In this paper we introduce a new surface representing, the displaced subdivision surface. It represents a detailed surface model as a scalar-valued displacement over a smooth domain surface. Our representation defines both the domain surface and the displacement function using a unified subdivision framework, allowing for simple and efficient evaluation of analytic surface properties. We present a simple, automatic scheme for converting detailed geometric models into such a representation. The challenge in this conversion process is to find a simple subdivision surface that still faithfully expresses the detailed model as its offset. We demonstrate that displaced subdivision surfaces offer a number of benefits, including geometry compression, editing, animation, scalability, and adaptive rendering. In particular, the encoding of fine detail as a scalar function makes the representation extremely compact.

We present a new method for user controlled morphing of two \nhomeomorphic triangle meshes of arbitrary topology. In particular we focus on the problem of establishing a correspondence map between source and target meshes. Our method employs the MAPS algorithm to parameterize both meshes over simple base domains and an additional harmonic map bringing the latter into correspondence. \nTo control the mapping the user specifies any number of \nfeature pairs, which control the parameterizations produced by the MAPS algorithm. Additional controls are provided through a direct manipulation interface allowing the user to tune the mapping between the base domains. We give several examples of æsthetically pleasing morphs which can be created in this manner with little user input. Additionally we demonstrate examples of temporal \nand spatial control over the morph.

An irregular connectivity mesh representative of a surface having an arbitrary topology is processed to generate a parameterization which maps points in a coarse base domain to points in the mesh. An illustrative embodiment uses a multi-level mesh simplification process in conjunction with conformal mapping to efficiently construct a parameterization of a mesh comprising a large number of triangles over a base domain comprising a smaller number of triangles. The parameterization in this embodiment corresponds to the inverse of function mapping each point in the original mesh to one of the triangles of the base domain, such that the original mesh can be reconstructed from the base domain and the parameterization. The mapping function is generated as a combination of a number of sub-functions, each of which relates data points in a mesh of one level in a simplification hierarchy to data points in a mesh of the next coarser level of the simplification hierarchy. The parameterization can also be used to construct, from the original irregular connectivity mesh, an adaptive remesh having a regular connectivity which is substantially easier to process than the original mesh.