Planar point location using persistent search trees
Communications of the ACM
New methods for computing visibility graphs
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Higher order Delaunay triangulations
Computational Geometry: Theory and Applications
A Pyramidal Data Structure for Triangle-Based Surface Description
IEEE Computer Graphics and Applications
Automatic extraction of Irregular Network digital terrain models
SIGGRAPH '79 Proceedings of the 6th annual conference on Computer graphics and interactive techniques
Hierarchical triangulation using terrain features
VIS '90 Proceedings of the 1st conference on Visualization '90
Visibility preserving terrain simplification: an experimental study
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
Constrained higher order Delaunay triangulations
Computational Geometry: Theory and Applications
Generating realistic terrains with higher-order Delaunay triangulations
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
An efficient depression processing algorithm for hydrologic analysis
Computers & Geosciences
An efficient depression processing algorithm for hydrologic analysis
Computers & Geosciences
Optimal higher order Delaunay triangulations of polygons
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Constructing interference-minimal networks
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Optimization for first order delaunay triangulations
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Optimal higher order Delaunay triangulations of polygons
Computational Geometry: Theory and Applications
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When a triangulation of a set of points and edges is required, the constrained Delaunay triangulation is often the preferred choice because of its well-shaped triangles. However, in applications like terrain modeling, it is sometimes necessary to have flexibility to optimize some other aspect of the triangulation, while still having nicely-shaped triangles and including a set of constraints. Higher order Delaunay triangulations were introduced to provide a class of well-shaped triangulations, flexible enough to allow the optimization of some extra criterion. But they are not able to handle constraints: a single constraining edge may cause that all triangulations with that edge have high order, allowing ill-shaped triangles at any part of the triangulation. In this paper we generalize the concept of the constrained Delaunay triangulation to higher order constrained Delaunay triangulations. We study several possible definitions that assure that an order-k constrained Delaunay triangulation exists for any k=0, while maintaining the character of higher order Delaunay triangulations of point sets. Several properties of these definitions are studied, and efficient algorithms to support computations with order-k constrained Delaunay triangulations are discussed. For the special case of k=1, we show that many criteria can be optimized efficiently in the presence of constraints.