MA 113 - Calculus III
Worksheet #4 Parametric Surface Plots
Professor Broughton −Winter 03-04
Name: Box #:
1. Cartesian parametric surface plots
•Download 3Dplots.mws do this worksheet
•You will have to look over section 10.6
•You will need to review material on hyperbolic sins and cosines
A Cartesian parametric surface is given by 3 functions of two variables
x=f(s, t)
y=g(s, t)
z=h(s, t)
Note that this generalizes the notion of a space curve. A parametric plot is an
explicit representation of a surface whereas an implicit representation of a surface
is given by an equation such as:
x2
4+y2
9+z2
16 = 1,(1.1)
which is the equation of an ellipsoid. Very often we will want to find a paramedic
representation of a surface to graph the surface or to do some sort of computation.
For instance smooth 3D modeling often results required find in certain good fitting
parametric plots.
1. Now consider a specific parametric plot given by
x= 2 sin(s) cos(t) (1.2)
y= 3 sin(s) sin(t)
z= 4 cos(s)
Plot the surface for 0 ≤s≤π/2 and 0 ≤t≤2π.
