CST: constructive solid trimming for rendering BReps and CSG

Abstract-To eliminate the need to evaluate the intersection curves in explicit representations of surface cutouts or of trimmed faces in BReps of CSG solids, we advocate using Constructive Solid Trimming (CST). A CST face is the intersection of a surface with a Blist representation of a trimming CSG volume. We propose a new GPU-based CSG rendering algorithm that trims the boundary of each primitive using a Blist of its active zone. This approach is faster than the previously reported Blister approach, eliminates occasional speckles of wrongly colored pixels, and provides additional capabilities: painting on surfaces, rendering semitransparent CSG models, and highlighting selected features in the BReps of CSG models.     

BetweenIT: An Interactive Tool for Tight Inbetweening

The generation of inbetween frames that interpolate a given set of key frames is a major component in the production of a 2D feature animation. Our objective is to considerably reduce the cost of the inbetweening phase by offering an intuitive and effective interactive environment that automates inbetweening when possible while allowing the artist to guide, complement, or override the results. Tight inbetweens, which interpolate similar key frames, are particularly time‐consuming and tedious to draw. Therefore, we focus on automating these high‐precision and expensive portions of the process. We have designed a set of user‐guided semi‐automatic techniques that fit well with current practice and minimize the number of required artist‐gestures. We present a novel technique for stroke interpolation from only two keys which combines a stroke motion constructed from logarithmic spiral vertex trajectories with a stroke deformation based on curvature averaging and twisting warps. We discuss our system in the context of a feature animation production environment and evaluate our approach with real production data.     

An unequal error protection method for progressively transmitted 3D models

In this paper, we present a packet-loss resilient system for the transmission of progressively compressed three-dimensional (3D) models. It is based on a joint source and channel coding approach that trades off geometry precision for increased error resiliency to optimize the decoded model quality on the client side. We derive a theoretical framework for the overall system by which the channel packet loss behavior and the channel bandwidth can be directly related to the decoded model quality at the receiver. First, the 3D model is progressively compressed into a base mesh and a number of refinement layers. Then, we assign optimal forward error correction code rates to protect these layers according to their importance to the decoded model quality. Experimental results show that with the proposed unequal error protection approach, the decoded model quality degrades more gracefully (compared to either no error protection or equal error protection methods) as the packet-loss rate increases.     

Blowing Bubbles for Multi-Scale Analysis and Decomposition of Triangle Meshes

Tools for the automatic decomposition of a surface into shape features will facilitate the editing, matching, texturing, morphing, compression and simplification of three-dimensional shapes. Different features, such as flats, limbs, tips, pits and various blending shapes that transition between them, may be characterized in terms of local curvature and other differential properties of the surface or in terms of a global skeletal organization of the volume it encloses. Unfortunately, both solutions are extremely sensitive to small perturbations in surface smoothness and to quantization effects when they operate on triangulated surfaces. Thus, we propose a multi-resolution approach, which not only estimates the curvature of a vertex over neighborhoods of variable size, but also takes into account the topology of the surface in that neighborhood. Our approach is based on blowing a spherical bubble at each vertex and studying how the intersection of that bubble with the surface evolves. We describe an efficient approach for computing these characteristics for a sampled set of bubble radii and for using them to identify features, based on easily formulated filters, that may capture the needs of a particular application.     

Edgebreaker: connectivity compression for triangle meshes

Edgebreaker is a simple scheme for compressing the triangle/vertex incidence graphs (sometimes called connectivity or topology) of three-dimensional triangle meshes. Edgebreaker improves upon the storage required by previously reported schemes, most of which can guarantee only an O(t log(t)) storage cost for the incidence graph of a mesh of t triangles. Edgebreaker requires at most 2t bits for any mesh homeomorphic to a sphere and supports fully general meshes by using additional storage per handle and hole. For large meshes, entropy coding yields less than 1.5 bits per triangle. Edgebreaker's compression and decompression processes perform identical traversals of the mesh from one triangle to an adjacent one. At each stage, compression produces an op-code describing the topological relation between the current triangle and the boundary of the remaining part of the mesh. Decompression uses these op-codes to reconstruct the entire incidence graph. Because Edgebreaker's compression and decompression are independent of the vertex locations, they may be combined with a variety of vertex-compressing techniques that exploit topological information about the mesh to better estimate vertex locations. Edgebreaker may be used to compress the connectivity of an entire mesh bounding a 3D polyhedron or the connectivity of a triangulated surface patch whose boundary need not be encoded. The paper also offers a comparative survey of the rapidly growing field of geometric compression     

Zipper: A compact connectivity data structure for triangle meshes

We propose Zipper, a compact representation of incidence and adjacency for manifold triangle meshes with fixed connectivity. Zipper uses on average only 6 bits per triangle, can be constructed in linear space and time, and supports all standard random-access and mesh traversal operators in constant time. Similarly to the previously proposed LR (Laced Ring) approach, the Zipper construction reorders vertices and triangles along a nearly Hamiltonian cycle called the ring. The 4.4× storage reduction of Zipper over LR results from three contributions. (1) For most triangles, Zipper stores a 2-bit delta (plus three additional bits) rather than a full 32-bit reference. (2) Zipper modifies the ring to reduce the number of exceptional triangles. (3) Zipper encodes the remaining exceptional triangles using 2.5× less storage. In spite of these large savings in storage, we show that Zipper offers comparable performance to LR and other data structures in mesh processing applications. Zipper may also serve as a compact indexed format for rendering meshes, and hence is valuable even in applications that do not require adjacency information.     

HelSweeper: Screw-sweeps of canal surfaces

A tube is a solid bounded by the union of a one-parameter family of circles that may be decomposed into canal-surfaces and planar disks or annuli. A screw-sweep is the region swept by a shape during a screw motion. HelSweeper computes the boundary of a screw-sweep of an arbitrary union of tubes and polyhedra. To do so, it generates a superset of faces, splits them at their intersections, and selects the face portions that form the desired boundary. The novelty of the proposed approach lies in the fact that the faces contributed to this superset by a tube are each a screw-sweeps of a rigid curve (generator), which is the locus of grazing points, and that each grazing point is formulated as the intersection of a circle of the tube with a corresponding screw-plane. Hence, each such face is a one-parameter family of helices, each being the screw-sweep of a grazing point.     

Finally Everyone Can Work With Highly Complex 3D Models

In the past, access to 3D databases was restricted to few specialists having the appropriate CAD skills, software, and graphics hardware. The availability of inexpensive graphics support on personal computers, the Internet’s impact on private and commercial communication, and the emergence of multimedia standards provide the basis for linking CAD databases with other personal productivity and communication tools and for making them accessible to everyone at home, in schools, in hospitals, or in the industry. For example, employees that have no design expertise, customers, and suppliers would benefit from having an easy access to the 3D databases of a company for: collaborative design review, 3D-based multi-media problem reports, collaborative problem solving and tracking, online training and documentation, internet-based part purchasing and subcontracting, demonstration to customers, or advertising. This presentation will address three of the key issues that have so far limited the non-specialist’s access to 3D databases. First-time or occasional non-expert users need to become instant experts in 3D navigation through Virtual Environments or in the interactive manipulation of digital 3D models, so that they may immediately focus on their tasks, and not waste precious time learning and fighting an unnatural user interface. Immersive VR is not the panacea – other more effective techniques show promise. The data complexity found in commercial CAD databases, especially in the automotive, aerospace, and construction industries, significantly exceeds the capabilities of any interactive graphics system. This situation is not likely to change, since the growth of the complexity and availability of 3D models outpaces the performance improvement of personal computers. Research on the automatic simplification of 3D models and on the use of levels of detail to accelerate the rendering of distant portions of the scene is growing rapidly. The still limited bandwidth of internet communication channels prohibits a pervasive access to large amounts of 3D data. Recent 3D compression techniques reduce the storage requirements for polyhedral 3D models by two orders of magnitudes.