
Notes for October 21 class  Parametric surfaces
Parametric cylinder
You can describe many surfaces parametrically,
using the two parameters
0 ≤ u ≤ 1 and
0 ≤ v ≤ 1
to define values of x, y and z over the surface.
For example,
the open cylindrical section to the right
is described by:
y = cos(θ)
x = sin(θ)
z = 2 * v  1
where:
θ = 2 π u



Parametric sphere
Similarly,
the longitude / latitude parameterization of a sphere to the right
is described by:
x = cos(φ) * cos(θ)
y = cos(φ) * sin(θ)
z = sin(φ)
where:
θ = 2 π u
φ = π v  π / 2



Parametric torus (donut)
The longitude / latitude parameterization of a torus
is described by:
x = (1 + r * cos(φ)) * cos(θ)
y = (1 + r * cos(φ)) * sin(θ)
z = r * sin(φ)
where:
θ = 2 π u
φ = 2 π v
r = the radius of the "inner tube".



Homework, due by start of class on Wednesday October 28
As always, you get extra points for making something that is fun, exciting, beautiful or original.

 