xcoord, ycoord)
end
end
function arcs()
NSEG = 8
theta = 0.0
dtheta = 360.0 / NSEG
pl.env( -10.0, 10.0, -10.0, 10.0, 1, 0 )
-- Plot segments of circle in different colors
for i = 0, NSEG-1 do
pl.col0( i%2 + 1 )
pl.arc(0.0, 0.0, 8.0, 8.0, theta, theta + dtheta, 0.0, 0)
theta = theta + dtheta
end
-- Draw several filled ellipses inside the circle at different
-- angles.
a = 3.0
b = a * math.tan( (dtheta/180.0*math.pi)/2.0 )
theta = dtheta/2.0
for i = 0, NSEG-1 do
pl.col0( 2 - i%2 )
pl.arc( a*math.cos(theta/180.0*math.pi), a*math.sin(theta/180.0*math.pi), a, b, 0.0, 360.0, theta, 1)
theta = theta + dtheta
end
end
----------------------------------------------------------------------------
-- main
--
-- Generates two kinds of plots:
-- - construction of a cycloid (animated)
-- - series of epitrochoids and hypotrochoids
----------------------------------------------------------------------------
-- 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, 7, 7, 3 }, -- Deltoid
{ 21, 7, 10, 3 },
{ 21, -7, 10, 3 },
{ 20, 3, 7, 20 },
{ 20, 3, 10, 20 },
{ 20, -3, 10, 20 },
{ 20, 13, 7, 20 },
{ 20, 13, 20, 20 },
{ 20,-13, 20, 20 } }
-- plplot initialization
-- Parse and process command line arguments
pl.parseopts(arg, pl.PL_PARSE_FULL)
-- Initialize plplot
pl.init()
-- Illustrate the construction of a cycloid
cycloid()
-- Loop over the various curves
-- First an overview, then all curves one by one
pl.ssub(3, 3) -- Three by three window
fill = 0
for i = 1, 9 do
pl.adv(0)
pl.vpor(0, 1, 0, 1)
spiro(params[i], fill)
end
pl.adv(0)
pl.ssub(1, 1) -- One window per curve
for i = 1, 9 do
pl.adv(0)
pl.vpor(0, 1, 0, 1)
spiro(params[i], fill)
end
-- fill the curves.
fill = 1
pl.adv(0)
pl.ssub(1, 1) -- One window per curve
for i = 1, 9 do
pl.adv(0)
pl.vpor(0, 1, 0, 1)
spiro(params[i], fill)
end
arcs()
pl.plend()