Renato B. Pajarola. Large Scale Terrain Visualization Using The Restricted Quadtree Triangulation. In D. Ebert, H. Rushmeier, and H. Hagen, editors, Proceedings of Visualization '98, pages 19--26. IEEE Computer Society Press, October 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....triangles. Related work has also been done by Evans et al. 5] who use a hierarchy of right triangles based on a regular decompostion to decompose the domain of a two dimensional scalar fields. Hierarchies of right triangles have been extensively used for multiresolution terrain modeling [4, 12, 15]. Coordinates are not explicitly stored since they can be calculated from the label (or location code) of the triangle. Since a pointer based binary tree structure would be inefficient in its use of space, Evans et al. use an array where the label of a node determines the node location in the ....

R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. In D. Ebert, H. Hagen, and H. Rushmeier, editors, Proceedings IEEE Visualization'98, pages 19--26, Research Triangle Park, NC, Oct. 1998.

....which can be constructed as described below. In hierarchies of right triangles, clusters are formed by pairs of modi cations. The corresponding conforming multiresolution mesh can be represented as a DAG in which each node (with the exception of boundary nodes) has two parents and four children [25,62] (see Figure 15) In higher dimensions, the clusters are also formed by a restricted number of cells, and, thus, each node has a bounded number of parents and children [53] The resulting model is able to generate conforming meshes with cells of di erent sizes. Figure 15 (c) shows an example of a ....

....of right triangles are not conforming. In order to guarantee that only conforming meshes are extracted, two approaches are possible: 1. an approach based on error saturation; 2. an approach which implements the conforming multiresolution mesh associated with the hierarchy. In the rst approach [56,61,62], a preprocessing step is performed. First, all triangles belonging to the same cluster are assigned the same error value, which is the maximum over their original error values. Moreover, the approximation error associated with each triangle is saturated to be greater than or equal to the error ....

R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. IEEE Visualization'98, Research Triangle Park, NC, IEEE Computer Society, 1998, 19-26.

....can be divided or grouped two by two by split and merge operations. In this work, the goal was to always draw the same amount of triangles at each redrawing, taking advantage of the last draw s triangulation. Other important works using regular mashes are those by Topo Vista [5] and by Pajarola [11]. They use a restricted and triangulated Quadtree structure. The structure proposed in the present article combines both mesh concepts, attempting to avoid problems related to each one while maintaining their qualities. 3 The QLOD structure QLOD is a variable resolution structure which supports ....

Renato B. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. IEEE Visualization '98, pages 19--26, October 1998.

....of these algorithms, while taking care to give enough detail to make end to end implementations of our algorithms reasonably straightforward. We will first describe an algorithm for efficient viewdependent refinement. Using the common vertex hierarchy induced by recursive edge triangle bisection [2 4], we show that it is possible to (1) construct an adaptive mesh from scratch each frame, 2) perform fast, hierarchical view frustum culling, 3) The authors are with the Lawrence Livermore National Laboratory, 7000 East Avenue, L 560, Livermore, CA 94551. E mail: pl, pascucci llnl.gov. ....

....implementing the dual queue algorithm, not to mention the many other components of their method, has proven difficult. Several other algorithms based on edge bisection have since been published, with different strengths and weaknesses in terms of visual accuracy and memory and time complexity [4, 5, 9 11]. These authors recognize the inherent complexity of doing input sensitive bottom up simplification, and use simple heuristics for output sensitive top down refinement. Gerstner [11] and Pajarola [4] both discuss how to remove some of the dependencies in the vertex hierarchy by implicitly coding ....

[Article contains additional citation context not shown here]

Renato B. Pajarola, "Large scale terrain visualization using the restricted quadtree triangulation," in IEEE Visualization '98, David Ebert, Hans Hagen, and Holly Rushmeier, Eds., Research Triangle Park, North Carolina, Oct. 1998, pp. 19--26, IEEE.

....affecting numerical stability and producing visual artifacts, Ber90] Mesh conformity refers to the requirement that the intersection of non disjoint triangles is either a common vertex or a common side. A vertex in the interior of an edge is non conforming and it is sometimes called a crack . [Paj98] presents a model that avoids cracks with a restricted selection of points according to a dependency graph defined between vertices. Our scheme to avoid cracks is similar to that but we use a longest edge based inclusions of points that yields the same result. A different approach is used in ....

....review of quadtree based data structures can be found in [Ba100] where it is also proposed a new quadtree data structure called semilinear quadtree with efficient navigation and compact storage. Contributions by Evans et al. Eva01] De Floriani et al. DeF84] Lindstrom et al. Lin96] Pajarola [Paj98] and [Aba00] also gives tree based data structures for coarsening algorithms. Note that a quadtree data structure on a (2 l)x (2 1) mesh can be implemented using index operations instead of using pointers and nodes, which is often called an implicit quadtree defined on a mesh. That is the ....

Pajarola, R. Large scale Terrain Visualization using the Restricted Quadtree Triangulation, in conf. proc. IEEE Visualization '98, pp. 19-26 & 515, 1998.

....connectivity can be obtained for example from subdivision surfaces. In terrain rendering applications, simple triangulation techniques are known to yield meshes with subdivision connectivity. For example, the so called quadtree triangulation is used to visualize matrices of elevation data [16]. The set of vertices in Figure 1c is connected using the procedure shown in Figure 5. Examples of tridimensional models having subdivision connectivity are shown in Figures 2a b. In order to obtain models with arbitrary shapes, a coarse base mesh composed of triangles or quads is used to fix the ....

....or 2b) which are formed of triangulated quadrilaterals. Subdivision surfaces based on Catmull Clark s or Loop s rule yield C surfaces, whereas Velho and Zorin have recently presented 4 8 subdivision rules leading to C surfaces [18] The quadtree triangulation as used in terrain applications [7,14,16] is also an instance of a 4 8 connected mesh (e.g. in Figure 6) However in this case the triangulation interpolates a given elevation matrix. Meshes with subdivision connectivity are inherently hierarchical constructions. Hence, it is natural to represent their structure using a tree. In ....

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R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. Proceedings of IEEE Visualization, pages 299--305, 1998. 31

....are preferred because of their superior performance and flexibility for processing [13] transmission [17] and compression [15] A particular class of semi regular triangulations are 4 8 meshes. In the strict regular setting, these meshes have been extensively used to visualize terrain data [3, 11, 19, 21]. In this context, 4 8 meshes are also called quadtree triangulations because quadtrees are often used to store them [18, 21, 22] Terrain models are given as amplitude matrices (i.e. the parametrization is implicit) and 4 8 meshes are used to connect the vertices (Figures la d) Recently, ....

....A particular class of semi regular triangulations are 4 8 meshes. In the strict regular setting, these meshes have been extensively used to visualize terrain data [3, 11, 19, 21] In this context, 4 8 meshes are also called quadtree triangulations because quadtrees are often used to store them [18, 21, 22]. Terrain models are given as amplitude matrices (i.e. the parametrization is implicit) and 4 8 meshes are used to connect the vertices (Figures la d) Recently, researchers have also used semi regular 4 8 meshes to compute approximations of subdivision surfaces [24] Subdivision surfaces are an ....

[Article contains additional citation context not shown here]

R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. Proceedings of IEEE Visualization, pages 299 305, 1998.

.... instead of the simple biased 1 dimensional system [11] Although not explicitly stated, he implied this method offered significant increase in the frame rates and a reduction in the tesselation times [11] 5 Another group from Switzerland used quadtrees to implement some of ROAM s functionality [13]. They also implemented the ability to generate triangle strips at runtime. This makes rendering easier on hardware by reducing the number of vertices to send to the video hardware. They were able to implement some of Hoppe s progressive meshes ideas and some of ROAM s patch stitching ideas. ROAM ....

R. B. Pajarola. Large Scale Terrain Visualization Using the Restricted Quadtree Triangulation. IEEE Visualization 98. pages 19-26, October 1998.

....with irregular boundaries. It can be shown, a constrained triangulation in parameter space of the critical vertices of a complete node front describes a decimated non cracked view of the surface [8] Terrain visualization has used the quadtree to achieve interactive rendering performance [6] [13]. However, these techniques have not been applied to visualizing a non manifold geometric model. We use the quadtree to build and visualize a non manifold geometric model. 4. ADAPTIVE VISUALIZATION FOR INTERACTIVE GEOMETRIC MODELING As mentioned earlier, SIGMA is designed for interactive ....

R. Pajarola, Large Scale Terrain Visualization using the Restricted Quadtree Triangulation, Proc. Visualization '98, pages 19-26.

....few. Their irregular counterparts have also been extensively studied [11] but regular meshes are preferred because of their superior performance and flexibility for processing [9] transmission [12] and compression [10] For example, 4 8 meshes have been extensively used to visualize terrain data [2,7,15,17]. In this context, these meshes are also called quadtree triangulations because quadtrees are often used to store them [14,17,18] Terrain models are given as amplitude matrices (i.e. the parametrization is implicit) and 4 8 meshes are used to connect the vertices (Figures 2a e) Recently, ....

.... performance and flexibility for processing [9] transmission [12] and compression [10] For example, 4 8 meshes have been extensively used to visualize terrain data [2,7,15,17] In this context, these meshes are also called quadtree triangulations because quadtrees are often used to store them [14,17,18]. Terrain models are given as amplitude matrices (i.e. the parametrization is implicit) and 4 8 meshes are used to connect the vertices (Figures 2a e) Recently, researchers have also used 4 8 meshes to compute approximations of subdivision surfaces [19] Subdivision surfaces are an increasingly ....

[Article contains additional citation context not shown here]

R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. Proceedings of IEEE Visualization, pages 299--305, 1998.

....we are not tied to using memory mapping, but propose this as a simple, yet effective method for handling large terrains. To accommodate fast display rates, it is essential to perform onthe fly simplification of the high resolution mesh. Similar to recent algorithms for view dependent refinement [8, 17,19], we use recursive edge bisection as a means of refining a coarse base mesh defined over a regular grid of elevation points. Our method performs a top down traversal of the mesh. A problem common to most algorithms based on top down refinement is how to ensure that a consistent mesh without cracks ....

....implementing the dual queue algorithm, not to mention the many other components of their method, has proven difficult. Several other algorithms based on edge bisection have since been published, with different strengths and weaknesses in terms of visual accuracy and memory and time complexity [3,10,19,23]. Most of these authors recognize the inherent complexity of doing input sensitive bottom up simplification, and use simple heuristics for output sensitive top down refinement. In this paper, we present improvements over some of these methods in several categories, including accuracy, mesh ....

[Article contains additional citation context not shown here]

R. B. Pajarola. Large Scale Terrain Visualization Using the Restricted Quadtree Triangulation. IEEE Visualization '98, 19--26. Oct. 1998.

....when triangulations between grid points of the DEM are generated. With larger DEMs, the sheer number of polygons can overwhelm many terrain rendering systems. Consequently, the DEM data is often broken into tiles, and some form of level of detail (LOD) hierarchy is employed (e.g. a quad tree [2, 3] or progressive mesh [1] Although the use of tiling and LOD techniques certainly help make the data more manageable, the sheer size of the terrain datasets can still tax the memory subsystems of even the most well endowed machines. Often one resorts to caching of tiles to make more efficient use ....

R. Pajarola, "Large Scale Terrain Visualization Using The Restricted Quadtree Triangulation," in Proceedings of the IEEE Visualization Conference, October 1998, pp. 19--26.

....This modular approach allows the management of data sets whose size exceeds the physical memory of a system. In the literature, other methods have been proposed for managing a multiresolution terrain model consisting of parts that are stored on disk separately and can be combined on line [4, 6]. Hoppe [4] proposes a method to fit a Progressive Mesh (PM) in a quadtree. A progressive mesh is a multiresolution model built from a high resolution triangulation through iterative edge collapses. Edge collapse is a simplification operator that shrinks an edge to a vertex, deforming the ....

....edge collapses in each quadtree node independently; then, every four adjacent nodes are merged and the process is iterated. In order to avoid collapses occurring across different quadtree nodes, the simplification process inside each node is forced to preserve the boundary vertices. Pajarola [6] imposes a grid over the domain and builds a hierarchy of right triangles inside each rectangle of the grid. The advantages of our method over the exiting ones are discussed in Section 5. 2. The Multi Triangulation A triangle based terrain model is specified by a plane triangulation covering the ....

[Article contains additional citation context not shown here]

R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. In Proceedings IEEE Visualization '98, pages 19--24, Research Triangle Park, NC, 1998. IEEE Comp. Soc. Press.

.... the tree satisfying the coplanarity requirement (Figure 5) Although this problem has been studied previously, either only particular cases such as deleting only leaf nodes have been solved [5] or computationally suboptimal algorithms based on a quadtree structure using pointers have been given [10]. We attribute this to a lack of adapted and efficient navigation method for the quadtree data structure. We sb. a. Figure 5: a) Quadtree corresponding to Figure 4a. b) Restricted quadtree (corresponding to Figure 4b. tart with the basic properties of quadtrees. Then, we introduce an indexing ....

R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. Proceedings of IEEE Visualization, 1998.

....with irregular boundaries. It can be shown, a constrained triangulation in parameter space of the critical vertices of a complete node front describes a decimated non cracked view of the surface [1] Terrain visualization has used the quadtree to achieve interactive rendering performance [17] [18]. However, these techniques have not been applied to visualizing a non manifold geometric model. We use the quadtree to build and visualize a non manifold geometric model. 4 Adaptive Visualization for Interactive Geometric Modeling As mentioned earlier, SIGMA is designed for interactive ....

R. Pajarola. Large Scale Terrain Visualization using the Restricted Quadtree Triangulation. In Proceedings of Visualization'98, pages 19-26.

....are various ways to represent geographical information. One of the most frequently used representations are quadtrees. Recent treatments of this data Data management and data warehousing in manufacturing systems 3 structure in the context of geographical information systems are available in [9,16]. The quad tree is an efficient method for indexing a two dimensional space. Algorithms for range searching for geometrical problems are discussed in [20] Information on the space efficiency and a discussion of approximation and compression methods for quadtrees can be found in [7,18] 3. ....

Renato Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. In roceedings of the conference on Visualization 1998, pages 19--26, 1998.

....application since often only a small subset of the whole data set can be processed and displayed interactively. Also, these models allow the definition of areas of greater interest, using e.g. magnifying glasses [10] or level of detail depending on the viewer s position and viewing direction [2, 15, 19]. 3 Hierarchical Triangulation In the following, we will consider DEMs based on a particular kind of adaptive hierarchical triangulations. In light of the previous section, they belong to the class of DEMs with implicit coordinates and explicit interpolation. As we will see, these DEMs allow ....

....v 3 T e ref ref v v 1 2 v v 3 T T 1 2 Figure 2: Triangle T is bisected into two subtriangles T 1 and T 2 . 17, 23] Basically the same method has been successfully applied also for the representation of terrain data [2, 4, 5, 6, 15, 20, 22] It is closely related to restricted quadtrees [19, 25]. But triangulations generated by recursive bisection are more flexible than those generated by a triangulation of the leaves of a quadtree. The main idea is to start with a coarse triangulation T 0 and to recursively construct finer triangulations T l 1 by splitting each triangle T # T ....

Pajarola, R.: Large scale Terrain Visualization using the Restricted Quadtree Triangulation, in Proc. IEEE Visualization '98, pp. 19--24, IEEE Computer Society Press, 1998.

....from a regular grid, most of them are optimized depending on the particular application. The quadtree representation is very compelling, since it is fairly simple, but powerful enough to represent large models. In this survey we will discuss one representation constructed by R. Pajarola in [66]. This particular paper has been chosen, because it describes a specific implementation of the Restricted Quadtree Triangulation (RQT) that can handle very large datasets. This section is organized as follow: in the first subsection the notion of a quadtree and of a restricted quadtree will be ....

....Report #335, Institute of Scientific Computing, February 28, 2000 129 9.2.1 Restricted Quadtree Triangulation (RQT) As already mentioned, there are multiple ways to construct a quadtree, for example using the wavelet theory and the Haar or Lazy wavelet basis functions. The hierarchy used in [66] is different: a few levels of the quadtree representation are shown in Figure 9.1. Figure 9.1 Quadtree hierarchy a) Full resolution grid b) Level 0 of the quadtree (root node) c) Level 1 of the quadtree d) Level 2 of the quadtree (leaf nodes) From now on, the term described the set of vertices ....

R. Pajarola. "Large scale terrain visualization using the restricted quadtree triangulation." In Proc. Visualization 1998. IEEE, 1998.

....according to the run time view and animation parameters implies that the method must be able to operate in real time. Various adaptive multi resolution methods have been proposed and the typical ones are discussed here. A few methods have been developed for managing large terrain models [7, 15, 18]. Basically, these methods regularly subdivide a large terrain surface. A hierarchical data structure, usually in the form of a quadtree, is constructed with the leaf nodes representing individual polygons, i.e. the highest resolution, and the root node representing the whole terrain surface, ....

R. Pajarola. Large Scale Terrain Visualization using the Restricted Quadtree Triangulation. In Proceedings of IEEE Visualization '98, October 1998.

.... years to convey the illusion of three dimensionality [Batson75] More recent, terrain rendering has become an important component of flight simulators, games and topographic applications, with realtime visualization of large scale surfaces attracting the attention of several researchers [Hoppe98] [Pajarola98]. Although terrain data is usually presented as irregular grids matching the high scale details of surfaces, relief texture representation for such data sets can be easily constructed. Figure 5 27 shows a view of Northern Vancouver, British Columbia, rendered using relief texture mapping. Such a ....

Pajarola, R. "Large Scale Terrain Visualization Using The Restricted Quadtree Triangulation". IEEE Visualization '98, Research Triangle Park, NC. October 18-23, 1998. pp. 19-26.

....structures have been developed for representing terrains, e.g. hierarchical TINs (de Floriani and Puppo [3] R trees for terrain data (Kofler et al. 9] restricted quadtree triangulations Figure 1: Terrain model consisting of a grid and additional microstructures provided as TINs. Pajarola [12]) and constrained Delaunay pyramids (Voigtmann et al. 16] Each data structure supports a specific type of input data such as arbitrarily distributed data points for triangulated irregular networks (TINs) or regularly distributed data points for grids. In general, real world data sets include ....

.... can be used by level of detail algorithms (de Berg and Dobrint [2] de Floriani and Puppo [3] Gross et al. 8] and Voigtmann et al. 16] Regular grids have been used for multiresolution modeling (Falby et al. 6] and for real time, continuous LOD rendering (Lindstrom et al. 10] and Pajarola [12]) These approaches suffer from the following limitations: ffl Most terrain modeling techniques are based on one single multiresolution geometric model (e.g. hierarchical TINs) and cannot integrate different types of terrain data into one hierarchical terrain model. However, for many ....

[Article contains additional citation context not shown here]

R. Pajarola. Large Scale Terrain Visualization Using The Restricted Quadtree Triangulation. Proceedings Visualization '98, 19-26, 1998.

....of the whole domain at low resolution can be obtained without the need to load every local MT. 10 Comparison with previous work Other methods have been proposed for managing a multiresolution terrain model consisting of parts that are stored on disk separately and can be combined on line [Hop98, Paj98]. In [Hop98] the high level organization is a quadtree; each quadtree block contains a Progressive Mesh (i.e. a special case of an MT built bottomup through edge collapse) whose coarsest mesh is the same as one quadrant of the full resolution mesh of its parent. The whole model is built ....

....bottom up by iteratively applying edge collapses to the full resolution mesh of each block. In order to avoid the creation of dependency links between collapses performed in different blocks, the coarsening process inside each block is forced to preserve the boundary vertices of the mesh. Pajarola [Paj98] imposes a grid over the domain and builds a hierarchy of right triangles (i.e. a special case of an MT where each node represents the subdivision of a right isosceles triangle into two equal right triangles) inside each rectangle of the grid. Dependency links occurring across adjacent ....

[Article contains additional citation context not shown here]

R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. In Proceedings IEEE Visualization'98, pages 19--24, Research Triangle Park, NC, 1998. IEEE Comp. Soc. Press.

....a depth mesh object. In the following we explain how a single depth mesh is initialized from a given depth image, and how an adaptively triangulated depth mesh is generated at rendering time. 3. 2 Multiresolution triangulation We use the restricted quadtree triangulation method presented in [Paj98] to generate a simplified triangulation of the z buffer, called a depth mesh. Figure 1 shows the basic refinement steps for this hierarchical triangulation method. Based on vertex dependency relations [LKR 96, Paj98] an adaptively refined and crack free triangle mesh can efficiently be extracted ....

....is performed recursively top down in the quadtree hierarchy with the bounding sphere information of each node used for view frustum culling. The vertex dependency rules explained in [LKR 96, Paj98] are used to guarantee a crack free triangulation. The triangle strip construction method proposed in [Paj98] is used and modified to incorporate segmentation of rubber sheet triangles as shown in Figure 6. While creating the triangle strip sequence for a selected set of vertices, the segmentation flags of each visited quadtree node are checked, and if necessary the strip is broken up into multiple ....

Renato Pajarola. Large scale terrain visualization using the restricted quadUnce uiangulation. In Proceedings IEEE Visualization 98, pages 19-26,515, 1998.

....advantages are handling of arbitrary point distributions and superior (smaller) triangle counts for given LOD thresholds. Adaptive quadtree based hierarchical multiresolution triangulations have been studied in the literature for adaptive triangulation of grid digital terrain elevation models [1, 7, 8, 10, 14, 16, 23]. In [18] we discuss advantages and differences between the various approaches of this class of quadtree [ 16, 23] or bintree [1, 7, 8, 14] triangulations. These methods take advantage of the regular grid structure to create an efficient multiresolution triangulation hierarchy. The main advantages ....

.... quadtree based hierarchical multiresolution triangulations have been studied in the literature for adaptive triangulation of grid digital terrain elevation models [1, 7, 8, 10, 14, 16, 23] In [18] we discuss advantages and differences between the various approaches of this class of quadtree [ 16, 23] or bintree [1, 7, 8, 14] triangulations. These methods take advantage of the regular grid structure to create an efficient multiresolution triangulation hierarchy. The main advantages are simple construction of the multiresolution hierarchy, fast LOD selection and efficient rendering. The main ....

[Article contains additional citation context not shown here]

Renato Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. In Proceedings IEEE Visualization 98, pages 19- 26,515, 1998.

....representation of the triangle bintree hierarchy. No detailed algorithms are given in [EKT97] on how to incorporate propagation of forced splits to generate a matching triangulation. 3. 6 Restricted quadtree triangulation The Restricted Quadtree Triangulation (RQT) approach presented in [Paj98a, Paj98b] is focused on large scale realtime terrain visualization. The triangulation method is based on a quadtree hierarchy as in [SS92] and uses the dependency relation presented in [LKR 96] to generate minimally matching quadtree triangulations. Both, top down and bottom up triangulation algorithms ....

....grid input data set by appropriate point indexing and recursive functions, and no hierarchical data structure actually needs to be stored. This reduces the storage cost effectively down to only the elevation and approximation error values per vertex for such an implicit quadtree. As shown in [Paj98b] for each point P i,j of the height field grid its level l in the implicit quadtree hierarchy can efficiently be determined by arithmetic and logical operations on the integer index values i and j, see also Figure 21. Furthermore, it is also observed that the dependency relation of Figure 13 can ....

[Article contains additional citation context not shown here]

R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. Technical Report 292, Dept. of Computer Science, ETH Zrich, 1998. ftp:// ftp.inf.ethz.ch/pub/publications/tech-reports/2xx/ 292.ps.

....and representation of the triangle bintree hierarchy. No detailed algorithms are given in [EKT97] on how to incorporate propagation of forced splits to generate a matching triangulation. 3. 6 Restricted quadtree triangulation The Restricted Quadtree Triangulation (RQT) approach presented in [Paj98a, Paj98b] is focused on large scale realtime terrain visualization. The triangulation method is based on a quadtree hierarchy as in [SS92] and uses the dependency relation presented in [LKR 96] to generate minimally matching quadtree triangulations. Both, top down and bottom up triangulation ....

....observed that the dependency relation of Figure 13 can be expressed by arithmetic expressions as functions of the point s index i,j. The implicit definition of quadtree levels and dependency relations between points by arithmetic functions allows the top down and bottom up algorithms presented in [Paj98a] to run very fast and directly on the height field grid data instead of relying on a hierarchical data structure (i.e. as in [SS92] FIGURE 21. Implicit quadtree hierarchy and point indexing defined on the height field grid. Similar to the RTIN approach in [EKT97] the RQT method in [Paj98a] ....

[Article contains additional citation context not shown here]

Renato Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. In Proceedings Visualization 98, pages 19--26 and 515. IEEE Computer Society Press, 1998.

No context found.

Renato Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. In Proceedings IEEE Visualization 98, pages 19--26,515, 1998.

....is, by definition, matching within the patch boundaries. Furthermore, continuous and smooth LOD transitions between all patches of the visible scene can be achieved with an additional reconciliation stage. For further technical details and complexity analysis refer to our technical report [17]. 6. Restricted quadtree The basic idea of the restricted quadtree was first used for parametric surfaces 24 and later for terrains. 15 We can directly apply the restricted quadtree method to the terrain data itself, and not to an intermediate parameter space. Additionally, in comparison to ....

....use the same restricted quadtree dependency graph. Many spatial access structures for points, together with the superimposed dependency graph will provide efficient point selection. However, the efficiency in access time and storage costs might differ quite a bit. See also our technical report [17] for a proposal of a very efficient storage and retrieval structure to maintain a height field and support extraction of restricted quadtrees. 7. Conclusion We have proposed an efficient visualization system for large scale terrain data. It turned out that we cannot simply glue together known ....

R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. Technical Report 292, Dept. of Computer Science, ETH Zurich, 1998. ftp://ftp.inf.ethz.ch/pub/publications/tech-reports/2xx/292.ps.

....6. Sections 8, 9 and 10 discuss dynamic data handling, continuous LOD rendering, and storage. Experiments are presented in Section 11, and Section 12 concludes the paper with a comparison to other multiresolution triangulation models. More detailed information on all sections can also be found in [11,10]. 2. Related work In [8,9] the restricted quadtree triangulation (RQT) was first applied to terrain visualization. Their contribution was an efficient screen space error metric calculation, and efficient scene culling and vertex selection according to this error metric. Furthermore, they ....

R. Pajarola. "Large scale terrain visualization using the restricted quadtree triangulation". Technical Report 292, Dept. of Computer Science, ETH Zürich, 1998. ftp://ftp.inf.ethz.ch/ pub/publications/tech-reports/2xx/292.ps.

.... refinement process is sometimes called Rivara refinement [9] If the initial polygonal region is a square, which is splitted in two rectangular, isosceles triangles, then the described refinement method leads to a restricted quadtree triangulation (RQT) structure which is thoroughly described in [7, 12]. The longest side bisection triangulation belongs to the larger class of bintree triangulations and is a generalization of the triangulation presented in [4] that is identical to the RQT) 3. Modified longest side bisection Let DeltaABC (see Fig. 1) be a given triangle with interior angles ff, ....

R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. In Proceedings Visualization 98, Los Alamitos, California, 1998. IEEE, Computer Society Press. Extended version available as technical report ftp://ftp.inf.ethz.ch/pub/publications/techreports /2xx/292.ps.

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Pajarola, R. (1998b), Large scale Terrain Visualization using the Restricted Quadtree Triangulation, in `Proceedings Visualization 98', IEEE, Computer Society Press, Los Alamitos, CA. Forthcoming.

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Renato B. Pajarola. Large Scale Terrain Visualization Using The Restricted Quadtree Triangulation. In D. Ebert, H. Rushmeier, and H. Hagen, editors, Proceedings of Visualization '98, pages 19--26. IEEE Computer Society Press, October 1998.

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Renato Pajarola. Large Scale Terrain Visualization Using The Restricted Quadtree. In Proceedings IEEE Visualization 1998.

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R. Pajarola, "Large scale terrain visualization using the restricted quadtree triangulation," in Proc. Visualization '98, vol. 515, Los Alamitos, CA, 1998, pp. 19--26.

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R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. In H. Rushmeier D. Elbert, H. Hagen, editor, Proceedings of Visualization `98, pages 19--26, 1998.

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PAJAROLA R.: Large scale terrain visualization using the restricted quadtree triangulation. In Proceedings IEEE Visualization '98 (1998), IEEE, pp. 19--26. 6

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R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. IEEE Visualization'98, Research Triangle Park, NC, IEEE Computer Society, 1998, 19--26.

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R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. In D. Ebert, H. Hagen, and H. Rushmeier, editors, Proceedings IEEE Visualization'98, IEEE Computer Society, pages 19--26, 1998.

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R. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. In H. Rushmeier D. Elbert, H. Hagen, editor, Proceedings of Visualization `98, pages 19--26, 1998. 2, 4

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Renato B. Pajarola. Large scale terrain visualization using the restricted quadtree triangulation. IEEE Visualization '98, pages 19--26, October 1998. ISBN 08186 -9176-X.

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