Search results
Results from the WOW.Com Content Network
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications
In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices. Triangulations of a three-dimensional volume would involve subdividing it into tetrahedra packed together.
A triangulated torus Another triangulation of the torus A triangulated dolphin shape. In mathematics, triangulation describes the replacement of topological spaces with simplicial complexes by the choice of an appropriate homeomorphism. A space that admits such a homeomorphism is called a triangulable space.
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.
A triangulation of a set of points in the Euclidean space is a simplicial complex that covers the convex hull of , and whose vertices belong to . [1] In the plane (when P {\displaystyle {\mathcal {P}}} is a set of points in R 2 {\displaystyle \mathbb {R} ^{2}} ), triangulations are made up of triangles, together with their edges and vertices.
Triangulation in a simple polygon. Triangulation means the partition of any planar object into a collection of triangles. For example, in polygon triangulation, a polygon is subdivided into multiple triangles that are attached edge-to-edge, with the property that their vertices coincide with the set of vertices of the polygon. [52]
The closest neighbor b to any point p is on an edge bp in the Delaunay triangulation since the nearest neighbor graph is a subgraph of the Delaunay triangulation. The Delaunay triangulation is a geometric spanner : In the plane ( d = 2 ), the shortest path between two vertices, along Delaunay edges, is known to be no longer than 1.998 times the ...
Triangulation of a surface means a net of triangles, which covers a given surface partly or totally, or the procedure of generating the points and triangles of such a net of triangles.