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Everything about Point-set triangulation
Simplicial complex in Euclidean geometry
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. In the plane, triangulations are made up of triangles, together with their edges and vertices. Some authors require that all the points of are vertices of its triangulations. In this case, a triangulation of a set of points in the plane can alternatively be defined as a maximal set of non-crossing edges between points of. In the plane, triangulations are special cases of planar straight-line graphs. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Point-set triangulationA 5-minute orientation
- Pick up a classic book: Algebraic topologyThe most-reprinted book on the subject
- Read the landmark paper: Neither the greedy nor the delaunay triangulation of a planar point set approximates the optimal triangulationCited 50 times
- Go sideways: Delaunay triangulationA closely related topic
- Go sideways: Triangulation (geometry)A closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Neither the greedy nor the delaunay triangulation of a planar point set approximates the optimal triangulation
A triangulation method of an arbitrary point set for biomagnetic problems
Efficient triangulation of Poisson-disk sampled point sets
Computing a Minimum Weight Triangulation of a Sparse Point Set*
Research on Algorithm of the Point Set in the Plane Based on Delaunay Triangulation
Triangulation based topology approach for 2D point sets registration
đź“š Books worth reading
Algebraic topologyWilliam S. Massey · 1967
Introduction to Constraint DatabasesPeter Revesz · 2002
Computational GeometryAlberto Márquez · 2012
Graph DrawingWalter Didimo · 2013
Discrete Geometry for Computer ImageryRocio Gonzalez-Diaz · 2013
International encyclopedia of human geographyN. J. Thrift, Rob Kitchin · 2009
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Delaunay triangulation In computational geometry, a Delaunay triangulation or Delone triangulation of a set of points in the plane subdivides their convex hull into triangles…
- Triangulation (geometry) In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object…
- Pseudotriangle In Euclidean plane geometry, a pseudotriangle (pseudo-triangle) is the simply connected subset of the plane that lies between any three mutually tangent…
- Constrained Delaunay triangulation In computational geometry, a constrained Delaunay triangulation is a generalization of the Delaunay triangulation that forces certain required segments…
- Polygon triangulation In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set of…
- Geometric graph theory Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter…
- Minimum-weight triangulation In computational geometry and computer science, the minimum-weight triangulation problem is the problem of finding a triangulation of minimal total edge…
- Simple polygon In geometry, a simple polygon is a polygon that does not intersect itself and has no holes. That is, it is a piecewise-linear Jordan curve consisting of…