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129 lines (98 loc) · 3.04 KB
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--[[ $Id$
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 General Library 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")
function cycloid()
-- TODO
end
function spiro( params )
NPNT = 20000
xcoord = {}
ycoord = {}
-- Fill the coordinates
windings = params[4]
steps = math.floor(NPNT/windings)
dphi = 8*math.acos(-1)/steps
xmin = 0 -- This initialisation is safe!
xmax = 0
ymin = 0
ymax = 0
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 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
if (xmax-xmin)>(ymax-ymin) then
scale = xmax - xmin
else
scale = ymax - ymin
end
xmin = -0.65*scale
xmax = 0.65*scale
ymin = -0.65*scale
ymax = 0.65*scale
pl.wind(xmin, xmax, ymin, ymax)
pl.col0(1)
pl.line(xcoord, ycoord)
end
----------------------------------------------------------------------------
-- main
--
-- Generates two kinds of plots:
-- - construction of a cycloid (animated)
-- - series of epitrochoids and hypotrochoids
----------------------------------------------------------------------------
-- R, r, p, N
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
for i = 1, 9 do
pl.adv(0)
pl.vpor(0, 1, 0, 1)
spiro(params[i])
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])
end
-- Don't forget to call plend() to finish off!
pl.plend()