Highly detailed geometric models are rapidly becoming commonplace in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new scheme for storing and transmitting arbitrary triangle meshes. This efficient, lossless, continuous-resolution representation addresses several practical problems in graphics: smooth geomorphing of level-of-detail approximations, progressive transmission, mesh compression, and selective refinement. In addition, we present a new mesh simplification procedure for constructing a PM representation from an arbitrary mesh. The goal of this optimization procedure is to preserve not just the geometry of the original mesh, but more importantly its overall appearance as defined by its discrete and scalar appearance attributes such as material identifiers, color values, normals, and texture coordinates. We demonstrate construction of the PM representation and its applications using several practical models.

We present an algorithm for real-time level of detail reduction and display of high-complexity polygonal surface data. The algorithm uses a compact and efficient regular grid representation, and employs a variable screen-space threshold to bound the maximum error of the projected image. A coarse level of simplification is performed to select discrete levels of detail for blocks of the surface mesh, followed by further simplification through repolygonalization in which individual mesh vertices are considered for removal. These steps compute and generate the appropriate level of detail dynamically in real-time, minimizing the number of rendered polygons and allowing for smooth changes in resolution across areas of the surface. The algorithm has been implemented for approximating and rendering digital terrain models and other height fields, and consistently performs at interactive frame rates with high image quality.

We construct smooth parameterizations of irregular connectivity triangulations of arbitrary genus 2-manifolds. Our algorithm uses hierarchical simplification to efficiently induce a parameterization of the original mesh over a base domain consisting of a small number of triangles. This initial parameterization is further improved through a hierarchical smoothing procedure based on Loop subdivision applied in the parameter domain. Our method supports both fully automatic and user constrained operations. In the latter, we accommodate point and edge constraints to force the align- # wailee@cs.princeton.edu + wim@bell-labs.com # ps@cs.caltech.edu cowsar@bell-labs.com dpd@cs.princeton.edu ment of iso-parameter lines with desired features. We show how to use the parameterization for fast, hierarchical subdivision connectivity remeshing with guaranteed error bounds. The remeshing algorithm constructs an adaptively subdivided mesh directly without first resorting to uniform subdivision followed by subsequent sparsification. It thus avoids the exponential cost of the latter. Our parameterizations are also useful for texture mapping and morphing applications, among others.

The key to real-time rendering of large-scale surfaces is to locally adapt surface geometric complexity to changing view parameters. Several schemes have been developed to address this problem of view-dependent level-of-detail control. Among these, the viewdependent progressive mesh (VDPM) framework represents an arbitrary triangle mesh as a hierarchy of geometrically optimized refinement transformations, from which accurate approximating meshes can be efficiently retrieved. In this paper we extend the general VDPM framework to provide temporal coherence through the runtime creation of geomorphs. These geomorphs eliminate "popping" artifacts by smoothly interpolating geometry. Their implementation requires new output-sensitive data structures, which have the added benefit of reducing memory use.

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

There are a variety of application areas in which there is a need for simplifying complex polygonal surface models. These models often have material properties such as colors, textures, and surface normals. Our surface simplification algorithm, based on iterative edge contraction and quadric error metrics, can rapidly produce high quality approximations of such models. We present a natural extension of our original error metric that can account for a wide range of vertex attributes. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling---surface and object representations Keywords: surface simplification, multiresolution modeling, level of detail, quadric error metric, edge contraction, surface properties, discontinuity preservation 1 INTRODUCTION Many applications in computer graphics and visualization can benefit from automatic simplification of complex polygonal models. Such models are usually not only geometrically complex, but they may also have ...

For twenty years, it has been clear that many datasets are excessively complex for applications such as real-time display, and that techniques for controlling the level of detail of models are crucial. More recently, there has been considerable interest in techniques for the automatic simplification of highly detailed polygonal models into faithful approximations using fewer polygons. Several effective techniques for the automatic simplification of polygonal models have been developed in recent years. This report begins with a survey of the most notable available algorithms. Iterative edge contraction algorithms are of particular interest because they induce a certain hierarchical structure on the surface. An overview of this hierarchical structure is presented,including a formulation relating it to minimum spanning tree construction algorithms. Finally, we will consider the most significant directions in which existing simplification methods can be improved, and a summary of o...

Modeling arbitrary real objects is difficult and rendering textured models typically does not result in realistic images. We describe a new method for displaying scanned real objects, called view-based rendering. The method takes as input a collection of colored range imagescovering the objectand creates a collection of partial object models. These partial models are rendered separately using traditional graphics hardware and blended together using various weights and soft z-buffering. We demonstrate interactive viewing of real, non-trivial objects that would be difficult to model using traditional methods.

We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, prune-and-search techniques for linear programming and related problems, and LPtype problems and their efficient solution. We then describe a variety of applications of these and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other query-type problems.

We present a simple,robust, and practical method for object simplification for applications where gradual elimination of high frequency details is desired. This is accomplished by converting an object into multi-resolution volume rastersusing a controlled filtering and sampling technique.Amultiresolution triangle-mesh hierarchycan then be generated by applying the Marching Cubes algorithm. We f urther propose an adaptive surface generation algorithm to reduce the number of triangles generated by the standardMarching Cubes. Our method simplifies the topology of objects in a controlled fashion. In addition, at eachlevel of detail, multi-layered meshes can be used for an efficient antialiased rendering.