Function plotter z = f ( x , y )

3D Waves

This function plotter displays functions of typical 3D waves z = f(x , y) that may contain up to 4 continuously variable parameters a, b, c, p. In the predefined waves p controls the speed of the waves in the xy plane

At start of the simulation you will first see the projection of a plane wave in space traveling in the x direction, viewed under perspective distortion. It is embedded into an xyz tripod, and is accompanied by the xy-plane z = 0. This plane can be deactivated by its check box.

Other predefined waves can by selected in the ComboBox.

By phase modulation of one or more of the variables the periodic waves are animated, so that they appear to be moving in space as a function of time. As you see in the formula field, for example, the periodic function sin(x-t) is creating the movement in the x direction. The program calculates functions in time in steps of ∆t = p*0.1 milliseconds. Slider p thus controls the speed of animation. p = 0 freezes the graph.

Play starts the animation, with time t starting at 0, as indicated in the t number field. With (x - t) rising linearly, the wave progresses in space. Sliders a, b, c define amplitude and orientation. Pause freezes the animation at any spatial position. Reset leads back to the initial conditions.

Scaling of all three axes has a range of ∓1. The xy-plane cuts the z-axis at the center of the z-arrow. The minimum and maximum position of the z-axis is marked by a red and a green point.

The orientation of the tripod in space can be changed by drawing with the mouse.

Other ways of visualization are described on the next page.

Predefined wave forms are selected in the ComboBox with a mouse click.

Parameters a,b,c can be varied by sliders while the animation is running. By editing the fomulas you can change the parts that are animated. You can input new formulas to create your own waves. Do not forget to press the ENTER key after a change!

Touching a wave with the mouse pointer lets its color filling disappear; the wire mesh of calculation will be pronouncedly visible.