I am trying to find references about generalizations of polygons with non-straight sides.
I am interested in both the convex and non-convex cases, and particularly in polynomial boundaries, and algorithms to compute their area. References about higher-dimensional analogues (bodies with piecewise polynomial boundaries) and numerical methods to calculate more general functions over such sets would also be highly welcome.
So far, I have been unable to find much myself, but that might be because I am not aware of the correct search terms.
Questions: What are some references and good search terms for the study of non-/convex polygons, -hedra, -topes with curved, especially polynomial, boundaries?