GEO DOUBEK - LISSAJOUS FIGURES - FIGURAS DE LISSAJOUS
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 :-)
