E. Puppo. Variable resolution triangulations. Computational Geometry, 11(3--4):219--238, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....by limiting the number of polygons at the time of generating the object. As regards the continuous level of detail, the multiresolution models that have appeared up to now can be classified in three main groups, according to their representation [Ribe02] Multi triangulation [Flor97] [Pupp98] is a structure that constitutes a general framework for continuous multiresolution schemes. In spite of these characteristics, the implementation presented in [Flor98] is based on a vertex decimation method. Incremental representations [Hopp96] Pupo97] Hopp98] were mainly developed for ....

E. Puppo, "Variable resolution triangulations" Computational Geometry, 11(3-4), pp. 219-238., 1998.

....surface modeling. A recent tutorial by Puppo and Scopigno [5] covers this more recent work as well as a wide range of surface simplification techniques. The most relevant work to our approach that has appeared in the surface approximation litera ture is the work by Lindstrom et al. 6] and Puppo [7, 8]. Both independently discovered hierarchies similar to the one discussed in this paper. We discuss and compare their approaches to ours in section 8. Another source of related work comes from the study of general lattice structures. Bell et al. 9] cite work on crystal lattice structures by ....

....Our hierarchical surface representation contains partitions, called RTIN partitions, of the two dimensional square into right angled, isosceles triangles. Such partitions have been studied in relation to crystal lattices [9] image encoding [12] and, in fact, geographic visualization systems [6, 7, 8]. The partitions contained in the hierarchy are defined inductively as follows. The partition composed of two triangles formed by dividing the square from northwest to southeast corner is the coarsest partition in the hierarchy (i.e. the one containing the largest triangles) From a partition in ....

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E. Puppo. Variable resolution triangulations. Technical Report 12/96, Institute for Applied Mathematics, National Research Council, Genova (Italy), November 1996. http: / /www.ima.ge.cnr.it /STAFF /P UP PO /PS /ima9612.ps.gz.

.... not symmetric in the same sense as f 3 ( it looks very much like f 3 ( compare Figures 3(c) and 3(d) 4 Hybrid frame rate control The majority of multiresolution models supporting selective refinement includes some criterion to guarantee an upper bound to the screen space geometric error [11, 20, 12, 1, 9, 14, 16]. However, for smooth animations in interactive applications, a constant frame rate is even more important than a constant approximation error bound. 4.1 Strategies In [9] the desired number m of active faces is slowly but directly adjusted due to frame time t. Therefore m can become ....

Enrico Puppo. Variable resolution triangulations. Computational Geometry, Vol.11, N.3--4:219--238, December 1998.

....mesh can be constructed either by refinement or simplification [9] 3 Variable Resolution Triangulations This section defines more precisely some basic notions concerning adaptive hierarchical structures. The idea of a variable resolution triangulation was introduced independently by Puppo [8] and De Berg et al. 2] Subsequently, Puppo developed an extensive theoretical framework for general variable resolution structures, which he called Multi Triangulations. This section summarizes these concepts. As mentioned above, hierarchical mesh structures are based on local modifications. In ....

....the same data structures. The implementation is very similar. We take advantage of the fact the each face has only one child in the context of this operation. Thus, we set f.children[1] NULL. The effectiveness of a variable resolution structure can be analyzed according to the following criteria [8]: Expressive Power; Depth; and Growth Rate. The variable resolution 4 # mesh structure has all the desirable properties, as will be shown below. A node of the DAG in the lattice representation of a 4 # mesh structure has some special characteristics because of the nature of the refinement ....

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E. Puppo. Variable resolution triangulations. Technical report, CNR, 1998.

....Bertocci Computer and Information Science Department, University of Genova Via Dodecaneso, 35, 16146 Genova (Italy) Tel. 39 10 3536704 Fax: 39 10 3536699 Email: fmagillo disi, bertocci educ.disig . unige.it 1 Introduction A Multi Triangulation (MT) is a multiresolution model proposed in [Pup96a, Pup96b] for the description of bivariate surfaces (such as terrains) The intuitive idea behind an MT is that of having a collection of local modifications progressively refining an initial triangulation of a plane domain, which are arranged according to a partial order. By selecting consistent subsets ....

....on a previous modification M 1 if and only if it removes some triangles introduced by M 1 . Dependency means that M 2 cannot be performed unless M 1 has been performed. Under suitable and reasonable constraints on the modifications of the sequence, the relation of dependency is a partial order [Pup96a, Pup96b]. The modifications of the given sequence can be applied to the initial triangulation in a different order, provided that such order is compatible with the relation of dependency. In any such permuted order, the final result is the same but the set of intermediate meshes is different (see Figure ....

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E. Puppo. Variable resolution triangulations. Technical Report 12/96, Institute for Applied Mathematics, C.N.R., Genova (Italy), November 1996.

....large body of very recent work that has appeared in SIGGRAPH96 [12, 3] and EuroGraphics96, both of which had sessions on multiresolution surface modeling. The most relevant work to our approach that has appeared in the surface approximation literature is the work by Lindstrom et al. 15] and Puppo [18, 17]. Both independently discovered hierarchies similar to the one discussed in this paper. Another source of related work comes from the study of general lattice structures. Bell et al. 1] cite work on crystal lattice structures by Subnikov in 1916 [21] and Laves [14] in 1931 that defined various ....

....partitions of the two dimensional square into rightangled, isosceles triangles. We refer to this partition as a Right Triangular Irregular Network (RTIN) Such partitions have been studied in relation to crystal lattices [1] image encoding [11] and, in fact, geographic visualization systems [15, 18, 17]. The partitions contained in the hierarchy are defined inductively as follows. The partition composed of two triangles formed by dividing the square from northwest to southeast corner is the coarsest partition in the hierarchy. From a partition in the hierarchy, a new, more detailed partition may ....

E. Puppo. Variable resolution triangulations. Technical report, Institute for Applied Mathematics, National Research Council, Genova (Italy), 1996.

.... above E 00 (i.e. T E 0 is contained in T E 00 ) then the size of PhiE 0 is smaller [larger] than the size of PhiE 00 : It is also easy to show that an MT can be reversed by substituting each internal fragment with its floor, and reversing all arrows in the lattice representation [19]. The resulting structure is also an MT, and it generates the same set of triangulations, being made of the same set of triangles. Furthermore, if an MT is increasing, its reverse will be decreasing, and vice versa. Therefore, it is sufficient to study the case of increasing MTs, while a ....

....solution can be found in time linear in its output size, hence optimal. A completely analogous algorithm and proof are valid for a monotonically decreasing MT. In this case, its reverse is visited. Since the data structure encodes also the reverse MT, it is not necessary to recompute it explicitly [19]. In this case, running the algorithm for the reverse MT is equivalent to visit T starting at the floor of its drain, and swapping FLOOR and fragment, as well as UPPER and LOWER, in the code. 5 Applications Applications of multi triangulations to terrain modeling is straightforward. For each ....

Puppo, E., 1996, Variable resolution triangulations, Technical Report n.12-96, Istituto per la Matematica Applicata - C.N.R., November 1996.

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E. Puppo. Variable resolution triangulations. Computational Geometry, 11(3--4):219--238, 1998.

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Puppo, E. Variable resolution triangulations. Computational Geometry, 11(3-4):219-238, 1998.

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Puppo, E. Variable resolution triangulations. Computational Geometry, 11(3-4):219-238, 1998.

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E. Puppo. Variable resolution triangulations. Computational Geometry, 11(3-4):219--238, 1998.

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