This function plotter displays animated 3D surfaces described by three coordinate functions of two variables p, q for the spatial coordinates x, y, z.
The coordinate functions fx , fy , fz , which in the simulation are shown in three editable text fields, map the points of the plane pq unambiguously into a surface in space xyz. If fx , fy ,, fz contain periodic functions of the parameters p and q, closed or intersecting surfaces may be produced.
The functions may contain four constants a, b, c, v that can be changed by sliders. In the predefined functions v is used to animate the surfaces by oscillating one or more of the coordinates via time dependent terms.
At the start of the simulation you will 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.
The formula for the plane (pi ≡ π) shows that v modulates the z-function periodically: z = cos(vt)(a - 0.6)p. For t = 0 the modulation factor is 1; a determines the degree of modulation; (a- 0.6) defines a reasonable initial value. The other variable constants b, c are not used with the plane.
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. Slider a defines the base orientation. Pause freezes the animation at any spatial position. Reset leads back to the initial conditions.
The range of p and q is ∓ π . Scaling of all three axes x, y, z has a range of ∓ 1. The xy-plane cuts the z axis at the center of the z- arrow. As variables p and q change in the range -π to +π, a periodic function as cos(p) completes a full period in the variable plane.
The orientation of the tripod in space can be changed by drawing with the mouse.
Other ways of visualization are described in the next page.
Predefined functions are selected in the ComboBox with a mouse click. Constants a,b,c can be varied by sliders while the animation is running. By editing the formulas you can change the terms that are animated. You can input new parametric 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.