Computational geometry: an introduction
Computational geometry: an introduction
Nonobtuse triangulation of polygons
Discrete & Computational Geometry
Triangulating Simple Polygons and Equivalent Problems
ACM Transactions on Graphics (TOG)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A Pyramidal Data Structure for Triangle-Based Surface Description
IEEE Computer Graphics and Applications
A new general triangulation method for planar contours
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Conversion of complex contour line definitions into polygonal element mosaics
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Automatic extraction of Irregular Network digital terrain models
SIGGRAPH '79 Proceedings of the 6th annual conference on Computer graphics and interactive techniques
Fast Horizon Computation at All Points of a Terrain With Visibility and Shading Applications
IEEE Transactions on Visualization and Computer Graphics
An Edge-preserving, Data-dependent Triangulation Scheme for Hierarchical Rendering
Dagstuhl '97, Scientific Visualization
Automatic generation of triangular irregular networks using greedy cuts
VIS '95 Proceedings of the 6th conference on Visualization '95
Towards a definition of higher order constrained Delaunay triangulations
Computational Geometry: Theory and Applications
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Triangulated Irregular Networks (TINs) have been used for surface approximation in many applications. A hierarchical representation is often desirable if the surface is to be rendered at different resolutions. Past work has emphasized techniques where a coarse triangulation is refined by focusing on plane geometry using very little the surface data. For example, a new point is introduced where the deviation of the surface is maximum and the triangle is subdivided into four others. Variants of Delauney triangulations have also been used. We propose a technique where we look more carefully into the features of the surface to be approximated. For example, if there is a ridge, the original triangle is divided by a line along the ridge and one of its vertices is used to subdivided the resulting quadrilateral. In this way the number of very thin triangles (slivers) is significantly reduced. Such triangles produced undesirable effects in animation. In addition the number of levels of the TIN tree is reduced which speeds up searching within the data structure. Tests on data with digital elevation input have confirmed the above theoretical expectations. On eight such sets the average "sliveriness" with the new method was between 1/5 and 1/10 of old triangulations and number of levels was about one third. There was an increase in the number of descendants at each level but the total number of triangles was also lower.Note: Because of space limitations many details and examples have been omitted from this version of the paper. Interested readers should request from the authors a technical report with the same title providing full details of the method, as well as additional examples of implementation than poresented here.