Displaced subdivision surface representation [13] is a new form of representing a polygonal surface model, where a detailed surface model is defined as a scaler-valued displacement map over a smooth domain surface; it puts forth a number of attractive features for editing, geometry compression, animation, scalability, and adaptive rendering of polygonal models. The construction of the smooth domain surface is a challenging task in the conversion process of a detailed polygonal surface model into this representation. In this paper, we propose a new efficient method for defining the smooth domain surface based on -subdivision scheme. The proposed algorithm not only performs better in terms of the quality of the generated surfaces but is computationally more efficient and occupies less memory as compared to the original algorithm [13] and generates surfaces with more levels of detail due to the specific nature of -subdivision when the prescribed target complexity of the generated mesh must not be exceeded. To corroborate the efficiency and the quality of the new technique, the conversion results for several public domain models have been presented.

Efficient representations of a 3-D object shape and its texture data have attracted wide attention for the transmission of computer graphics data and for the development of multi-view real image rendering systems on computer networks. Polygonal mesh data, which consist of connectivity information, geometry data, and texture data, are often used for representing 3-D objects in many applications. This paper presents a wavelet coding technique for coding the geometry data structured on a triangular lattice plane obtained by structuring the connectivity of the polygonal mesh data. Since the structured geometry data have an arbitrarily-shaped support on the triangular lattice plane, a shape-adaptive wavelet transform was used to obtain the wavelet coefficients, whose number is identical to the number of original data, while preserving the self-similarity of the wavelet coefficients across subbands. In addition, the wavelet coding technique includes extensions of the zerotree entropy (ZTE) coding for taking into account the rate-distortion properties of the structured geometry data. The parent-children dependencies are defined as the set of wavelet coefficients from different bands that represent the same spatial region in the triangular lattice plane, and the wavelet coefficients in the spatial tree are optimally pruned based on the rate-distortion properties of the geometry data. Experiments in which proposed wavelet coding was applied to some sets of polygonal mesh data showed that the proposed wavelet coding achieved better coding efficiency than the Topologically Assisted Geometry Compression scheme adopted in the MPEG-4 standard.

In this letter, we address geometry coding of 3-D mesh models. Using a joint prediction, the encoder predicts vertex positions in the layer traversal order. After we apply the joint prediction algorithm to eliminate redundancy among vertex positions using both position and angle values of neighboring triangles, we encode those prediction errors using a uniform quantizer and an entropy coder. The proposed scheme demonstrates improved coding efficiency for various VRML test data.