Previous approaches for constructing a multiresolution hierarchy for irregular meshes have investigated how to overcome the connectivity and topology constraints during decomposition, but not considered the effects of sampling density on subsequent editing and signal processing. These approaches produce lower resolution meshes with unbalanced sampling density, and the details are not encoded in a frequency dependent order. Consequently, operations such as editing in low resolution and filtering of details do not always produce the desired results. Using the idea of local support of wavelets and with the aid of discrete fairing, we present a new decomposition method that produces a hierarchy of meshes with decreasing maximum sampling density and smoother parameter information. The result...[ Read more ]

Previous approaches for constructing a multiresolution hierarchy for irregular meshes have investigated how to overcome the connectivity and topology constraints during decomposition, but not considered the effects of sampling density on subsequent editing and signal processing. These approaches produce lower resolution meshes with unbalanced sampling density, and the details are not encoded in a frequency dependent order. Consequently, operations such as editing in low resolution and filtering of details do not always produce the desired results. Using the idea of local support of wavelets and with the aid of discrete fairing, we present a new decomposition method that produces a hierarchy of meshes with decreasing maximum sampling density and smoother parameter information. The resulting mesh hierarchy has triangles of good quality, enabling more stable editing. Moreover, the detail vectors better approximate the frequency spectrum of the mesh, making signal filtering more accurate. We demonstrate the advantages of our hierarchy in several applications including signal filtering, editing, and remeshing.