Math 3298 - Hampton - Lab 9 - Due 11/13

Parametric Surfaces

In this lab we will investigate parametric surfaces.  Below are some examples of ParametricPlot3D.

A torus with radii 1 and 2 can be parameterized as follows:

T[u_,v_]:={(2+Cos[v])Cos[u],(2+Cos[v])Sin[u],Sin[v]}
torus = ParametricPlot3D[T[u,v],{u,0,2*Pi},{v,0,2*Pi}]

Combining two surfaces:

plane = ParametricPlot3D[{3,y,z},{y,-2,2},{z,-2,2}];
Show[plane,torus, PlotRange->All]

Exercises

1. Create a parametric plot of the part of the paraboloid x = y^2 + z^2 which is cut out by the cylinder y^2 + z^2 = 1.
2.  Construct an ice-cream cone shaped surface out of two parametric surface plots: one piece should be a cone, the other a spherical cap.