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Multiresolution meshes provide an efficient and structured representation of geometric objects. To increase the
mesh resolution only at vital parts of the object, adaptive refinement is widely used. We propose a lossless compression
scheme for these adaptive structures that exploits the parent-child relationships inherent to the mesh
hierarchy. We use the rules that correspond to the adaptive refinement scheme and store bits only where some
freedom of choice is left, leading to compact codes that are free of redundancy. Moreover, we extend the coder to
sequences of meshes with varying refinement. The connectivity compression ratio of our method exceeds that of
state-of-the-art coders by a factor of 2 to 7.
For efficient compression of vertex positions we adapt popular wavelet-based coding schemes to the adaptive
triangular and quadrangular cases to demonstrate the compatibility with our method. Akin to state-of-the-art
coders, we use a zerotree to encode the resulting coefficients. Using improved context modeling we enhanced the
zerotree compression, cutting the overall geometry data rate by 7% below those of the successful Progressive
Geometry Compression. More importantly, by exploiting the existing refinement structure we achieve compression
factors that are 4 times greater than those of coders which can handle irregular meshes.
We introduce hexagonal global parameterizations, a new
type of surface parameterizations in which parameter lines respect six-fold rotational symmetries (6-RoSy). Such parameterizations enable the tiling of surfaces with nearly regular hexagonal or triangular patterns, and can be used for triangular remeshing.
To construct a hexagonal parameterization on a surface, we provide an automatic algorithm to generate a 6-RoSy field that respects directional and singularity features of the surface. This field is then used to direct a hexagonal global parameterization. The framework, called HexCover, extends the QuadCover algorithm and formulates necessary conditions for hexagonal parameterization.
We demonstrate the usefulness of our geometry-aware global parameterization with applications such as surface tiling with nearly regular textures and geometry patterns, as well as triangular and hexagonal remeshing.
Despite the success of quad-based 2D surface parameterization methods, effective parameterization algorithms for 3D volumes with cubes, i.e. hexahedral elements, are still missing. CubeCover is a first approach which provides both, a consistent theoretical framework for volume parameterization plus a full pipeline for generating
a hexahedral tessellation of a given volume with boundary aligned cubes which are guided by a frame field.
The input of CubeCover is a tetrahedral volume mesh. First, a frame field is designed with manual input from
the designer. It guides the interior and boundary layout of the parameterization. Then, the parameterization and
the hexahedral mesh are computed so as to align with the given frame field.
CubeCover has similarities to the QuadCover algorithm and extends it from 2D surfaces to 3D volumes. The
paper also provides theoretical results for 3D hexahedral parameterizations and analyses topological properties
of the appropriate function space.
Abstract—We present a novel coder for lossless compression
of adaptive multiresolution meshes that exploits their special
hierarchical structure. The heart of our method is a new
progressive connectivity coder that can be combined with
leading geometry encoding techniques. The compressor uses
the parent/child relationships inherent to the hierarchical mesh.
We use the rules that accord to the refinement scheme and
store bits only where it leaves freedom of choice, leading to
compact codes that are free of redundancy. To illustrate our
scheme we chose the widespread red-green refinement, but
the underlying concepts can be directly transferred to other
adaptive refinement schemes as well. The compression ratio of
our method exceeds that of state-of-the-art coders by a factor
of 2 to 3 on most of our benchmark models.