vertex
Let an agent explain vertices across geometry, graph theory and graphics, relay definitions, counts such as Euler s formula and uses from mathematics and computing sources, describe the Voronoi pole alias, and distinguish vertices from edges, faces, nodes in networks generally, apexes and the astrological or anatomical senses of vertex.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent explain vertices across geometry, graph theory and graphics, relay definitions, counts such as Euler s formula and uses from mathematics and computing sources, describe the Voronoi pole alias, and distinguish vertices from edges, faces, nodes in networks generally, apexes and the astrological or anatomical senses of vertex.
A point where two or more lines, edges or curves meet, as in the corners of polygons and polyhedra, the extreme points of polytopes and simplices, the nodes of graphs, where vertices are joined by edges, and the vertex of a parabola or other conic, its turning point; in computational geometry a Voronoi pole is a Voronoi vertex farthest from a sample point, used to approximate the medial axis in surface reconstruction. In computer graphics vertices carry positions and attributes such as colour and normals for rendering meshes.
What it is for: Naming meeting points in geometry and graphs.
It can be explain vertices across fields; relay Euler s formula and counts; describe the Voronoi pole; distinguish other senses.
Distinguishing features
Meeting point
Degree or valence
Cross-disciplinary
Data carrier in graphics
What it looks like
Not a physical object; drawn as corners of shapes or dots in graphs.
Physical character
Euler s polyhedron formula: V - E + F = 2 note - convex polyhedra
cube vertices: 8 count
Voronoi poles in surface reconstruction: Amenta and Bern, 1998-1999 note - power crust and crust algorithms
How it is recognised
Meeting point of edges or curves
Voronoi pole, corner, node, extreme point
Edges join vertices; faces are bounded regions; network nodes may carry data; apex is a top vertex; anatomical vertex is the top of the head
Related models
is a kind of - in registry terms
is joined by -
appears in -
is contrasted with -
In practice
Families and kinds
polygon and polyhedron vertices
graph vertices
conic vertices
Voronoi vertices and poles
mesh vertices
Standards and regulation
No regulation; graphics API specifications define vertex formats
Failure modes and hazards
Confusing vertex and edge counts
Mixing mathematical and anatomical senses
Treating Voronoi poles as generic vertices
Also called
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.vertex
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Understand What a vertex is.
Definition.
Definition
Definition.
Definition
Definition.
- What is a vertex, and how does it differ from edges, faces, network nodes, apexes and anatomical senses? definition
- Is the question about geometry, graphs, graphics or another field? boundary
Voronoi pole
Voronoi pole.
Voronoi pole
Voronoi pole.
- What is a Voronoi pole, and how is it used in surface reconstruction? definition
- Which entry fits Voronoi diagram? action
Geometry Geometry.
Science.
Polytopes
Polytopes.
Polytopes
Polytopes.
- How are vertices defined for polytopes and simplices? provenance
- Which references are standard? provenance
Euler
Euler s formula.
Euler
Euler.
- How does Euler s formula relate vertices, edges and faces? measurement
- Which sources are cited? provenance
Graphs Graph theory.
Science.
Degree
Vertex degree.
Degree
Degree.
- What is vertex degree, and what does the handshake lemma say? provenance
- Which entry fits degree (graph theory)? action
Colouring
Vertex colouring.
Colouring
Colouring.
- What is vertex colouring, and what does the four colour theorem state? provenance
- Which entry fits four color theorem? action
Context Graphics.
Context.
Graphics
Vertices in rendering.
Graphics
Graphics.
- How do vertex shaders process mesh vertices? provenance
- Which entry fits vertex shader? action
Conics
Parabola vertex.
Conics
Conics.
- How is the vertex of a parabola found? measurement
- Which entry fits parabola? action
What the second pass must settle
- Should Voronoi pole be a separate entry?
- Should graph vertex be disambiguated from polytope vertex?
- How should mathematics references be linked?