After a short introduction on the fundamentals of subdivision surfaces, the more advanced material of this chapter focuses on two main aspects. First, shape interrogation issues are discussed; in particular, artifacts, typical of subdivision surfaces, are analysed. The second aspect is related to how structuring the geometric information: a multi-resolution approach is a natural choice for this geometric representation, and it can be seen as a possible way to structure geometry. Moreover, a first
structure can be given by a set of meaningful geometric constraints that the shape has to preserve, often due to the specific application context. How subdivision surfaces can cope with constraint-based modelling is treated in the chapter with a special attention to applications.
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