Many real-world polygonal surfaces contain topological singularities that represent a challenge for processes such as simplification, compression, and smoothing. We present an algorithm that removes singularities from nonmanifold sets of polygons to create manifold (optionally oriented) polygonal surfaces. We identify singular vertices and edges, multiply singular vertices, and cut through singular edges. In an optional stitching operation, we maintain the surface as a manifold while joining boundary edges. We present two different edge stitching strategies, called pinching and snapping. Our algorithm manipulates the surface topology and ignores physical coordinates. Except for the optional stitching, the algorithm has a linear complexity and requires no floating point operations. In addition to introducing new algorithms, we expose the complexity (and pitfalls) associated with stitching. Finally, several real-world examples are studied.

Geometric models are often annotated to provide additional information during visualization. Maps may be marked with rivers, roads or topographical information, and CAD data models may highlight the underlying mesh structure. While this additional information may be extremely useful, there is a rendering cost associated with it. Texture maps have often been used to convey this information at relatively low cost, but they suffer from blurring and pixelization at high magnification. We present a technique for simplifying surface annotations based on directed, asymmetric tolerance. By maintaining the annotations as geometry, as opposed to textures, we are able to simplify them while still maintaining the overall appearance of the model over a wide range of magnifications. Texture maps may still be used to provide low-resolution surface detail, such as color. We demonstrate a significant gain in rendering performance while retaining the original appearance of objects from many application domains.

In this paper we introduce the Progressive Forest Split (PFS) representation, a new adaptive refinement scheme for storing and transmitting manifold triangular meshes in progressive and highly compressed form. As in the Progressive Mesh (PM) method of Hoppe, a triangular mesh is represented as a low resolution polygonal model followed by a sequence of refinement operations, each one specifying how to add triangles and vertices to the previous level of detail to obtain a new level. The PFS format shares with PM and other refinement schemes the ability to smoothly interpolate between consecutive levels of detail. However, it achieves much higher compression ratios than PM by using a more complex refinement operation which can, at the expense of reduced granularity, be encoded more efficiently. A forest split operation doubling the number n of triangles of a mesh requires a maximum of approximately 3:5n bits to represent the connectivity changes, as opposed to approximately #5 + log 2 #n## n bits in PM. We describe

Many real world polygonal surfaces contain topological singularities that represent a challenge for processes such as simplification, compression, smoothing, etc. We present an algorithm for removing such singularities, thus converting non manifold sets of polygons to manifold polygonal surfaces (orientable if necessary). We identify singular vertices and edges, multiply singular vertices, and cut through singular edges. In an optional stitching phase, we join surface boundary edges that were cut, or whose endpoints are sufficiently close, while guaranteeing that the surface is a manifold. We study two different stitching strategies called "edge pinching" and "edge snapping"; when snapping, special care is required to avoid re-creating singularities. The algorithm manipulates the polygon vertex indices (surface topology) and essentially ignores vertex coordinates (surface geometry). Except for the optional stitching, the algorithm has a linear complexity in the number of vertices edges and faces, and require no floating point operation.

The virtual-reality modeling language (VRML) is rapidly becoming the standard file format for transmitting three-dimensional (3-D) virtual worlds across the Internet. Static and dynamic descriptions of 3-D objects, multimedia content, and a variety of hyperlinks can be represented in VRML files. Both VRML browsers and authoring tools for the creations of VRML files are widely available for several different platforms. In this paper, we describe the topologically assisted geometric compression technology included in our proposal for the VRML compressed binary format. This technology produces significant reduction of file sizes and, subsequently, of the time required for transmission of such filed across the Internet. Compression ratios of 50:1 or more are achieved for large models. The proposal also includes a binary encoding to create compact, rapidly parsable binary VRML files. The proposal is currently being evaluated by the Compressed Binary Format Working Group of the VRML consortium as a possible extension of the VRML standard. In the topologically assisted compression scheme, a polyhedron is represented using two interlocking trees: a spanning tree of vertices and a spanning tree of triangles. The connectivity information represented in other compact schemes, such as triangular strips and generalized triangular meshes, can be directly derived from this representation. Connectivity information for large models is compressed with storage requirements approaching one bit per triangle. A variable-length, optionally lossy compression technique is used for vertex positions, normals, colors, and texture coordinates. The format supports all VRML property binding conventions.