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\hfill    k\'od zad\'an\'\i\ :      {\Huge 225.f }
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{\Large Semestr\'aln\'\i\ pr\'ace  z PJW - ZS  1999}
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T\'ema:
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{\Huge Lisajousovy obrazce\\Lissajous figures}
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Student:                                  
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{\Large Jan Hn\'atek}
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Ro\v cn\'\i k/kruh/email:
\begin{center}			II./?/hnatekj@fel.cvut.cz
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Prohla\v suji, \v ze jsem tuto pr\' aci vypracoval samostatn\v e,
\v r\'adn\v e  uvedl v\v sechny informa\v cn\'\i\ zdroje a nem\'am n\'amitek proti
jej\'\i\ mu nekomer\v cn\'\i\ mu vyu\v zit\'\i\ Fakultou elektrotechnickou \v CVUT.
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V Praze dne: \makebox[3cm]{}     Podpis    \makebox[3cm]{}

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{\large\bf Abstract}
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This document is a description of my semestral work in Programming Languages
for WWW. The issue was to write an application or an applet which can draw 
Lissajous figures according to some user input parameters, for educational purposes.

\section {Introduction} 

Lissajous figures are curves you get as a result of superposition of two harmonic
oscillations in perpendicular directions to each other. The motion can be described 
for example by two time-dependent sinusoidal functions:
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$x(t) = A_x \sin (\omega _x t+\phi _x)$
\par
$y(t) = A_y \sin (\omega _y t+\phi _y)$
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\begin{tabular}{lll}
where &x,y&are the coordinates of the moving point\\
      &$A_x$,$A_y$&are amplitudes\\
      &$\omega _x$,$\omega _y$&are frequencies\\
      &$\phi _x$,$\phi _y$&are phases\\
      &t&is time \\
\end{tabular}

\section {Features} 
This java program was primarily written as an applet, but it is also possible to run
it as a java application. 
\par
User can control three parameters - amplitude, frequency and phase - of both signals.
Input is possible using a slidebar or a textbox. The slidebar values are limited as 
folows, while the textboxes have no limitations: 
\par
\begin{tabular}{lll}
amplitudes &(0..1)&\\
frequencies &(0..50)&the input value is only the $f_x$ of $\omega _x = 2\pi f_x$ \\
phases &(0..360)&in degrees \\ 
\end{tabular}

\section {Implementation}
When one of the input frequencies for the Lissajous figures is an iracional number
(like $\pi$), the result should be an unclosed curve. 
However this is not possible to implement on the computer, since the input frequencies 
are always limited by the 
variable type I use for them. So I could presume, that the curve will be always closed.
It always depends mainly 
on the commensurableness of the two given frequencies, so it might happen, that 
when these are not "very commensurable", the whole drawing area will be filled.
\par
The output is kind of "self-repairing" so don't be bothered by some fast wrong 
outputs and sudden redraws, when entered "wild" frequencies, it's just the stage,
when the time constants are being adjusted. The slidebar-adjustable values 
should be the reasonable input.

%\section {?}  

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