The lissajous3d program allows the plotting of 3 dimensional Lissajous graphics. Below is a reduced picture of this (Windows) program at work: Program features
- choice of 4 pen styles:
- cube - square - circle - single dots or connected (smooth) lines - step count from 100..1000 - save settings to disc (*.l3d extension attached) - load settings from disc - save picture (*.bmp) For the constants a,b,c,d : - a left mouseclick adds the (+/-) value - a right click subtracts the (+/-) value. The (+/-) value itself may be changed also by left- or right mouseclicks. Interim variable t counts from 0 to the selected stepcount. Stepcount is selectable between 100 and 1000 in steps of 50. The menu and buttons are self-explanetory. Below is pictured a "dotted" and the same "smooth" function
What are Lissajous functions? The commonly used functions have the format
For a given value of x, only one value of y may result. So, the painting of circles or ellipses is not possible. This may be overcome by using so called parametric functions, which have the format
y = ...t... Lissajous functions have the form
y = sin(...t) Note: sin and cos are interchangeble. A circle with radius 5 and center at (0,0) is represented by
y = 5sin(t) 360 degrees make a full period. So, in the picture below, t has to increment from 0 to 360 to paint the complete circle. addition or multiplication of periodic functions.
Above picture was made with graphics explorer a functions and equations grapher program. Lissajous 3D For 3D, a z axis is added to the X and Y axis.
y = sin(..t)... z = sin(..t)... The picture at the top of this page represents
y = 0.5sin(5t) + 0.5sin(t) z = sin(2t) For each value of t, a sphere is painted. Additional information Click [here] for programming information.This page also has a link to the complete Delphi-7 project source code. Click on the download (lightning) button at the top of this page to load the Lissajous-3D program. |
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