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Lumpy Torus and its Sublevel Sets

Below is an embedding of the graph of the function , where . I was interested in the sublevel sets , and this is my visualization. There's a little bit of fail in it--the image is accurate at , but I didn't solve for the limits on the coordinates (so you see boxes where we might expect ellipsish boundaries). In any case, is a scalar on the height function --drop it to zero and you have a donut. That height is interpreted here in the direction of the outward pointing normal vector of a point on the surface. The slider controls the minor radius of the torus.