L. Kettner. Using generic programming for designing a data structure for polyhedral surfaces. Computational Geometry { Theory and Applications, 13:65-90, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to the feature skeleton for sampling along its backbones. 3. 4 Diffusion over feature edges As for the triangles of surface parts, we design an error diffusion algorithm that distributes some samples along every backbone, the processing path being deduced from the ordering over its halfedges [32]. The diffusion process starts by picking the first edge of a feature backbone and do the following for every current edge : 1. read the total amount of density on the edge; number of samples to distribute on the current edge. This number is rounded to the nearest integer value, such a rounding ....

KETTNER, L. Using generic programming for designing a data structure for polyhedral surfaces. Comput. Geom. Theory Appl. 13 (1999), pp.65--90.

....per step, because an edge does not encode its orientation explicitly. The half edge data structure solves this problem by splitting each edge into two halves, where each half edge points to its opposite half edge, an incident vertex and an incident polygon. For a detailed description see [7]. The Computational Geometry Algorithm Library, CGAL , is closely related to our mesh data structure. It is based on half edges and consists of three main parts. The first part manages and organizes the geometric primitives (vertices, edges and faces) the second part handles the topological ....

.... kernel (e.g. a VertexHandle may be a Vertex or an int) the kernel itself depends on the mesh items (in order to construct the handle types) and the items require the handles (a vertex must store a halfedge handle) we have to use template forward declarations to get safe handle types (see [7]) Using this technique, the item types know each other and their respective handle types, thereby avoiding to use and cast void pointers. This also enables us to use the handles types in the traits classes, e.g. if the face type should contain a vertex handle, see Listing 4. Here the class ....

Lutz Kettner, Using Generic Programming for Designing a Data Structure for Polyhedral Surfaces, in Proc. 14th Annual ACM Symp. on Computational Geometry, 1998.

....v. The lists L0 (v) are easily created in O(gn) time, and updated in O(n) time, each time an edge is converted by a traversal of the corresponding loop. Step 3. Omitted from this version. 6. IMPLEMENTATION We have implemented both the incremental and Brahana s algorithm in C , using the CGAL [7] 1 polyhedron data structure. Both source codes are approximately 3,000 lines long. The remaining issue in the implementation is the representation of loops. In practice, a PL loop is speci ed by the list of edges it crosses. Also, each edge of the combinatorial surface points to the list of ....

L. Kettner. Using generic programming for designing a data structure for polyhedral surfaces. Computational Geometry: Theory and Applications, 13:65-90, 1999.

....a face and around a vertex, and efficient point location. The basic representation which we use is the Doubly Connected Edge List (DCEL) structure. This representation belongs to a family of edge based data structures in which each edge is represented as a pair of opposite halfedges; see e.g. [5, 13, 15, 21]. Consider Figure 1 for an illustration. A halfedge e is connecting two vertices its endpoints: it is directed from its source endpoint to its target endpoint. Its twin halfedge, twin( e) connects the same endpoints in the reverse order. We regard a halfedge as bounding the face on its ....

....makes the package modular and convenient to extend, as we show in the subsequent sections. Before we delve into the underlying structures and algorithms, we give a brief overview of the package. Figure 2 depicts an outline of the package. The design follows Cgal s polyhedron design introduced in [13]. The bottom layer holds base classes for vertices, halfedges and faces. Their responsibilities are the actual storage of the incidence relations between the map features, the geometry and other attributes. The middle layer is the topological map. This layer uses the DCEL as its data structure. ....

L. Kettner. Using generic programming for designing a data structure for polyhedral surfaces. Computational Geometry: Theory and Applications, 13:65--90, 1999.

....by using a template programming idiom similar to the Barton Nackman trick [5, 11] that uses a derived class as a template argument for a base class template. A similar idiom has been used in CGAL to solve cyclic template dependencies in the halfedge data structure and polyhedral surface design [21]. 3 The Kernel Concept and Architecture A geometry kernel consists of types used to represent geometric objects and operations on these types. Although from a C point of view both will be classes, we refer only to the former as (geometric) types whereas we call the latter (geometric) ....

KETTNER, L. Using generic programming for designing a data structure for polyhedral surfaces. Comput. Geom. Theory Appl. 13 (1999), 65--90.

.... time is presented in [15] and the project goals in [14] A more recent overview can be found in [16] Precision and robustness aspects of a computational geometry library are discussed in [17] Further topics on designing combinatorial data structures in CGAL, such as polyhedra, are described in [18]. Many implementations of computational geometry algorithms exist in loosely coupled collections only. Use and combination of such algorithms usually requires some adaptation effort. If well designed, the components of a library work seamlessly together. First implementation efforts for ....

....as the sequence of edges around a vertex in a triangulation. See the next section for more details on circulators. In a few places we also made use of the object oriented programming paradigm, for example the protected access to the internal representation of the polyhedral surface data structure [18], which is no time critical operation compared to the work that is supposed to be performed with the internal representation. Another example is the return value of the intersection of two polygons, which might contain points, segments, or polygons in general. In CGAL, a polymorphic list is used ....

Lutz Kettner, `Using generic programming for designing a data structure for polyhedral surfaces', Computational Geometry: Theory and Applications (1999). to appear.

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L. Kettner. Using generic programming for designing a data structure for polyhedral surfaces. Computational Geometry { Theory and Applications, 13:65-90, 1999.

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L. Kettner. Using generic programming for designing a data structure for polyhedral surfaces. Computational Geometry -- Theory and Applications, 13:65--90, 1999.

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Lutz Kettner. Using generic programming for designing a data structure for polyhedral surfaces. Computational Geometry: Theory and Applications, 13(1):65--90, May 1999. 13

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L. Kettner. Using generic programming for designing a data structure for polyhedral surfaces. Comput. Geom. Theory Appl., 13:6590, 1999.

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