Joining primal/dual subdivision surfaces

Abstract : In this article we study the problem of constructing an intermediate surface between two other surfaces defined by different iterative construction processes. This problem is formalised with Boundary Controlled Iterated Function System model. The formalism allows us to distinguish between subdivision of the topology and subdivision of the mesh. Although our method can be applied to surfaces with quadrangular topology subdivision, it can be used with any mesh subdivision (primal scheme, dual scheme or other.) Conditions that guarantee continuity of the intermediate surface determine the structure of subdivision matrices. Depending on the nature of the initial surfaces and coefficients of the subdivision matrices we can characterise the differential behaviour at the connection points between the initial surfaces and the intermediate one. Finally we study the differential behaviour of the constructed surface and show the necessary conditions to obtain an almost everywhere differentiable surface.