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-- Drawing "spirograph" curves - epitrochoids, cycolids, roulettes
-- Copyright (C) 2008 Jerry Bauck
-- 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
with
Ada.Numerics,
Ada.Numerics.Long_Elementary_Functions,
PLplot_Auxiliary,
PLplot_Traditional;
use
Ada.Numerics,
Ada.Numerics.Long_Elementary_Functions,
PLplot_Auxiliary,
PLplot_Traditional;
------------------------------------------------------------------------------
-- Generates two kinds of plots:
-- - construction of a cycloid (animated)
-- - series of epitrochoids and hypotrochoids
------------------------------------------------------------------------------
procedure x27a is
-- 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 : Real_Matrix(0 .. 8, 0 .. 3) :=
((21.0, 7.0, 7.0, 3.0),
(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));
fill : Boolean;
-- To understand why spiro is written this way you need to understand the
-- C code from which this was derived. In the main C program, params
-- is a two-dimensional array with 9 rows numbered 0 .. 8 and 4 columns
-- numbered 0 .. 3. When spiro is called, it is passed the _address_ of the
-- element of params's ith row, 0th column--nothing else. Then, inside spiro,
-- the corresponding entity (also called params!) appears as a
-- _one-dimensional_ array whose 0th element shares the same address as what
-- was passed from the main program. So memory locations starting there,
-- and numbered from 0, represent the 1D array equivalent to the ith row of
-- params in the main program. Wilma, call Barney--we're programming a
-- micaprocessor here.
procedure spiro(params : Real_Matrix; row : Integer; fill : Boolean) is
NPNT : constant Integer := 2000;
xcoord, ycoord : Real_Vector(0 .. NPNT);
windings : Integer;
steps : Integer;
phi : Long_Float;
phiw : Long_Float;
dphi : Long_Float;
xmin : Long_Float;
xmax : Long_Float;
xrange_adjust : Long_Float;
ymin : Long_Float;
ymax : Long_Float;
yrange_adjust : Long_Float;
function Trunc(a : Long_Float) return Integer renames PLplot_Auxiliary.Trunc;
-- Calculate greatest common divisor following pseudo-code for the
-- Euclidian algorithm at http://en.wikipedia.org/wiki/Euclidean_algorithm
function gcd(a, b : Integer) return Integer is
t : Integer;
aa : Integer := a;
bb : Integer := b;
begin
aa := abs(aa);
bb := abs(bb);
while bb /= 0 loop
t := bb;
bb := aa mod bb;
aa := t;
end loop;
return aa;
end gcd;
begin -- spiro
-- Fill the coordinates.
-- Proper termination of the angle loop very near the beginning
-- point, see http://mathforum.org/mathimages/index.php/Hypotrochoid
windings := Trunc(abs(params(row, 1)) /
Long_Float(gcd(Trunc(params(row, 0)), Trunc(params(row, 1)))));
steps := NPNT / windings;
dphi := 2.0 * pi / Long_Float(steps);
for i in 0 .. windings * steps loop
phi := Long_Float(i) * dphi;
phiw := (params(row, 0) - params(row, 1)) / params(row, 1) * phi;
xcoord(i) := (params(row, 0)-params(row, 1))*cos(phi)+params(row, 2)*cos(phiw);
ycoord(i) := (params(row, 0)-params(row, 1))*sin(phi)-params(row, 2)*sin(phiw);
if i = 0 then
xmin := xcoord(i);
xmax := xcoord(i);
ymin := ycoord(i);
ymax := ycoord(i);
end if;
if xmin > xcoord(i) then xmin := xcoord(i); end if;
if xmax < xcoord(i) then xmax := xcoord(i); end if;
if ymin > ycoord(i) then ymin := ycoord(i); end if;
if ymax < ycoord(i) then ymax := ycoord(i); end if;
end loop;
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;
plwind(xmin, xmax, ymin, ymax);
plcol0(1);
declare
xcoord_local, ycoord_local : Real_Vector(0 .. steps * windings);
begin
xcoord_local := xcoord(0 .. steps * windings);
ycoord_local := ycoord(0 .. steps * windings);
if fill then
plfill(xcoord_local, ycoord_local);
else
plline(xcoord_local, ycoord_local);
end if;
end;
end spiro;
procedure cycloid is
begin
null; -- TODO
end cycloid;
procedure arcs is
NSEG : constant Integer := 8;
theta : Long_Float;
dtheta : Long_Float;
a : Long_Float;
b : Long_Float;
begin
theta := 0.0;
dtheta := 360.0/Long_Float(NSEG);
plenv( -10.0, 10.0, -10.0, 10.0, 1, 0 );
-- Plot segments of circle in different colors
for i in 0 .. NSEG-1 loop
plcol0( (i mod 2) + 1 );
plarc(0.0, 0.0, 8.0, 8.0, theta, theta + dtheta, 0.0, False);
theta := theta + dtheta;
end loop;
-- 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 0 .. NSEG-1 loop
plcol0( 2 - (i mod 2 ) );
plarc( a*cos(theta/180.0*pi), a*sin(theta/180.0*pi), a, b, 0.0, 360.0, theta, True);
theta := theta + dtheta;
end loop;
end arcs;
begin
-- Parse and process command line arguments
plparseopts(PL_PARSE_FULL);
-- Initialize plplot
plinit;
-- Illustrate the construction of a cycloid
cycloid;
-- Loop over the various curves.
-- First an overview, then all curves one by one
plssub(3, 3) ; -- Three by three window
-- Overview
fill := False;
for i in params'range(1) loop
pladv(0);
plvpor(0.0, 1.0, 0.0, 1.0);
spiro(params, i, fill);
end loop;
-- Don't fill the curves.
pladv(0) ;
plssub(1, 1) ; -- One window per curve
for i in params'range(1) loop
pladv(0) ;
plvpor(0.0, 1.0, 0.0, 1.0);
spiro(params, i, fill);
end loop;
-- Fill the curves
fill := True;
pladv(0);
plssub(1, 1); -- One window per curve
for i in params'range(1) loop
pladv(0) ;
plvpor(0.0, 1.0, 0.0, 1.0);
spiro(params, i, fill);
end loop;
arcs;
-- Don't forget to call plend to finish off!
plend;
end x27a;
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