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Polygon triangulation. In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, [1] i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs.
Cell-based models are mathematical models that represent biological cells as discrete entities. Within the field of computational biology they are often simply called agent-based models [1] of which they are a specific application and they are used for simulating the biomechanics of multicellular structures such as tissues. to study the influence of these behaviors on how tissues are organised ...
[4] [5] The run-time complexity of this problem crucially depends on whether the raw polygon is allowed to have holes. If the raw polygon is hole-free , then an optimal partition can be found in time O ( n 4 ) {\displaystyle O(n^{4})} , where n is the number of vertices of the polygon.
However, this polygon also has other ears that are not evident in this triangulation. In geometry , the two ears theorem states that every simple polygon with more than three vertices has at least two ears , vertices that can be removed from the polygon without introducing any crossings.
By the 1950s, cell biologists verified the existence of plasma membranes through the use of electron microscopy (which accounted for higher resolutions). J. David Robertson used this method to propose the unit membrane model. [4] Basically, he suggested that all cellular membranes share a similar underlying structure, the unit membrane. Using ...
Cell is the intersection of all of these half-spaces, and hence it is a convex polygon. [6] When two cells in the Voronoi diagram share a boundary, it is a line segment , ray , or line, consisting of all the points in the plane that are equidistant to their two nearest sites.
Head and cerebral structures (hidden) extracted from 150 MRI slices using marching cubes (about 150,000 triangles). Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, [1] for extracting a polygonal mesh of an isosurface from a three-dimensional discrete scalar field (the elements of which are sometimes called voxels).
Cellular compartments in cell biology comprise all of the closed parts within the cytosol of a eukaryotic cell, usually surrounded by a single or double lipid layer membrane. These compartments are often, but not always, defined as membrane-bound organelles. The formation of cellular compartments is called compartmentalization.