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<html>
<head>
<title>
LISSAJOUS_OPENGL - Display a Lissajous Figure using OpenGL
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LISSAJOUS_OPENGL <br> Display a Lissajous Figure using OpenGL
</h1>
<hr>
<p>
<b>LISSAJOUS_OPENGL</b>
is a C++ program which
computes a Lissajous figure based on user input, and uses OpenGL to display it.
</p>
<p>
The user specifies information about the number of points, and the form of the
two sine curves involved. Depending on these parameters, the resulting shape
may or may not be a closed curve. The user also specifies a range for the
underlying T parameter. Again, depending on the parameters, this value
may result in a closed curve being drawn several times, or a closed curve
being only partially drawn.
</p>
<p>
The program plots <b>N</b> points along the curve
<blockquote>
t(i) = i * T2 / ( N - 1 )<br>
x(i) = R1 * sin ( ( A1 * t(i) + B1 ) * 2 * pi )<br>
y(i) = R2 * sin ( ( A2 * t(i) + B2 ) * 2 * pi )
</blockquote>
for 0 <= I <= N - 1.
</p>
<p>
The user specifies N, T2, A1, B1, A2 and B2. The parameters R1 and
R2 are currently fixed at 1.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>lissajous_opengl</b> <i>n</i> <i>t2</i> <i>a1</i> <i>b1</i> <i>a2</i> <i>b2</i>
</blockquote>
where
<ul>
<li>
<i>n</i> the number of points to plot;
</li>
<li>
<i>t2</i> the final value of T.
</li>
<li>
<i>a1</i>, <i>b1</i> defines x(i)=sin((a1*t(i)+b1)*2*pi);
</li>
<li>
<i>a2</i>,<i>b2</i> defines y(i)=sin((a2*t(i)+b2)*2*pi);
</li>
</ul>
</p>
<h3 align = "center">
OpenGL on Macintosh OS X
</h3>
<p>
<b>OpenGL</b> ships with OS X for the Macintosh. You can obtain
the latest software version on
<a href = "http://www.apple.com/opengl/">the Apple OpenGL web site</a>.
</p>
<p>
Note that this source code and compilation script have been adapted for
use on a Macintosh running OS X.
</p>
<p>
For that reason, the include file references have been changed from:
<pre><code>
# include <GL/glut.h>
</code></pre>
to:
<pre><code>
# include <GLUT/glut.h>
</code></pre>
</p>
<p>
The compilation statement, which might ordinarily be
<pre><code>
g++ lissajous_opengl.C -m -lGL -lGLU -lglut
</code></pre>
was modified to:
<pre><code>
g++ lissajous_opengl.C -m -framework OpenGL -framework GLUT
</code></pre>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>LISSAJOUS_OPENGL</b> is available in
<a href = "../../cpp_src/lissajous_opengl/lissajous_opengl.html">a C++ version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/caustic_opengl/caustic_opengl.html">
CAUSTIC_OPENGL</a>,
a C++ program which
computes a caustic curve and displays it using OpenGL.
</p>
<p>
<a href = "../../cpp_src/fern_opengl/fern_opengl.html">
FERN_OPENGL</a>,
a C++ program which
uses OpenGL to display the Barnsley fractal fern.
</p>
<p>
<a href = "../../c_src/flood_opengl/flood_opengl.html">
FLOOD_OPENGL</a>,
a C program which
allows a user to select a region and flood it with color,
using OpenGL, by Art Wetzel.
</p>
<p>
<a href = "../../c_src/life_opengl/life_opengl.html">
LIFE_OPENGL</a>,
a C program which
simulates a version of John Conway's "Game of Life", displaying the
results using OpenGL.
</p>
<p>
<a href = "../../cpp_src/lights_out_opengl/lights_out_opengl.html">
LIGHTS_OUT_OPENGL</a>,
a C++ program which
sets up a "Lights Out" game and allows the user to solve it,
using the OpenGL graphics window.
</p>
<p>
<a href = "../../cpp_src/opengl/opengl.html">
OPENGL</a>,
C++ programs which
illustrate the use of the OpenGL graphics library;
</p>
<p>
<a href = "../../pl_src/obj2opengl/obj2opengl.html">
OBJ2OPENGL</a>,
a PERL script which
converts OBJ files of 3D data
into C include files, which can then be used in an OpenGL
program to display the object.
</p>
<p>
<a href = "../../cpp_src/polygonal_surface_display_opengl/polygonal_surface_display_opengl.html">
POLYGONAL_SURFACE_DISPLAY_OPENGL</a>,
a C++ program which
displays a surface in 3D described as a set of polygons, using OpenGL.
</p>
<p>
<a href = "../../cpp_src/rotating_cube_display_opengl/rotating_cube_display_opengl.html">
ROTATING_CUBE_DISPLAY_OPENGL</a>,
a C++ program which
displays a rotating color cube in 3D, using OpenGL;
</p>
<p>
<a href = "../../data/ppma/ppma.html">
PPMA</a>,
a data directory which
describes the ASCII Portable Pixel Map (PPM) format,
which is a possible means of storing the
graphics information displayed by <b>OpenGL</b>. One of the example
programs shows how this can be done.
</p>
<p>
<a href = "../../cpp_src/sphere_xyz_display_opengl/sphere_xyz_display_opengl.html">
SPHERE_XYZ_DISPLAY_OPENGL</a>,
a C++ program which
reads XYZ information defining points in 3D,
and displays a unit sphere and the points, using OpenGL.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_display_opengl/tet_mesh_display_opengl.html">
TET_MESH_DISPLAY_OPENGL</a>,
a C++ program which
reads a pair of files defining
a tetrahedral mesh and displays an image using OpenGL.
</p>
<p>
<a href = "../../cpp_src/tri_surface_display_opengl/tri_surface_display_opengl.html">
TRI_SURFACE_DISPLAY_OPENGL</a>,
a C++ program which
displays the 3D graphics information
in a TRI_SURFACE file
using OpenGL.
</p>
<p>
<a href = "../../cpp_src/triangulation_display_opengl/triangulation_display_opengl.html">
TRIANGULATION_DISPLAY_OPENGL</a>,
a C++ program which
reads a pair of files defining
a triangulation and displays an image using OpenGL.
</p>
<p>
<a href = "../../cpp_src/xy_display_opengl/xy_display_opengl.html">
XY_DISPLAY_OPENGL</a>,
a C++ program which
reads an XY file of 2D point coordinates, and displays
an image of those points using OpenGL.
</p>
<p>
<a href = "../../cpp_src/xyl_display_opengl/xyl_display_opengl.html">
XYL_DISPLAY_OPENGL</a>,
a C++ program which
reads XYL information defining points and lines in 2D, and displays
an image using OpenGL.
</p>
<p>
<a href = "../../cpp_src/xyz_display_opengl/xyz_display_opengl.html">
XYZ_DISPLAY_OPENGL</a>,
a C++ program which
reads an XYZ file of 3D point coordinates, and displays
an image of those points using OpenGL.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Edward Angel,<br>
Interactive Computer Graphics,
a Top-Down Approach with OpenGL,<br>
Addison-Wesley, 2000,<br>
ISBN: 0-201-38597-X,<br>
LC: T385.A514.
</li>
<li>
Renate Kempf, Chris Frazier, editors,<br>
OpenGL Reference Manual,<br>
Fourth Edition,<br>
Addison-Wesley, 2004,<br>
ISBN: 032117383X,<br>
LC: T385.O642.
</li>
<li>
Mason Woo, Jackie Neider, Tom Davis,<br>
OpenGL Programming Guide,<br>
Addison-Wesley, 1997,<br>
ISBN: 0-201-46138-2,<br>
LC: T385.N435.
</li>
<li>
Richard Wright, Michael Sweet,<br>
OpenGL Superbible,<br>
Third Edition,<br>
Sams, 2004,<br>
ISBN: 0672326019,<br>
LC: T385.W73.
</li>
<li>
<a href = "http://www.opengl.org/">
http://www.opengl.org/ </a> <br>
The official OpenGL site.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "lissajous_opengl.cpp">lissajous_opengl.cpp</a>, the source code.
</li>
<li>
<a href = "lissajous_opengl.sh">lissajous_opengl.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "figure1.png">figure1.png</a>,
the output from "lissajous_opengl 1000 1.0 5.0 0.5 6.0 0.0".
</li>
<li>
<a href = "figure2.png">figure2.png</a>,
the output from "lissajous_opengl 1000 2.0 7.0 0.5 8.1 0.0".
</li>
<li>
<a href = "figure3.png">figure3.png</a>,
the output from "lissajous_opengl 1000 1.0 7.0 0.2 8.0 0.0".
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for LISSAJOUS_OPENGL.
</li>
<li>
<b>DISPLAY</b> generates the graphics output.
</li>
<li>
<b>MYINIT</b> initializes OpenGL state variables dealing with viewing and attributes.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 01 December 2008.
</i>
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