Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models. The algorithm uses iterative contractions of vertex pairs to simplify models and maintains surface error approximations using quadric matrices. By contracting arbitrary vertex pairs (not just edges), our algorithm is able to join unconnected regions of models. This can facilitate much better approximations, both visually and with respect to geometric error. In order to allow topological joining, our system also supports non-manifold surface models. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling---surface and object representations Keywords: surface simplificatio...

Advances in 3D scanning technologies have enabled the practical creation of meshes with hundreds of millions of polygons. Traditional algorithms for display, simplification, and progressive transmission of meshes are impractical for data sets of this size. We describe a system for representing and progressively displaying these meshes that combines a multiresolution hierarchy based on bounding spheres with a rendering system based on points. A single data structure is used for view frustum culling, backface culling, level-of-detail selection, and rendering. The representation is compact and can be computed quickly, making it suitable for large data sets. Our implementation, written for use in a large-scale 3D digitization project, launches quickly, maintains a user-settable interactive frame rate regardless of object complexity or camera position, yields reasonable image quality during motion, and refines progressively when idle to a high final image quality. We have demonstrated the system on scanned models containing hundreds of millions of samples.

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.

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 ...

In many applications the need for an accurate simplification of surface meshes is becoming more and more urgent. This need is not only due to rendering speed reasons, but also to allow fast transmission of 3D models in network-based applications. Many different approaches and algorithms for mesh simplification have been proposed in the last few years. We present a survey and a characterization of the fundamental methods. Moreover, the results of an empirical comparison of the simplification codes available in the public domain are discussed. Five implementations, chosen to give a wide spectrum of different topology-preserving methods, were run on a set of sample surfaces. We compared empirical computational complexities and the approximation accuracy of the resulting output meshes. 1 Introduction Triangles are the most popular drawing primitive. They are managed by all graphics libraries and hardware subsystems, and triangular meshes are thus very common in computer graphics. Very c...

A surface light field is a function that assigns a color to each ray originating on a surface. Surface light fields are well suited to constructing virtual images of shiny objects under complex lighting conditions. This paper presents a framework for construction, compression, interactive rendering, and rudimentary editing of surface light fields of real objects. Generalizations of vector quantization and principal component analysis are used to construct a compressed representation of an object's surface light field from photographs and range scans. A new rendering algorithm achieves interactive rendering of images from the compressed representation, incorporating view-dependent geometric level-of-detail control. The surface light field representation can also be directly edited to yield plausible surface light fields for small changes in surface geometry and reflectance properties.

Conventional wisdom says that in order to produce high-quality simplified polygonal models, one must retain and use information about the original model during the simplification process. We demonstrate that excellent simplified models can be produced without the need to compare against information from the original geometry while performing local changes to the model. We use edge collapses to perform simplification, as do a number of other methods. We select the position of the new vertex so that the original volume of the model is maintained and we minimize the per-triangle change in volume of the tetrahedra swept out by those triangles that are moved. We also maintain surface area near boundaries and minimize the per-triangle area changes. Calculating the edge collapse priorities and the positions of the new vertices requires only the face connectivity and the the vertex locations in the intermediate model. This approach is memory efficient, allowing the simplification of very large polygonal models, and it is also fast. Moreover, simplified models created using this technique compare favorably to a number of other published simplification methods in terms of mean geometric error.

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...

Most systems that support the visual interaction with 3D models use shape representations based on triangle meshes. The size of these representations imposes limits on applications, where complex 3D models must be accessed remotely. Techniques for simplifying and compressing 3D models reduce the transmission time. Multi-resolution formats provide quick access to a crude model and then refine it progressively. Unfortunately, compared to the best non-progressive compression methods, previously proposed progressive refinement techniques impose a significant overhead when the full resolution model must be downloaded. The CPM (Compressed Progressive Meshes) approach proposed here eliminates this overhead. It uses a new “patching ” technique, which refines the topology of the mesh in batches, which each increase the number of vertices by up to 50%. Less than 4 bits per triangle encode where and how the topological refinements should be applied. We estimate the position of new vertices from the positions of their topological neighbors in the less refined mesh using a new estimator that leads to representations of vertex coordinates that are 50 % more compact than previously reported progressive geometry compression techniques. 1.

Many graphics applications, and interactive systems in particular, rely on hierarchical surface representations to efficiently process very complex models. Considerable attention has been focused on hierarchies of surface approximations and their construction via automatic surface simplification. Such representations have proven effective for adapting the level of detail used in real time display systems. However, other applications such as raytracing, collision detection, and radiosity benefit from an alternative multiresolution framework: hierarchical partitions of the original surface geometry. We present a new method for representing a hierarchy of regions on a polygonal surface which partition that surface into a set of face clusters. These clusters, which are connected sets of faces, represent the aggregate properties of the original surface a different scales rather than providing geometric approximations of varying complexity. We also describe the combination of an effective error metric and a novel algorithm for constructing these hierarchies.