The lissajous3d program allows the plotting of 3 dimensional Lissajous graphics.
Below is a reduced picture of this (Windows) program at work:
- choice of 4 pen styles:
- 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 3DFor 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 informationClick [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.