## 184 Citations

Construction of three-dimensional Delaunay triangulations using local transformations

- Computer Science, MathematicsComput. Aided Geom. Des.
- 1991

Three-dimensional triangulations from local transformations

- Computer Science
- 1989

A new algorithm is presented that uses a local transformation procedure to construct a triangulation of a set of n three-dimensional points that is pseudo-locally optimal with respect to the sphere…

Adapting (Pseudo)-Triangulations with a Near-Linear Number of Edge Flips

- MathematicsWADS
- 2003

In geometric data processing, structures that partition the geometric input, as well as connectivity structures for geometric objects, play an important role and triangular meshes, often called triangulations, are a versatile tool.

Construction of the Voronoi Diagram and Secondary Polytope

- Mathematics
- 2003

A set S of n points in general position in R^d defines the unique Voronoi diagram of S. Its dual tessellation is the Delaunay triangulation (DT) of S. In this paper we consider the parabolic…

Two simple algorithms for constructing a two-dimensional constrained Delaunay triangulation

- Computer Science
- 1993

Pseudo-tetrahedral complexes

- Computer ScienceEuroCG
- 2005

This paper defines pseudo-simplices and pseudo-Simplicial complexes in d-space in a way consistent to pseudo-triangulations in the plane, and unifies several well-known structures, namely pseudo-Triangulations, constrained Delaunay triangulations and regular simplicial complexes.

Properties of the Delaunay triangulation

- Computer ScienceSCG '97
- 1997

This work defined several functional on the set of all triangulations of the finite system of sites in Rd attaining global minimum on the Delaunay triangulation (DT), and considers a so called “parabolic” functional and proves that it attains its minimum on DT in all dimensions.

Incremental topological flipping works for regular triangulations

- MathematicsSCG '92
- 1992

If the points are added one by one, then flipping in a topological order will succeed in constructing this triangulation and the algorithm takes expected time at mostO(nlogn+n[d/2]).

Incremental topological flipping works for regular triangulations

- MathematicsAlgorithmica
- 2005

If the points are added one by one, then flipping in a topological order will succeed in constructing this triangulation and the algorithm takes expected time at mostO(nlogn+n[d/2]).

## References

SHOWING 1-10 OF 13 REFERENCES

Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams

- Computer ScienceSTOC
- 1983

Two algorithms are given, one that constructs the Voronoi diagram of the given sites, and another that inserts a new site in O(n) time, based on the use of the Vor onoi dual, the Delaunay triangulation, and are simple enough to be of practical value.

Algorithm 624: Triangulation and Interpolation at Arbitrarily Distributed Points in the Plane

- Computer ScienceTOMS
- 1984

This algorithm is a 1966 American National Standard FORTRAN implementation of the methods discussed in [1] and [2]. The software consists of a set of triangulation modules (which have application in…

Computing Dirichlet Tessellations in the Plane

- Computer ScienceComput. J.
- 1978

A recursive algorithm for computing the Dirichlet tessellation in a highly efficient way is described, and the problems which arise in its implementation are discussed.

Interpolation of data on the surface of a sphere

- MathematicsTOMS
- 1984

Methods and software that extend the C ~ interpolant of data values associated with arbitrarily distributed nodes on the surface of a sphere method are described and test results are presented.

A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points

- MathematicsTOMS
- 1978

A method of blvariate interpolation and smooth surface fitting is developed for z values given at points irregularly distributed in the x-y plane for Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points.

$C^1$ surface interpolation for scattered data on a sphere

- Mathematics
- 1984

An algorithm is described for constructing a smooth computable function, f, defined over the surface of a sphere and interpolating a set of n data values, u sub i, associated with n locations, P sub…

The Stable Evaluation of Multivariate B-Splines.

- Computer Science
- 1984

A general method for the stable evaluation of multivariate B-splines via their recurrence relations and the problem of evaluation along mesh boundaries is discussed in detail.

Three- and four-dimensional surfaces

- Mathematics
- 1984

The representation and approximation of three- and four-dimensional surfaces is accomplished by means of local, piecewise defined, smooth interpolation methods. In order to interpolate to arbitrarily…

A Storage-efficient Method for Construction of a Thiessen Triangulation

- Business
- 1982

This paper describes a storage-efficient method and associated algorithms for constructing and representing a triangulation of arbitrarily distributed points in the plane.