GEO DOUBEK - LISSAJOUS FIGURES - FIGURAS DE LISSAJOUS

VERSÃO EM PORTUGUÊS

This is an applet that draws the famous Lissajous Figures. It do that preliminarly determining dots : (1) in the vertical axis according to the cos (ang); (2) in the horizontal axis according to the sin (ang). After that, conecting with lines the succesively defined dots.

The domain used in the equation is [ 0,2pi [, or [ 0, 360°[, that corresponds to a complete round  in the trigonometric cincunference.

The applet has some ressources that allow it to modify the parameters and produces very singular effects.

• The first of them is  of sampling. By sampling are determinated how many points are defined inside the domain. The minimum are two to be posssible to define a single line. For example: if the number of points is defined as 36, the considered step between them will be 10°.

• The second one is the deflexion x and the deflexion y, that permit to adjust, respectively, the size of the figure in its width and height.

• The third one is the relation  angle (sin) x angle (cos). When the applet is loaded, the values are defined as 2 x 3 . It means that the angle used in the sin(ang) is multiplyed for 2, or, in mathematical language, is sin(2*ang), while the angle used in the cos(ang) is cos(3*ang). It is interesting to see that the coeficients for multiplication were the same, the result is a circular or star figure (since, of course, the criteria of sampling be high enought to permit it).

• The fourth ressource is the difference of phase between the angle (sin) and the angle (cos). It defines if one angle will be always a little bit "ahead of schedule" ou "delayed" relatively to the other. For example, if the values choosed be -15°, it means that the angle use to calculate the sin will be all the time 15° smaller than the one used to calculate the cos. Modifying this value quickly generates the effect of a 3D rotating figure.

• The fifth and the last ressource is the color of the line, that obviously define the color used to plot the figure.

I am studying another Java ressources to make this apllet more interactive and efficient.

I leave here my e-mail for any suggestions, critics or doubts. All of them are welcome :-)

geodoubek@bol.com.br