Parameterized Surfaces in Spherical Coordinates

Parameterized surfaces in spherical coordinates are given by equations of the form ρ = f (s, t), θ = g(s, t), and $\varphi$ = 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 the defining expressions as the three components of a vector.

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


The 3D spherical plot of the vector $\left[\vphantom{ \rho ,\theta ,1}\right.$ρ, θ, 1$\left.\vphantom{ \rho ,\theta ,1}\right]$ gives the cone $\varphi$ = 1. For the following plot, the view is set with -1≤ρ≤1 and 0≤θ≤2π.

$\blacktriangleright$ Plot 3D + Spherical

$\left[\vphantom{ \rho ,\theta ,1}\right.$ρ, θ, 1$\left.\vphantom{ \rho ,\theta ,1}\right]$

dtbpF3in2.0003in0ptFigure


You can plot the surface defined by ρ = s, θ = s2 + t2, $\varphi$ = t by entering the three expressions as coordinates of a vector. For the following plot, take 0≤s≤1 and -1≤t≤1.

$\blacktriangleright$ Plot 3D + Spherical

$\left(\vphantom{
\begin{array}{c}
s \\
s^{2}+t^{2} \\
t
\end{array}
}\right.$$\begin{array}{c}
s \\
s^{2}+t^{2} \\
t
\end{array}$$\left.\vphantom{
\begin{array}{c}
s \\
s^{2}+t^{2} \\
t
\end{array}
}\right)$

dtbpF2.9992in1.9995in0ptFigure