Explicit surfaces, such as triangulations or wireframe models, have been extensively used to represent the deformable 3-D models that are used to fit 3-D point and 2-D silhouette data. The resulting approaches, however, suffer from the fact that fitting typically involves finding the facets that are closest to the 3-D data points or most likely to be silhouette facets. This requires searching, which is slow, and dealing with the non-differentiability of the distance function. By contrast, implicit surface representations allow fitting without search, since one can simply evaluate a differentiable field function at every data point. However, implicit representations are not necessarily the most intuitive ones and users, such as graphics designers, tend to prefer explicit models.