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2014, IEEE Transactions on Visualization and Computer Graphics
Fig. 1. Grouper represents a triangle mesh as groups of vertices and triangles stored as fixed-size records, most of which encode two adjacent triangles and one incident vertex. A VTT group (tan: 93%) represents one vertex and two adjacent triangles incident upon it; a VT group (blue: 3%) represents one vertex and one incident triangle; a T group (red: 4%) represents one triangle; and a V group (black: 1%) represents one vertex. Thick edges separate groups; thin edges separate triangles within the same group.
The SQuad data structure represents the connectivity of a triangle mesh by its "S table" of about 2 rpt (integer references per triangle). Yet it allows for a simple implementation of expected constant-time, random-access operators for traversing the mesh, including in-order traversal of the triangles incident upon a vertex. SQuad is more compact than the Corner Table (CT), which stores 6 rpt, and than the recently proposed SOT, which stores 3 rpt. However, in-core access is generally faster in CT than in SQuad, and SQuad requires rebuilding the S table if the connectivity is altered. The storage reduction and memory coherence opportunities it offers may help to reduce the frequency of page faults and cache misses when accessing elements of a mesh that does not fit in memory. We provide the details of a simple algorithm that builds the S table and of an optimized implementation of the SQuad operators.
We propose Zipper, a compact representation of incidence and adjacency for manifold triangle meshes with fixed connectivity. Zipper uses on average only 6 bits per triangle, can be constructed in linear space and time, and supports all standard random-access and mesh traversal operators in constant time. Similarly to the previously proposed LR (Laced Ring) approach, the Zipper construction reorders vertices and triangles along a nearly Hamiltonian cycle called the ring. The 4.4x storage reduction of Zipper over LR results from three contributions: (1) For most triangles, Zipper stores a 2-bit delta (plus three additional bits) rather than a full 32-bit reference. (2) Zipper modifies the ring to reduce the number of exceptional triangles. (3) Zipper encodes the remaining exceptional triangles using 2.5x less storage. In spite of these large savings in storage, we show that Zipper off ers comparable performance to LR and other data structures in mesh processing applications. Zipper may also serve as a compact indexed format for rendering meshes, and hence is valuable even in applications that do not require adjacency information.
We propose LR (Laced Ring)--a simple data structure for representing the connectivity of manifold triangle meshes. LR provides the option to store on average either 1.08 references per triangle or 26.2 bits per triangle. Its construction, from an input mesh that supports constant-time adjacency queries, has linear space and time complexity, and involves ordering most vertices along a nearly-Hamiltonian cycle. LR is best suited for applications that process meshes with fixed connectivity, as any changes to the connectivity require the data structure to be rebuilt. We provide an implementation of the set of standard random-access, constant-time operators for traversing a mesh, and show that LR often saves both space and traversal time over competing representations.
Future Generation Computer Systems, 2004
Triangle meshes are the most popular standard model used to represent polygonal surfaces. Drawing these meshes as a set of independent triangles involves sending a vast amount of information to the graphics system. Taking advantage of the connectivity information between the triangles in a mesh dramatically diminishes the amount of information the graphics system must handle. Multiresolution Triangle Strips (MTS) represent a triangle mesh as a collection of multiresolution triangles strips. These strips are the basis of both the storage and the rendering stage. The coherence between the extraction of two levels of detail is used in the model in order to decrease the visualisation time.
Mathematics and Visualization, 2003
A triangulated surface S with V vertices is sometimes stored as a list of T independent triangles, each described by the 3 floating-point coordinates of its vertices. This representation requires about 576V bits and provides no explicit information regarding the adjacency between neighboring triangles or vertices. A variety of boundary-graph data structures may be derived from such a representation in order to make explicit the various adjacency and incidence relations between triangles, edges, and vertices. These relations are stored to accelerate algorithms that visit the surface in a systematic manner and access the neighbors of each vertex or triangle. Instead of these complex data structures, we advocate a simple Corner Table, which explicitly represents the triangle/vertex incidence and the triangle/triangle adjacency of any manifold or pseudo-manifold triangle mesh, as two tables of integers. The Corner Table requires about 12Vlog 2 V bits and must be accompanied by a vertex table, which requires 96V bits, if Floats are used. The Corner Table may be derived from the list of independent triangles. For meshes homeomorphic to a sphere, it may be compressed to less that 4V bits by storing the "clers" sequence of triangle-labels from the set {C,L,E,R,S}. Further compression to 3.6V bits may be guaranteed by using context-based codes for the clers symbols. Entropy codes reduce the storage for large meshes to less than 2V bits. Meshes with more complex topologies may require O(log 2 V) additional bits per handle or hole. We present here a publicly available, simple, state-machine implementation of the Edgebreaker compression, which traverses the corner table, computes the CLERS symbols, and constructs an ordered list of vertex references. Vertices are encoded, in the order in which they appear on the list, as corrective displacements between their predicted and actual locations. Quantizing vertex coordinates to 12 bits and predicting each vertex as a linear combinations of its previously encoded neighbors leads to short displacements, for which entropy codes drop the total vertex location storage for heavily sampled typical meshes below 16V bits. Introdction 3D graphics plays an increasingly important role in applications where 3D models are accessed through the Internet. Due to improved design and model acquisition tools, to the wider acceptance of this technology, and to the need for higher accuracy, the number and complexity of these models are growing more rapidly than phone and network bandwidth. Consequently, it is imperative to continue increasing the terseness of 3D data transmission formats and the performance and reliability of the associated compression and decompression algorithms. Although many representations have been proposed for 3D models, polygon and triangle meshes are the de facto standard for exchanging and viewing 3D models. A triangle mesh may be represented by its vertex data and by its connectivity. Vertex data comprises coordinates of all the vertices and optionally the vertex colors and the coordinates of the associated normal vectors and textures. In its simplest form, connectivity captures the incidence relation between the triangles of the mesh and their bounding vertices. It may be represented by a triangle-vertex incidence table, which associates with each triangle the references to its three bounding vertices. In practice, the number of triangles is roughly twice the number of vertices. Consequently, when pointers or integer indices are used as vertex-references and when floating point coordinates are used to encode vertex locations, uncompressed connectivity data consumes twice more storage than vertex coordinates. Vertex coordinates may be compressed through various forms of vector quantization. Most vertex compression approaches exploit the coherence in vertex locations by using local or global predictors to encode corrections instead of absolute vertex data. Both the encoder and the decoder use the same prediction formula. The encoder transmits the difference between the predicted and the correct vertex data. It uses variable length codes for the corrections. The better the prediction-the shorter the codes. The decoder receives the correction, decodes it and adds it to the predicted to obtain the correct information for the next vertex. Thus the prediction can only exploit data that has been previously received and decoded. Most predictive schemes require only local connectivity between the next vertex and its previously decoded neighbors.
Proceedings Computer Graphics International, 2004.
We often need to refer to adjacent elements (e.g., vertices, edges and faces) in triangle meshes for rendering, mesh simplification and other processes. It is, however, sometimes impossible to prepare the enormous memory needed to represent element connectivity in gigantic triangle meshes. We proposed a memory efficient scheme for referring to adjacent faces around a vertex in non-manifold triangle meshes [AM04]. But the scheme has a redundancy in case of two-manifold triangle meshes. This paper proposes new schemes for referring to adjacent faces around a face in two-manifold triangle meshes. First, as our previous scheme, we introduce the constraints to allow random access to a triangle in a sequence of triangle strips. Then, for each face, we construct a list of references to adjacent strips as a representation of triangle connectivity. Experimental results show that, compared with conventional indexed triangle set based methods, our schemes reduce total strage for a triangle mesh and adjacent triangle connectivity by less than 50%.
2008
Recent advances in acquisition and modelling techniques led to generating an exponentially increasing amount of 3D shapes available both over the Internet or in specific databases. While the number grows it becomes more and more difficult to keep an organized knowledge over the content of this repositories. It is commonly intended that in the near future 3D shapes and models will be indexed and searched using procedure and instruments mimicking the same operations performed on images while using algorithms, data structures and instruments peculiar to the domain. In this context it is thus important to have tools for automatic characterization of 3D shapes, and skeletons and partitions are the two most prominent ones among them. In this paper we will describe an experience of building some of this tools on the top of a popular and robust library for manipulating meshes (OpenMesh). The preliminary results we present are promising enough to let us expect that the sum of the tools will be a useful aid to improving indexing and retrieval of digital 3D objects. The work presented here is part of a larger project: Three-Dimensional Shape Indexing and Retrieval Techniques (3-SHIRT), in collaboration with the Universities of Genoa, Padua, Udine, and Verona.
Indian Conference on Computer Vision, Graphics & Image Processing, 2002
In this paper we present a new algorithm for compressing large 3D triangle meshes through the successive conquest of triangle fans. In this algorithm, a triangle fan is the se- quence of adjacent triangles incident on a start vertex of a boundary edge called as the "gate." As each fan is con- quered, the current mesh boundary is advanced by
International Journal for …, 2003
In this paper, we present a new point of view for e ciently managing general mesh representations. After reviewing some mesh representation basics, we introduce the new Algorithm Oriented Mesh Database (AOMD). Some hypotheses are taken in order to be able to manage any set of adjacencies. Then, we present the design of the AOMD in terms of classes and algorithms. The Standard Template Library (STL) is used for managing the AOMD. Finally, we present some results and discuss technical choices that were made in the AOMD design and implementation. AOMD is available as open source at http : ==www:scorec:rpi:edu=AOMD.
Future Generation Computer Systems, 2004
Triangle meshes are the most popular standard model used to represent polygonal surfaces. Drawing these meshes as a set of independent triangles involves sending a vast amount of information to the graphics system. Taking advantage of the connectivity information between the triangles in a mesh dramatically diminishes the amount of information the graphics system must handle. Multiresolution Triangle Strips (MTS) represent a triangle mesh as a collection of multiresolution triangles strips. These strips are the basis of both the storage and the rendering stage. The coherence between the extraction of two levels of detail is used in the model in order to decrease the visualisation time.
2000
This work introduces a scalable topological data structure for manifold triangular meshes called Compact Half-Edge (CHE). It provides a high degree of scalability, since it is able to optimize the memory consumption / execution time ratio for different applications and data by using features of its different levels. An object-oriented API using class inheritance and virtual instantiation enables a unique
Current mesh compression schemes encode triangles and vertices in an order derived from systematically traversing the connectivity graph. These schemes struggle with gigabyte-sized mesh input where the construction and the usage of the data structures that support topological traversal queries become I/O-inefficient and require large amounts of temporary disk space. Furthermore they expect the entire mesh as input. Since meshes cannot be compressed until their generation is complete, they have to be stored at least once in uncompressed form. We radically depart from the traditional approach to mesh compression and propose a scheme that incrementally encodes a mesh in the order it is given to the compressor using only minimal memory resources. This makes the compression process essentially transparent to the user and practically independent of the mesh size. This is especially beneficial for compressing large meshes, where previous approaches spend significant memory, disk, and I/O resources on pre-processing, whereas our scheme starts compressing after receiving the first few triangles.
IEEE Transactions on Visualization and Computer Graphics, 1998
We present a method to produce a hierarchy of triangle meshes that can be used to blend different levels of detail in a smooth fashion. The algorithm produces a sequence of meshes 0 0 , 0 1 , 0 2 , ..., 0 n , where each mesh 0 i can be transformed to mesh 0 i+1 through a set of triangle-collapse operations. For each triangle, a function is generated that approximates the underlying surface in the area of the triangle, and this function serves as a basis for assigning a weight to the triangle in the ordering operation and for supplying the points to which the triangles are collapsed. The algorithm produces a limited number of intermediate meshes by selecting, at each step, a number of triangles that can be collapsed simultaneously. This technique allows us to view a triangulated surface model at varying levels of detail while insuring that the simplified mesh approximates the original surface well.
2010
ABSTRACT The Corner Table (CT) represents a triangle mesh by storing 6 integer references per triangle (3 vertex references in the Vertex table and 3 references to opposite corners in the Opposite table, which accelerate access to adjacent triangles). The Compact Half Face (CHF) representation extends CT to tetrahedral meshes, storing 8 references per tetrahedron (4 in the Vertex table and 4 in the Opposite table).
The FanGrower algorithm proposed here segments a manifold triangle mesh into regions (called caps), which may each be closely approximated by a triangle-fan. Once the caps are formed, their rims, which form the inter-cap boundaries, are simplified, replacing each fan by its frame-a fan with the same apex but fewer triangles. The resulting collection of frames is an approximation of the original mesh with a guaranteed maximum error bound. As such, it may be viewed as a powerful extension of Kalvin and Taylor's super-faces, which were restricted to nearly planar configurations and approximated by nearly planar fans. In contrast, our caps simplify to frames that need not be planar, but may contain convex or concave corners or saddle points. We propose a new and efficient solution for evaluating a tight bound on the deviation between a cap and its approximating fan and frame. We also introduce a new solution for computing the location of the apex of a fan as the point minimizing Garland and Heckbert's quadric error for a set of planes defined by the vertices of the cap and their normals. We discuss several capgrowing approaches. Finally, we propose a compact representation of a triangle mesh from which one can easily extract the frames and execute selective refinements needed to reconstruct the original caps in portions of the mesh that are closer to the viewer, to a silhouette, or in an area of interest. Some frames are automatically upgraded to partly simplified fans to ensure a watertight transition between frames and application-selected caps.
1998
The Multi-Triangulation (MT) is a general framework for managing the Level-of-Detail in large triangle meshes, which we have introduced in our previous work. In this paper, we describe an efficient implementation of an MT based on vertex decimation. We present general techniques for querying an MT, which are independent of a specific application, and which can be applied for solving problems, such as selective refinement, windowing, point location, and other spatial interference queries. We describe alternative data structures for encoding an MT, which achieve different trade-offs between space and performance. Experimental results are discussed.
1999
Abstract 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.
2011
The use of 3D shapes in different domains such as in engineering, entertainment, cultural heritage or medicine, is essential for representing 3D physical reality. Regardless of whether the 3D shapes are representing physically or digitally born objects, meshes are a versatile and common representation for the 3D reality. Nonetheless, the mesh generation process does not always produce qualitative results, thus incomplete, non-orientable or non-manifold meshes frequently are the input for the domain application. The domain application itself also demands special requirements, e.g. an engineering simulation requires a volumetric mesh either tetrahedral or hexahedral, while a cultural heritage color enhancement uses a triangular or quadrangular mesh, or in both cases even hybrid meshes. Moreover, the processes applied on the meshes (e.g. modeling, simulation, visualization) need to support some operations, such as querying neighboring information or enabling dynamic changes of geometry and topology. These operations need to be robust, hence the neighboring information can be consistently updated, during the dynamic changes. Dealing with this mesh diversity usually requires dedicated data structures for performing in the given domain application. This paper compiles the considerations toward designing a data structure for dynamic meshes in a generic and robust manner, despite the type and the quality of the input mesh. These aspects enable a flexible representation of 3D shapes toward general purpose geometry processing for dynamic meshes in 2D and 3D.
2012
Abstract: We consider the problem of designing space efficient solutions for representing the connectivity information of manifold triangle meshes. Most mesh data structures are quite redundant, storing a large amount of information in order to efficiently support mesh traversal operators. Several compact data structures have been proposed to reduce storage cost while supporting constant-time mesh traversal.
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