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 present an algorithm for out-of-core simplification of large polygonal datasets that are too complex to fit in main memory. The algorithm extends the vertex clustering scheme of Rossignac and Borrel [13] by using error quadric information for the placement of each cluster's representative vertex, which better preserves fine details and results in a low mean geometric error. The use of quadrics instead of the vertex grading approach in [13] has the additional benefits of requiring less disk space and only a single pass over the model rather than two. The resulting linear time algorithm allows simplification of datasets of arbitrary complexity. In order

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...

Abstract—Two important tools for manipulating polygonal models are simplification and repair and we present voxel-based methods for performing both of these tasks. We describe a method for converting polygonal models to a volumetric representation in a way that handles models with holes, double walls, and intersecting parts. This allows us to perform polygon model repair simply by converting a model to and from the volumetric domain. We also describe a new topology-altering simplification method that is based on 3D morphological operators. Visually unimportant features such as tubes and holes may be eliminated from a model by the open and close morphological operators. Our simplification approach accepts polygonal models as input, scan converts these to create a volumetric description, performs topology modification, and then converts the results back to polygons. We then apply a topologypreserving polygon simplification technique to produce a final model. Our simplification method produces results that are everywhere manifold. Index Terms—Mesh simplification, mesh repair, volumetric models, morphological operators. æ 1

The growing availability of massive polygonal models, and the inability of most existing visualization tools to work with such data, has created a pressing need for memory efficient methods capable of simplifying very large meshes. In this paper, we present a method for performing adaptive simplification of polygonal meshes that are too large to fit in-core.

We present an algorithm and a system for accelerated display of massive static and dynamic environments using hierarchical simplification. Given a geometric dataset, we represent it using a scene graph and compute levels of detail (LODs) for each node in the graph. We augment the LODs with automatically-generated hierarchical levels of detail (HLODs) that serve as higher fidelity drastic simplifications of entire branches of the scene graph. We extend the algorithm to handle a class of dynamic environments by incrementally recomputing a subset of the HLODs on the fly when objects move. We leverage the properties of the HLOD scene graph in our system, using them to render the environment in a specified image quality or target frame rate mode. The resulting algorithms have been implemented as part of a system named SHAPE. We demonstrate its performance on complex CAD environments composed of tens of millions of polygons. Overall, SHAPE is able to achieve considerable speedups in frame rate with little loss in image quality.

As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because they are either too slow (requiring the simplified model to be pre-computed) or produce models that are too poor in quality. These shortcomings become particularly acute when models are extremely large. We present an algorithm suitable for simplification of large models at interactive speeds. The algorithm is fast and can guarantee displayable results within a given time limit. Results also have good quality. Inspired by splitting algorithms from vector quantization literature, we simplify models in reverse, beginning with an extremely coarse approximation and refining it. Approximations of surface curvature guide the simplification process. Previously produced simplifications can be further refined by using them as input to the algorithm. 1

We present a new approach for simplifying polygonal objects. Our method is general in that it works on models that contain both non-manifold geometry and surface attributes. It is automatic since it requires no user input to execute and returns approximate error bounds used to calculate switching distances between levels of detail, or LODs. Our algorithm, called General and Automatic Polygonal Simplification, or GAPS for short, uses an adaptive distance threshold and surface area preservation along with a quadric error metric to join unconnected regions of an object. Its name comes from this ability to "fill in the gaps" of an object. Our algorithm uses a new object space error metric that combines approximations of geometric and surface attribute error. GAPS efficiently produces high quality and drastic simplifications of a wide variety of objects, including complicated pipe structures. This ability to perform drastic simplification allows us to create levels of detail to accelerate t...

We introduce the permission grid, a spatial occupancy grid used to guide almost any standard polygonal surface simplification algorithm into generating an approximation with a guaranteed geometric error bound. In particular, the distance between any point on the approximation and the original surface is bounded by a user-specified tolerance. Such bounds are notably absent from most current simplification methods, and are becoming increasingly important for applications such as collision detection and scientific computing. Conceptually simple, the permission grid defines a volume in which the approximation must lie, and does not permit the underlying simplification algorithm to generate approximations outside of this volume. The permission grid makes three important, practical improvements over current error-bounded simplification methods. First, it works on arbitrary triangular models, handling all manners of mesh degeneracies gracefully. Further, the error tolerance may be expanded as simplification proceeds, allowing the construction

This paper presents a framework that uses the outputs of model simplification to guide the construction of bounding volume hierarchies for use in, for example, collision detection. Simplified models, besides their application to multiresolution rendering, can provide clues to the object’s shape. These clues help in the partitioning of the object’s model into components that may be more tightly bounded by simple bounding volumes. The framework naturally employs both the bottom-up and the topdown approaches of hierarchy building, and thus can have the advantages of both approaches. Experimental results show that our method built on top of the framework can indeed improve the bounding volume hierarchy, and as a result, significantly speedup the collision detection.