Selective refinement of progressive meshes using vertex hierarchies (original) (raw)
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Truly selective refinement of progressive meshes
This paper presents a novel selective refinement scheme of progressive meshes. In previous schemes, topology information in the neighborhood of a collapsed edge is stored in the analysis phase. A vertex split or edge collapse transformation is possible in the synthesis phase only if the configuration of neighborhood vertices in the current mesh corresponds to the stored topology information. In contrast, the proposed scheme makes it possible to apply a vertex split or an edge collapse to any selected vertex or edge in the current mesh without a precondition. Our main observation is that the concept of a dual piece can be used to clearly enumerate and visualize the set of all possible selectively refined meshes for a given mesh. Our refinement scheme is truly selective in the sense that each vertex split or edge collapse can be performed without incurring additional vertex split and/or edge collapse transformations.
Progressive Meshes with Controlled Topology Modifications
Due to the rapid evolution of 3D acquisition and modeling methods highly complex and detailed models became ubiquitous. In order to be able to cope with the complexity, concentrated efforts were dedicated to the development of new mesh decimation methods in the recent years. In works of Garland and Heckbert [Garland and Heckbert 1997] and Popović and Hoppe [Popović and Hoppe 1997], the traditional edge contraction operator was generalized to vertex contraction, which allowed for topology modification during the decimation. The vertex contraction facilitates the joining of originally disconnected regions of the mesh by contracting vertices lying in different connected components of the model. While this operation provides considerable topological flexibility during the mesh simplification, in some cases joining of disconnected regions might be desirable only along the boundaries of the model. As a combination of two already available techniques, we present a mesh decimation technique allowing for increased control over topology changes induced by the decimation process. Our method proceeds in essence by applying two types of operators: the well known edge contraction and the vertex-edge contraction introduced recently by Borodin et al [Borodin et al. n. d.]. This facilitates efficient mesh simplification and gradual closing of gaps along the boundaries of the model. The process is controlled by a geometric error and since inverse operations may be implemented for both of the operators, it is conducted in a progressive manner.
Transitive mesh space of a progressive mesh
IEEE Transactions on Visualization and Computer Graphics, 2003
This paper investigates the set of all selectively refined meshes that can be obtained from a progressive mesh. We call the set the transitive mesh space of a progressive mesh and present a theoretical analysis of the space. We define selective edge collapse and vertex split transformations, which we use to traverse all selectively refined meshes in the transitive mesh space. We propose a complete selective refinement scheme for a progressive mesh based on the transformations and compare the scheme with previous selective refinement schemes in both theoretical and experimental ways. In our comparison, we show that the complete scheme always generates selectively refined meshes with smaller numbers of vertices and faces than previous schemes for a given refinement criterion. The concept of dual pieces of the vertices in the vertex hierarchy plays a central role in the analysis of the transitive mesh space and the design of selective edge collapse and vertex split transformations.
Selectively refinable subdivision meshes
2006
We introduce RGB triangulations, an extension of red-green triangulations that can support selective refinement over subdivision meshes generated through quadrisection of triangles. Our purpose is to define a mechanism based on local operators that act on subdivision meshes while supporting operations similar to those available in Continuous Level Of Detail models. Our mechanism permits to take an adaptive mesh at intermediate level of subdivision and process it through both refinement and coarsening operations, by remaining consistent with an underlying Loop subdivision scheme. Our method does not require any hierarchical data structure, being based just on color codes and level numbers assigned to elements of a mesh, which can be encoded in a standard topological data structure with a small overhead.
A Theoretical Framework For Generalized Hierarchical Approaches Referred To Local Mesh Refinement
This paper proposes a theoretical framework in which generalized hierarchical approaches for the adaptive finite element mesh refinement can be easily designed. Such a generalized approach aims at coupling the classical h version hierarchical adaptive finite element method and the adaptive remeshing strategy. On one hand, the hierarchical aspect should provide such an approach with its iterative multi-mesh solvers and a multi-layer representation of numerical results, which constitutes an appropriate formalism to introduce multi-scale or multi-model analyses. On the other hand the remeshing technique should provide a great flexibility in the generation of new meshes, which becomes necessary when, for example, anisotropic mesh adaptation should be somewhere envisaged.
CPH: A Compact Representation for Hierarchical Meshes Generated by Primal Refinement
Computer Graphics Forum, 2015
We present CPH (Compact Primal Hierarchy): a compact representation of the hierarchical connectivity of surface and volume manifold meshes generated through primal subdivision refinements. CPH is consistently defined in several dimensions and supports multiple kinds of tessellations and refinements, whether regular or adaptive. The basic idea is to store only the finest mesh, encoded in a classical monoresolution structure that is enriched with a minimal set of labels. These labels allow traversal of any intermediate level of the mesh concurrently without having to extract it in an additional structure. Our structure allows attributes to be stored on the cells not only on the finest level, but also on any intermediate level. We study the trade-off between the memory cost of this compact representation and the time complexity of mesh traversals at any resolution level.
Highly detailed geometric models are rapidly becoming commonplace in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new scheme for storing and transmitting arbitrary triangle meshes. This efficient, loss-less, continuous-resolution representation addresses several practical problems in graphics: smooth geomorphing of level-of-detail approximations, progressive transmission, mesh compression, and selective refinement. In addition, we present a new mesh simplification procedure for constructing a PM representation from an arbitrary mesh. The goal of this optimization procedure is to preserve not just the geometry of the original mesh, but more importantly its overall appearance as defined by its discrete and scalar appearance attributes such as material identifiers, color values, normals, and texture coordinates. We demonstrate construction of the PM representation and its applications using several practical models.