Parametric Plots

Parameterized surfaces in rectangular coordinates are given by equations of the form x = f (s, t), y = g(s, t) and z = h(s, t). These are very general and allow you to generate a wide variety of interesting plots.

$\blacktriangleright$ To plot a parameterized surface

1.
Enter expressions in a vector, making each expression a separate component.

2.
With the insertion point in the vector, from the Plot 3D submenu, choose Rectangular.

The parameterized surface defined by the equations


x = s sin s cos t  
y = s cos s cos t  
z = s sin t  

can be created as the 3D rectangular plot of the vector $\left[\vphantom{ s\sin s\cos
t,s\cos s\cos t,s\sin t}\right.$s sin s cos t, s cos s cos t, s sin t$\left.\vphantom{ s\sin s\cos
t,s\cos s\cos t,s\sin t}\right]$. In the following plots, 0≤s≤2π and 0≤tπ.

$\blacktriangleright$ Plot 3D + Rectangular

$\left[\vphantom{ s\sin s\cos
t,s\cos s\cos t,s\sin t}\right.$s sin s cos t, s cos s cos t, s sin t$\left.\vphantom{ s\sin s\cos
t,s\cos s\cos t,s\sin t}\right]$

itbpFU2.0903in1.9977in0inPlot Style: Patch

Figure itbpFU2.092in1.9995in0inPlot Style: Wire FrameFigure

Although Patch produces high-quality graphics, certain surfaces, such as the one here, can be easier to visualize in WireFrame.