The following free book is for anyone interested in learning about combination maps.
About the book (by the author)
A combinatorial map is a combinatorial object that models topological structures with subdivided objects. Historically, the concept has been informally referred to by J. Edmunds for polyhedral surfaces that are planar graphs.
a. Jacques gave it its first formally defined expression under the name “constellation”, but the concept was widely used under the name “rotation” by Gerhard Ringel and JWT Youngs in their famous solution to the Heywood map color problem.
The term “constellation” was not retained and instead a “combinatorial map” was favored. The concept was later expanded to represent highly dimensionally oriented subdivided objects. In geometric modeling, combination maps are used as efficient data structures in image rendering and processing.
This model deals with simple complexes and combinatorial topologies. Note that combinatorial maps were extended to generalized maps that also allow non-orientable objects such as the Möbius strip and the Klein bottle to be represented. A composite map is a boundary representation model; Represents an object by its limits.
Various applications require a data structure to represent a subdivision of an object. For example, a 2D object can be exploded into vertices (0 cells), edges (1 cell), and faces (2 cells).
More generally, an n-dimensional object is made up of cells of dimensions 0 to n. In addition, it is often necessary to represent the neighborhood relationships between these cells as well.
Therefore, we want to describe all the cells in the subsection, as well as all the events and adjacent relationships between these cells.
When all the cells represented are simple, a simple complex can be used, but when we want to represent any type of cells, we need to use a cell topological model, e.g. Whether combinatorial maps or generalized maps. (wikipedia)
data sheet
year: 2007
Editor: Latvian University
Language: English
Shape: 284 KB
License: pending review
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