Vertex data compression through vector quantization

Rendering geometrically detailed 3D models requires the transfer and processing of large amounts of triangle and vertex geometry data. Compressing the geometry bit stream can reduce bandwidth requirements and alleviate transmission bottlenecks. In this paper, we show vector quantization to be an effective compression technique for triangle mesh vertex data. We present predictive vector quantization methods using unstructured code books as well as a product code pyramid vector quantizer. The technique is compatible with most existing mesh connectivity encoding schemes and does not require the use of entropy coding. In addition to compression, our vector quantization scheme can be used for complexity reduction by accelerating the computation of linear vertex transformations. Consequently, an encoded set of vertices can be both decoded and transformed in approximately 60 percent of the time required by a conventional method without compression     

Edgebreaker: connectivity compression for triangle meshes

Edgebreaker is a simple scheme for compressing the triangle/vertex incidence graphs (sometimes called connectivity or topology) of three-dimensional triangle meshes. Edgebreaker improves upon the storage required by previously reported schemes, most of which can guarantee only an O(t log(t)) storage cost for the incidence graph of a mesh of t triangles. Edgebreaker requires at most 2t bits for any mesh homeomorphic to a sphere and supports fully general meshes by using additional storage per handle and hole. For large meshes, entropy coding yields less than 1.5 bits per triangle. Edgebreaker's compression and decompression processes perform identical traversals of the mesh from one triangle to an adjacent one. At each stage, compression produces an op-code describing the topological relation between the current triangle and the boundary of the remaining part of the mesh. Decompression uses these op-codes to reconstruct the entire incidence graph. Because Edgebreaker's compression and decompression are independent of the vertex locations, they may be combined with a variety of vertex-compressing techniques that exploit topological information about the mesh to better estimate vertex locations. Edgebreaker may be used to compress the connectivity of an entire mesh bounding a 3D polyhedron or the connectivity of a triangulated surface patch whose boundary need not be encoded. The paper also offers a comparative survey of the rapidly growing field of geometric compression     

Advancing fan-front: 3D triangle mesh compression using fan based traversal

Connectivity compression techniques for very large 3D triangle meshes are based on clever traversals of the graph representing the mesh, so as to avoid the repeated references to vertices. In this paper we present a new algorithm for compressing large 3D triangle meshes through the successive conquest of triangle fans. The connectivity of vertices in a fan is implied. As each fan is traversed, the current mesh boundary is advanced by the fan-front. The process is recursively continued till the entire mesh is traversed. The mesh is then compactly encoded as a sequence of fan configuration codes. The fan configuration code comprehensively encodes the connectivity of the fan with the rest of the mesh. There is no need for any further special operators like split codes and additional vertex offsets. The number of fans is typically one-fourth of the total number of triangles. Only a few of the fan configurations occur with high frequency, enabling excellent connectivity information compression using range encoding. A simple implementation shows significant improvements, on the average, in bit-rate per vertex, compared to earlier reported techniques.     

Robust Spherical Parameterization of Triangular Meshes

Parameterization of 3D mesh data is important for many graphics and mesh processing applications, in particular for texture mapping, remeshing and morphing. Closed, manifold, genus-0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parameterizing a 3D triangle mesh onto the 3D sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity do not overlap. This is called a spherical triangulation. In this paper we formulate a set of necessary and sufficient conditions on the spherical angles of the spherical triangles for them to form a spherical triangulation. We formulate and solve an optimization procedure to produce spherical triangulations which reflect the geometric properties of a given 3D mesh in various ways.     

Delphi: geometry-based connectivity prediction in triangle mesh compression

Delphi is a new geometry-guided predictive scheme for compressing the connectivity of triangle meshes. Both compression and decompression algorithms traverse the mesh using the EdgeBreaker state machine. However, instead of encoding the EdgeBreaker clers symbols that capture connectivity explicitly, they estimate the location of the unknown vertex, v , of the next triangle. If the predicted location lies sufficiently close to the nearest vertex, w , on the boundary of the previously traversed portion of the mesh, then Delphi estimates that v coincides with w . When the guess is correct, a single confirmation bit is encoded. Otherwise, additional bits are used to encode the rectification of that prediction. When v coincides with a previously visited vertex that is not adjacent to the parent triangle (EdgeBreaker S case), the offset, which identifies the vertex v , must be encoded, mimicking the cut-border machine compression proposed by Gumhold and Strasser. On models where 97% of Delphi predictions are correct, the connectivity is compressed down to 0.19 bits per triangle. Compression rates decrease with the frequency of wrong predictors, but remains below 1.50 bits per triangle for all models tested.     

Priority-based encoding of triangle mesh connectivity for a known geometry

In certain practical situations, the connectivity of a triangle mesh needs to be transmitted or stored given a fixed set of 3D vertices that is known at both ends of the transaction (encoder/decoder). This task is different from a typical mesh compression scenario, in which the connectivity and geometry (vertex positions) are encoded either simultaneously or in reversed order (connectivity first), usually exploiting the freedom in vertex/triangle re-indexation. Previously proposed algorithms for encoding the connectivity for a known geometry were based on a canonical mesh traversal and predicting which vertex is to be connected to the part of the mesh that is already processed. In this paper, we take this scheme a step further by replacing the fixed traversal with a priority queue of open expansion gates, out of which in each step a gate is selected that has the most certain prediction, that is one in which there is a candidate vertex that exhibits the largest advantage in comparison with other possible candidates, according to a carefully designed quality metric. Numerical experiments demonstrate that this improvement leads to a substantial reduction in the required data rate in comparison with the state of the art.     

三角形条带网格模型几何压缩方法研究

三角形条带为三角形网格提供了一种紧凑的表示方法，使快速的绘制和传输三角形网格成为可能，因此对由三角形条带构成的网格压缩进行研究具有重要的意义．本文使用Triangle Fixer方法对三角形条带构成的三维模型拓扑信息进行了压缩，并采用3阶自适应算术编码进一步提高压缩率；同时结合量化、平行四边形顶点坐标预测以及算术编码来实现三角形网格几何信息的压缩，在几何模型质量基本没有损失的情况下，获得了很好的压缩性能．     

基于距离场的三维模型网格重建

根据任意亏格和任意边界的3D网格模型,给出一种网格重建算法。该算法通过对原始网格进行一系列自适应的局部修改操作,改进网格中三角形的质量和顶点位置分布。为减少优化过程中误差的累积,提出基于距离场的算法将新生成的顶点保留到原始网格曲面上,该算法实现简单,不需要复杂的全局参数化操作。实验结果表明,该算法有效、快速、稳定。     

基于插值多项式的可验证随机数

信息安全协议中使用的随机数通常由协议参与者任意选取,其他参与方无法验证,从而影响协议的公平性。针对上述问题,提出一个基于插值多项式的可验证随机数生成方案。该方案无需可信任的第三方,计算中心只承担计算职责,不承担可信任第三方的验证职责,并且方案中任意参与者都能验证随机数的随机性,保证了协议的公平性。     

Efficient Coding of Nontriangular Mesh Connectivity

We describe an efficient algorithm for coding the connectivity information of general polygon meshes. In contrast to most existing algorithms which are suitable only for triangular meshes, and pay a penalty for treatment of nontriangular faces, this algorithm codes the connectivity information in a direct manner. Our treatment of the special case of triangular meshes is shown to be equivalent to the Edgebreaker algorithm. Using our methods, any triangle mesh may be coded in no more than 2 bits/triangle (approximately 4 bits/vertex), a quadrilateral mesh in no more than 3.5 bits/quad (approximately 3.5 bits/vertex), and the most common case of a quad mesh with few triangles in no more than 4 bits/polygon.