ComputationalGeometry`
ComputationalGeometry`

BoundedDiagram

As of Version 10, all the functionality of the ComputationalGeometry package is built into the Wolfram System. »

BoundedDiagram[{{a1,b1},},{{x1,y1},}]

yields the bounded Voronoi diagram of the points {x1,y1},{x2,y2}, where the bound is the convex polygon formed from the points {{a1,b1},}.

BoundedDiagram[{{a1,b1},},{{x1,y1},},val]

takes val to be the Delaunay triangulation vertex adjacency list.

BoundedDiagram[{{a1,b1},},{{x1,y1},},val,hull]

takes hull to be the convex hull index list.

Details and Options

• BoundedDiagram functionality is now available in the built-in Wolfram Language function VoronoiMesh.
• To use BoundedDiagram, you first need to load the Computational Geometry Package using Needs["ComputationalGeometry`"].
• The bounded Voronoi diagram is represented by two lists, a vertex coordinate list and a vertex adjacency list.
• An element {i,{v1,}} of the vertex adjacency list corresponds to the point {xi,yi}, and the indices v1, identify the vertices in the vertex coordinate list that form its bounding polygon.
• BoundedDiagram begins by finding the unbounded Voronoi diagram and then incorporating the bounding polygon vertices into the diagram.
• The bounding polygon should be large enough to contain all the points {xi,yi}.
• The optional arguments val and hull may be used to speed up the initial Voronoi diagram computation if the Delaunay triangulation and convex hull are available.
Wolfram Research (2012), BoundedDiagram, Wolfram Language function, https://reference.wolfram.com/language/ComputationalGeometry/ref/BoundedDiagram.html.

Text

Wolfram Research (2012), BoundedDiagram, Wolfram Language function, https://reference.wolfram.com/language/ComputationalGeometry/ref/BoundedDiagram.html.

CMS

Wolfram Language. 2012. "BoundedDiagram." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ComputationalGeometry/ref/BoundedDiagram.html.

APA

Wolfram Language. (2012). BoundedDiagram. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ComputationalGeometry/ref/BoundedDiagram.html

BibTeX

@misc{reference.wolfram_2024_boundeddiagram, author="Wolfram Research", title="{BoundedDiagram}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ComputationalGeometry/ref/BoundedDiagram.html}", note=[Accessed: 16-September-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_boundeddiagram, organization={Wolfram Research}, title={BoundedDiagram}, year={2012}, url={https://reference.wolfram.com/language/ComputationalGeometry/ref/BoundedDiagram.html}, note=[Accessed: 16-September-2024 ]}