Algebraic equations to surface geometries

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Would like to have SWx evaluate, solve and create surface geometries of equations (instead of using Mathmatica, etc.). Please see this page for some equations for a Dini surface model:


https://mathoverflow.net/questions/149842/geodesics-on-the-twisted-pseudosphere-dinis-surface

If it can be done, how do I enter these equations in SW and have it evaluate the equations and render the geometry?