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ItemOrthoMap: Homeomorphism-guaranteeing normal-projection map between surfaces(Georgia Institute of Technology, 2004) Chazal, Frederic ; Lieutier, Andre ; Rossignac, JarekConsider two (n—1)-dimensional manifolds, S and Sʹ in Rn. We say that they are projection-homeomorphic when the closest projection of each one onto the other is a homeomorphism. We give tight conditions under which S and Sʹ are projection-homeomorphic. These conditions involve the local feature size for S and for Sʹ and the Hausdorﬀ distance between them. Our results hold for arbitrary n.
ItemSimulation of Bubbles and Liquid Films(Georgia Institute of Technology, 2006) Kim, Byungmoon ; Liu, Yingjie ; Llamas, Ignacio ; Rossignac, JarekLiquid and gas interactions often contain bubbles surrounded by thin liquid films. Simulation of these liquid films is challenging since they quickly become thinner than the grid resolution, which leads to premature bursting or merging of the bubbles. We prevent this thinning process by applying a disjoining force to the film, obtaining bubbles that last much longer without bursting or merging. The surface tension on the liquid film is the next diffuculty. Since the level set is not differentiable at the center of the thin liquid film, the curvature computed from the level set gradient is noisy, and the thin liquid film ruptures quickly. To prevent this, we compute the surface tension from the local isosurface, obtaining long-lasting liquid films. However, since bubbles stay longer without bursting or merging, the volume loss of each bubble is noticeable. To solve this problem, we modify the pressure projection to produce a velocity field whose divergence is controlled by the proportional and integral feedback. This allows us to preserve the volume or, if desired, to inflate or deflate the bubbles. In addition to premature bursting and volume change, another difficulty is the complicated liquid surface, which increases memory and computational costs. To reduce storage requirement, we collocate the velocity and pressure to simplify the octree mesh. To reduce the computational complexity of the pressure projection, we use a multigrid method.
ItemEDGEBREAKER: Compressing the Incidence Graph of Triangle Meshes(Georgia Institute of Technology, 1998) Rossignac, JarekEdgebreaker is a simple scheme for compressing the triangle/vertex incidence graphs (sometimes called topology) of three-dimensional triangle meshes. Edgebreaker improves upon the worst case and the expected compression ratios of previously reported schemes, most of which require O(nlogn) bits to store the incidence graph of a mesh of n triangles. Edgebreaker requires only 2n bits or less for simple meshes and can also support fully general meshes by using additional storage per handle and hole. Edgebreaker's compression and decompression processes perform an identical traversal 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, Edgebreaker 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 transfer the entire surface bounding a 3D polyhedron or only a triangulated surface patch, for which the bounding loops are already known and need not be transferred. Its superior compression capabilities, the simplicity of its implementation, and its versatility make Edgebreaker the perfect candidate for the emerging 3D data exchange standards for interactive graphic applications. The paper sets geometric compression in a formal topological framework and offers a new comparative perspective on prior art.
ItemAn Efficient Subdivision Inversion for Wavemesh-Compression of 3D Triangle Meshes(Georgia Institute of Technology, 2003) Valette, Sebastien ; Rossignac, Jarek ; Prost, RemyWavemesh is a powerful scheme for 3D triangular mesh processing. In sharp contrast with other approaches using wavelets for mesh compression which apply only to meshes having subdivision connectivity, Wavemesh can simplify, approximate, and compress meshes even if they do not respect this constraint, with unmatched results for progressive lossless compression when compared to other approaches. We propose in this paper an improvement for our scheme : higher efficiency for meshes with large subdivision connectivity sets, as shown by experimental results. Also, in some cases, Wavemesh can even perform better than mono-resolution approaches in terms of connectivity compression.
ItemConnectivity Compression for Irregular Quadrilateral Meshes(Georgia Institute of Technology, 1999) King, Davis ; Szymczak, Andrzej ; Rossignac, JarekMany 3D models used in engineering, scientific, and visualization applications are represented by an irregular mesh of bounding quadrilaterals. We propose a scheme for compressing the connectivity of irregular quadrilateral meshes in 0.26-1.7 bits/quad, a 25-45% savings over randomly splitting quads into triangles and applying triangle mesh compression. Our approach is an extension of the Edgebreaker compression approach and of the Wrap&Zip decompression technique.
ItemMultiple Object Selection in Pattern Hierarchies(Georgia Institute of Technology, 2007) Jang, Justin ; Rossignac, JarekHierarchies of patterns of features, of subassemblies, or of CSG sub-expressions are used in architectural and mechanical CAD to eliminate laborious repetitions from the design process. Yet, often the placement, shape, or even existence of a selection of the repeated occurrences in the pattern must be adjusted. The specification of a desired selection of occurrences in a hierarchy of patterns is often tedious (involving repetitive steps) or difficult (requiring interaction with an abstract representation of the hierarchy graph). The OCTOR system introduced here addresses these two drawbacks simultaneously, offering an effective and intuitive solution, which requires only two mouse-clicks to specify any one of a wide range of possible selections. It does not require expanding the graph or storing an explicit list of the selected occurrences and is simple to compute. It is hence well suited for a variety of CAD applications, including CSG, feature-based design, assembly mock-up, and animation. We discuss a novel representation of a selection, a technology that makes it possible to use only two mouse-clicks for each selection, and the persistence of these selections when the hierarchy of patterns is edited.
ItemFlowFixer: Using BFECC for Fluid Simulation(Georgia Institute of Technology, 2005) Kim, Byungmoon ; Liu, Yingjie ; Llamas, Ignacio ; Rossignac, JarekBack and Forth Error Compensation and Correction (BFECC) was recently developed for interface computation by using the level set method. We show that it can be applied to reduce dissipation and diffusion encountered in various advection steps in fluid simulation such as velocity, smoke density and image advections. BFECC can be implemented easily on top of the first order upwinding or semi-Lagrangian integration of advection equations, while providing second order accuracy both in space and time. When applied to level set evolution, BFECC reduces volume loss significantly. We combine these techniques with variable density projection and show that they yield a realistic animations of two-phase flows. We demonstrate the benefits of this approach on the image advection and on the simulation of smoke, of bubbles in water, and of a highly dynamic interaction between water, a solid, and air.
ItemMatchmaker: Manifold Breps for Non-manifold r-sets(Georgia Institute of Technology, 1999) Rossignac, Jarek ; Cardoze, David Enrique FabregaMany solid modeling construction techniques produce non-manifold r-sets (solids). With each non-manifold model N we can associate a family of manifold solid models that are infinitely close to N in the geometric sense. For polyhedral solids, each non-manifold edge of N with 2k incident faces will be replicated k times in any manifold model M of that family. Furthermore, some non-manifold vertices of N must also be replicated in M, possibly several times. M can be obtained by defining, in N, a single adjacent face TA(E,F) for each pair (E,F) that combines an edge E and an incident face F. The adjacency relation satisfies TA(E,TA(E,F))=F. The choice of the map A defines which vertices of N must be replicated in M and how many times. The resulting manifold representation of a non-manifold solid may be encoded using simpler and more compact data-structures, especially for triangulated model, and leads to simpler and more efficient algorithms, when it is used instead of a non-manifold representation for a variety of tasks, such as simplification, compression, interference detection or rendering. Most choices of the map A lead to invalid (self-intersecting) boundaries and to unnecessary vertex replications for M. We propose an efficient algorithm, called Matchmaker, which computes a map A, such that there exists an infinitely small perturbation of the vertices and edges of M that produces a valid (non self-intersecting) boundary of a manifold solid. Furthermore, our approach avoids most unnecessary vertex replications.
ItemDesigning and processing parametric models of steady lattices( 2018) Gupta, Ashish ; Kurzeja, Kelsey ; Rossignac, Jarek ; Allen, George ; Kumar, Pranav Srinivas ; Musuvathy, Suraj ; Georgia Institute of Technology. College of Computing ; Georgia Institute of Technology. School of Interactive ComputingOur goal is to facilitate the design, analysis, optimization, and additive manufacturing of a specific class of 3D lattices that may comprise an extremely large number of elements. We target curved lattices that exhibit periodicity and uniform geometric gradations in three directions, along possibly curved axes. We represent a lattice by a simple computer program with a carefully selected set of exposed control parameters that may be used to adjust the overall shape of the lattice, its repetition count in each direction, its microstructure, and its gradation. In our Programmed-Lattice Editor (PLE), a typical lattice is represented by a short program of 10 to 50 statements. We propose a simple API and a few rudimentary GUI tools that automate the creation of the corresponding expressions in the program. The overall shape and gradation of the lattice is controlled by three similarity transformations. This deliberate design choice ensures that the gradation in each direction is regular (i.e., mathematically steady), that each cell can be evaluated directly, without iterations, and that integral properties (such as surface area, volume, center of mass and spherical inertia) can be obtained rapidly without having to calculate them for each individual element of the lattice.
ItemTetStreamer: Compressed Back-to-Front Transmission of Delaunay Tetrahedra Meshes(Georgia Institute of Technology, 2004) Bischoff, Urs ; Rossignac, JarekWe use the shorts tet and tri for tetrahedron and triangle. TetStreamer encodes a Delaunay tet mesh in a back-to-front visibility order and streams it from a server to a client (volumetric visualizer). During decompression, the server performs the viewdependent back-to-front sorting of the tets by identifying and deactivating one free tet at a time. A tet is free when all its back faces are on the sheet. The sheet is a tri mesh separating active and inactive tets. It is initialized with the back-facing boundary of the mesh. It is compressed using EdgeBreaker and transmitted first. It is maintained by both the server and the client and advanced towards the viewer passing one free tet at a time. The client receives a compressed bit stream indicating where to attach free tets to the sheet. It renders each free tet and updates the sheet by either flipping a concave edge, removing a concave valence-3 vertex, or inserting a new vertex to split a tri. TetStreamer compresses the connectivity of the whole tet mesh to an average of about 1.7 bits per tet. The footprint (in-core memory required by the client) needs only to hold the evolving sheet, which is a small fraction of the storage that would be required by the entire tetmesh. Hence, TetStreamer permits to receive, decompress, and visualize or process very large meshes on clients with a small in-core memory. Furthermore, it permits to use volumetric visualization techniques, which require that the mesh be processed in viewdependent back-to-front order, at no extra memory, performance or transmission cost.