Shape and Space

5.6 Summary

In this chapter we demonstrated that a solid and an implicit function are related by dual structures: the medial axis of the solid and the maximal tubular neighborhood of its boundary. These fundamental structures define the embedding of a shape in space and, therefore the characteristics of the implicit function. Finally, we discussed a set of criteria which could be used for analyzing implicit models. From an interpretation of the implicit function as a distance function, we identified two classes of implicit models — the ones based on a true metric and on a pseudo-metric.