This function plotter displays standard functions z = f(x , y) that may contain up to four continuously variable parameters a, b, c, p.
At the start of the simulation you will first see the projection of a plane in space, viewed under perspective distortion. It is embedded into an x y z tripod, and is accompanied by the x y- plane z = 0. This plane can be deactivated by its check box.
Other predefined surfaces in space can by selected in the ComboBox.
By time modulation of parameters a(t), b(t), c(t) the surfaces are animated, so that they appear moving in space. As you see in the formula field, the periodic function cos(t) is creating the animation effect. The program calculates functions in time steps of ∆t = p*0.1 milliseconds. Slider p thus controls the speed of animation. p = 0 freezes the graph.
In the formula of the plane cos(t) is multiplied to (bx+ay). t = 0 leads to cos(t) = 1. Play starts the animation, with time t starting at 0, as indicated in the t number field. With cos(t) fluctuating periodically, the plane oscillates in space. Sliders a, b, c define its base orientation. Pause freezes the animation at any spatial position. Reset leads back to the initial conditions.
Only those surfaces are animated whose formula has cos(t) as a factor.
Scaling of all three axes has a range of ∓2.5. 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 dot.
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 functions 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 formulas you can change the parts that are animated. You can input new formulas to create your own surfaces. Do not forget to press the ENTER key after a change!
Touching a surface with the mouse pointer lets its color filling disappear; the wire mesh of calculation will be pronouncedly visible.
The program can only demonstrate real values of z. If variables x, y lead to imaginary solutions z = 0 will be shown. This artefact can not be avoided, so ignore it!