Examples
- The simplest type of parametric surfaces is given by the graphs of functions of two variables:
- Surfaces of revolution give another important class of surfaces that can be easily parametrized. If the graph z = f(x), a ≤ x ≤ b is rotated about the z-axis then the resulting surface has a parametrization
- The straight circular cylinder of radius R about x-axis has the following parametric representation:
- Using the spherical coordinates, the unit sphere can be parameterized by
- This parametrization breaks down at the north and south poles where the azimuth angle θ is not determined uniquely.
The same surface admits many different parametrizations. For example, the coordinate z-plane can be parametrized as
for any constants a, b, c, d such that ad − bc ≠ 0, i.e. the matrix is invertible.
Read more about this topic: Parametric Surface
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