Procedural elements for computer graphics
Procedural elements for computer graphics
Real-time rendering of trimmed surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Computational Geometry: Theory and Applications
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
A unified approach for hierarchical adaptive tesselation of surfaces
ACM Transactions on Graphics (TOG)
Triangulation and shape-complexity
ACM Transactions on Graphics (TOG)
Triangulating Simple Polygons and Equivalent Problems
ACM Transactions on Graphics (TOG)
Hidden surface removal using polygon area sorting
SIGGRAPH '77 Proceedings of the 4th annual conference on Computer graphics and interactive techniques
Interactive Display of Large NURBS Models
IEEE Transactions on Visualization and Computer Graphics
Robust Tesselation of Trimmed Rational B-Spline Surface Patches
CGI '98 Proceedings of the Computer Graphics International 1998
SMI '03 Proceedings of the Shape Modeling International 2003
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Medial Axis Transformation of a Planar Shape
IEEE Transactions on Pattern Analysis and Machine Intelligence
Surface Triangulation and the Downstream Effects on Flattening
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
A robust efficient tracing scheme for triangulating trimmed parametric surfaces
Computer-Aided Design
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This paper presents a new robust uniform triangulation algorithm that can be used in CAD/CAM systems to generate and visualize geometry of 3D models. Typically, in CAD/CAM systems 3D geometry consists of 3D surfaces presented by the parametric equations (e.g. surface of revolution, NURBS surfaces) which are defined on a two dimensional domain. Conventional triangulation algorithms (e.g. ear clipping, Voronoi-Delaunay triangulation) do not provide desired quality and high level of accuracy (challenging tasks) for 3D geometry. The approach developed in this paper combines lattice tessellation and conventional triangulation techniques and allows CAD/CAM systems to obtain the required surface quality and accuracy. The algorithm uses a Cartesian lattice to divide the parametric domain into adjacent rectangular cells. These cells are used to generate polygons that are further triangulated to obtain accurate surface representation. The algorithm allows users to control the triangle distribution intensity by adjusting the lattice density. Once triangulated, the 3D model can be used not only for rendering but also in various manufacturing and design applications. The approach presented in this paper can be used to triangulate any parametric surface given in S(u,v) form, e.g. NURBS surfaces, surfaces of revolution, and produces good quality triangulation which can be used in CAD/CAM and computer graphics applications.