I'm looking for some references that would help me better understand finding parametric representations for different surface equations. For example:



That's an equation for an ellipsoid and I need to create a parametric equation that represents the top half of it.

The textbook that I have does not give any good examples of approaching these problems. The book just gives the equation, says something along the lines of "let's choose parameters and ", then jumps to the new parameterized equation.

I feel like I'm missing an important step for understanding this and most of the things I find online and in the textbooks appear to assume that the reader can just make the jump once the parameters are chosen.

Any links or help would be appreciated. Preferably a site that details the work done when parameterizing a surface.

Sometimes you can use spherical coordinates. They work when modeling an ellipsoid in parametrics.

For your ellipsoid:



Enter these into your equation and you get 1. Sometimes we have to choose the one that will work for z by knowing x and y.

The above parametrics are for the entire ellipsoid though.