There are Generalized Voronoi Diagram A Geometry Based Approach Toputational Intelligence Studies Inputational Intelligence a minimum of the next kinds of Inputational Intelligence: Chart-like Inputational Intelligence, which take an amount of items and relationships together, and express them giving each item a 2D position, even though the relationships are expressed as connections between your items or overlaps relating to the items examples of such techniques: tree diagram network diagram flowchart Venn diagram existential graph Graph-based diagrams these display rapport between two variables that take either discrete or even a continuous ranges of values examples: histogram bar graph pie chart function graph scatter plot Schematics and other diagrams, e.g., train schedule diagram exploded view population density map Pioneer plaque Three-dimensional diagram Several kinds of diagrams can be generated using diagramming software like Visio and Gliffy. A large number of diagram techniques exist. Even more examples follow. Diagrams are often classified as outlined by use or purpose, as an example, explanatory and/or the way to diagrams.

A Activity diagram used in UML 6/9 and SysML B Bachman diagram Booch used in software engineering Block diagram Block Definition Diagram BDD used in SysML C Carroll diagram Cartogram Catalytic cycle Chemical equation Curly arrow diagram Category theory diagrams Cause-and-effect diagram Chord diagram Circuit diagram Class diagram from UML 1/9 Collaboration diagram from UML 2.0 Communication diagram from UML 2.0 Commutative diagram Comparison diagram Component diagram from UML 3/9 Composite structure diagram from UML 2.0 Concept map Constellation diagram Context diagram Control flow diagram Contour diagram Cordier diagram Cross functional flowchart D Data model diagram Data flow diagram Data structure diagram Dendrogram Dependency diagram Deployment diagram from UML 9/9 Dot and cross diagram Double bubble map used in education Drakon-chart E Entity-Relationship diagram ERD Event-driven process chain Euler diagram Eye diagram a diagram of a received telecommunications signal Express-G Extended Functional Flow Block Diagram EFFBD F Family tree Feynman diagram Flow chart Flow process chart Flow diagram Fusion diagram Free body diagram G Gantt chart shows the timing of tasks or activities used in project management Grotrian diagram Goodman diagram shows the fatigue data example: for a wind turbine blades H Hasse diagram HIPO diagram I Internal Block Diagram IBD used in SysML IDEF0 IDEF1 entity relations Interaction overview diagram from UML Ishikawa diagram J Jackson diagram K Karnaugh map Kinematic diagram L Ladder diagram Line of balance Link grammar diagram M Martin ERD Message Sequence Chart Mind map used for learning, brainstorming, memory, visual thinking and problem solving Minkowski spacetime diagram Molecular orbital diagram N N2 Nassi Shneiderman diagram or structogram a representation for structured programming Nomogram Network diagram O Object diagram from UML 2/9 Organigram Onion diagram also known as "stacked Venn diagram" P Package diagram from UML 4/9 and SysML Parametric diagram from SysML PERT Petri net shows the structure of a distributed system as a directed bipartite graph with annotations Phylogenetic tree - represents a phylogeny evolutionary relationships among groups of organisms Piping and instrumentation diagram P&ID Phase diagram used to present solid/liquid/gas information Plant Diagram Pressure volume diagram used to analyse engines Pourbaix diagram Process flow diagram or PFD used in chemical engineering Program structure diagram R Radar chart Radial Diagram Requirement Diagram Used in SysML Rich Picture R-diagram Routing diagram S Sankey diagram represents material, energy or cost flows with quantity proportional arrows in a process network. Sentence diagram represents the grammatical structure of a natural language sentence. Sequence diagram from UML 8/9 and SysML SDL/GR diagram Specification and Description Language. SDL is a formal language used in computer science. Smith chart Spider chart Spray diagram SSADM Structured Systems Analysis and Design Methodology used in software engineering Star chart/Celestial sphere State diagram are used for state machines in software engineering from UML 7/9 Swim lane Syntax diagram used in software engineering to represent a context-free grammar Systems Biology Graphical Notation a graphical notation used in diagrams of biochemical and cellular processes studied in Systems biology System context diagram System structure Systematic layout planning T Timing Diagram: Digital Timing Diagram Timing Diagram: UML 2.0 TQM Diagram Treemap U UML diagram Unified Modeling Language used in software engineering Use case diagram from UML 5/9 and SysML V Value Stream Mapping Venn diagram Voronoi diagram W Warnier-Orr Williot diagram Y Yourdon-Coad see Edward Yourdon, used in software engineering

Generalized Voronoi Diagram: A Geometry Based Approach to putational Intelligence (Studies in putational Intelligence) 2008th Edition by Marina L. Gavrilova (Editor)

The main ideas expressed by G. Voronoi’s through his fundamental works have influenced and shaped the key developments in computation geometry, image recognition, artificial intelligence, robotics, computational science, navigation and obstacle avoidance, geographical information systems, molecular modeling, astrology, physics, quantum computing, chemical engineering, material sciences, terrain modeling, biometrics and other domains.

Generalized Voronoi Diagram: A Geometry Based Approach to putational Intelligence

Generalized Voronoi diagrams Introduction. Voronoi diagrams of points in the Euclidean plane were first defined one and a half centuries ago by Lejeune Dirichlet when investigating quadratic forms. 1 Besides the basic Voronoi diagrams of points, various generalizations have been of interest in the field computational geometry: 2

The partition of space into V(A1), V(A2), …, V(Ak) is called the generalized Voronoi diagram. The (ordinary) Voronoi diagram corresponds to the case when each Ai is an individual point. The boundaries of the regions V(Ai) are called Voronoi boundaries.

generalized Voronoi diagram. The (ordinary) Voronoi diagram corresponds to the case when each Ai is an individual point. When the primitives are linear elements (points, lines, polygons), the bisectors are algebraic curves or surfaces. 3.2 Discrete Voronoi Diagrams To compute a discrete Voronoi diagram, we start with a uniform

In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane. For each seed there is a corresponding region consisting of all points of the plane closer to that seed than to any other. These regions are called Voronoi cells. The Voronoi diagram of a set of points is dual to its Delaunay triangulation. The Voronoi diagram is named after Russian mathematician Georgy V

The Voronoi diagram in the Laguerre geometry may be applied to solving effectively a number of geometrical problems such as those of determining whether or not a point belongs to the union of n circles, of finding the connected components of n circles, and of finding the contour of the union of n circles.

We present a transformation that can be used to compute Voronoi diagrams with a sweepline technique. The transformation is used to obtain simple algorithms for computing the Voronoi diagram of point sites, of line segment sites, and of weighted point sites. All algorithms have Ο(n log n) worst case running time and use Ο(n) space.