This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also for speeding-up the off-line rendering of complex scenes. Unfortunately, generating these levels of detail is a time-consuming task usually left to a human modeler. This paper shows how a new set of vertices can be distributed over the surface of a model and connected to one another to create a re-tiling of a surface that is faithful to both the geometry and the topology of the original surface. Themain contributions of this paper are: 1) a robust method of connecting together new vertices over a surface, 2) a way of using an estimate of surface curvature to distribute more new vertices at regions of higher curvature and 3) a method of smoothly interpolating between models that represent the same object at different levels of detail. The key notion in the re-tiling procedure is the creation of an intermediate model called the mutual tessellation of a surface that contains both the vertices from the original model and the new points that are to become vertices in the re-tiled surface. The new model is then created by removing each original vertex and locally re-triangulating the surface in a way that matches the local connectedness of the initial surface. This technique for surface retessellation has been successfully applied to iso-surface models derived from volume data, Connolly surface molecular models and a tessellation of a minimal surface of interest to mathematicians. CRCategoriesandSubjectDescriptors: I.3.3 [ComputerGraph- ics]: Picture/Image Generation -- Display algorithms

This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3-D defined by a set of polygons

We survey the computational geometry relevant to finite element mesh generation. We especially focus on optimal triangulations of geometric domains in two- and three-dimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some criterion that measures the size, shape, or number of triangles. We discuss algorithms both for the optimization of triangulations on a fixed set of vertices and for the placement of new vertices (Steiner points). We briefly survey the heuristic algorithms used in some practical mesh generators.

In many cases the surfaces of geometric models consist of a large number of triangles. Several algorithms were developed to reduce the number of triangles required to approximate such objects. Algorithms that measure the deviation between the approximated object and the original object are only available for special cases. In this paper we use the Hausdorff distance between the original and the simplified mesh as a geometrically meaningful error value which can be applied to arbitrary triangle meshes. We present a new algorithm to reduce the number of triangles of a mesh without exceeding a user-defined Hausdorff distance between the original and simplified mesh. As this distance is parameterization-independent, its use as error measure is superior to the use of the L 1 -Norm between parameterized surfaces. Furthermore the Hausdorff distance is always less than the distance induced by the L 1 -Norm. This results in higher reduction rates. Excellent results were achieved by the new ...

Interactive visualization is complicated by the complexity of the objects being visualized. Sampled or computed scientific data is often dense, in order to capture high frequency components in measured data or to accurately model a physical process. Common visualization techniques such as isosurfacing on such large meshes generate more geometric primitives than can be rendered in an interactive environment. Geometric mesh reduction techniques have been developed in order to reduce the size of a mesh with little compromise in image quality. Similar techniques have been used for functional surfaces (terrain maps) which take advantage of the planar projection. We extend these methods to arbitrary surfaces in 3D and to any number of variables defined over the mesh by developing a algorithm for mapping from a surface mesh to a reduced representation and measuring the introduced error in both the geometry and the multivariate data. Furthermore, through error propagation, our algorithm ensures that the errors in both the geometric representation and multivariate data do not exceed a user-specified upper bound.

Abstract not found

Introduction Scientific data is often sampled or computed over a dense mesh in order to capture high frequency components or achieve a desired error bound. Interactive display and navigation of such large meshes is impeded by the sheer number of triangles required to sufficiently model highly complex data. A number of simplification techniques have been developed which reduce the number of triangles to a particular desired triangle count or until a particular error Preprint submitted to Elsevier Preprint 3 December 1997 threshold is met. Given an initial triangulation M of a domain D and a function F(x) defined over the triangulation, the simplified mesh can be called M 0 and the resulting function F 0 (x). The measure of error in a simplified mesh M i is usually represented as: ffl(M 0<F1

. A mesh refinement and a mesh simplification algorithm are presented. Both algorithms guarantee a user-defined error tolerance and deliver a multiresolution model. After the computation of the multiresolution model triangulation of the surface patches at variable resolutions can be incrementally generated on-the-fly at rendering time. The resulting triangulations form hierarchical Delaunay triangulations in parameter space. 1 Introduction and Previous work The visualization of large CAD-models, like cars, trains, aero planes, etc. becomes a major challenge in the context of virtual reality. In most experiments a number of such models have to be visualized and animated simultaneously. Examples are the optimization of the cabin of a train or the optimization of a driver's position in a car. To examine the panorama in such a place, not only the train or car themselves have to be visualized but also other cars, pedestrians, buildings, etc. Despite the performance of modern graphics hardw...

The triangulation of boundary representation geometries (BRep geometries) is neccessary for display generation, stereo-lithography applications and also finite element mesh (FE mesh) generation. The accuracy of the tesselation is of great significance not only for stereo-lithography and rendering algorithms but also for FE mesh generation, since even minor simplifications of the geometry of the solid can lead to large errors in the FE computation. We therefore turn our attention to a new incremental algorithm for the accurate triangulation of meshes of trimmed parametric surfaces. Instead of triangulating each face seperately, the faces of the solid are glued and triangulated together according to the neighbourhood information of the BRep. By this procedure, glueing together faces with different triangulations is avoided. Another advantage of the algorithm is that the error between the linear approximation of the boundary and the boundary itself is controlled step by step until it lies...

We present a new method for (1) automatically generating multiple Levels Of Detail (LODs) of a polygonal surface, (2) progressively loading, or transmitting, and displaying a surface, and for (3) changing interactively the LOD when displaying. We build the LODs using any algorithm that performs edge collapses and certain vertex removals to simplify surfaces, and provides an ordered list of ordered vertex pairs (edge collapse specifications). We propose a Surface Partition for encoding surface LODs: we define vertex and triangle levels during simplification; vertices and triangles are partitioned and sorted according to their level, and are passed to the display algorithm in decreasing level order, one level at a time, together with a vertex representatives array. Each level of vertices and triangles, together with higher levels and the vertex representatives, form a valid surface. The vertex representatives array encodes a succession of simplicial maps between the highest resolution LOD and other LODs. We propose a data structure using a Directed Acyclic Graph (DAG) for recording a partial ordering among edge collapses, and varying the LODs across the surface. We describe an implementation of our method in VRML.