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Rossignac, Jarek

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Now showing 1 - 10 of 71
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    SQUINT Fields, Maps, Patterns, and Lattices
    (Georgia Institute of Technology, 2018-07-23) Rossignac, Jarek
    The proposed Steady QUad INTerpolating (SQUINT) map is formulated in terms of a SQUINT Field of Similarities (FoS). It is controlled by four coplanar points. It maps the unit square onto a curved planar quad, R, which has these points as corners. Uniformly spaced, log-spiral isocurves decompose R into tiles that are similar to each other and, hence, each have equal angles at opposite corners. We provide closed-form expressions for computing the representation of the SQUINT map and for evaluating the map and its inverse. We discuss extensions and potential applications to texture maps and field warps and to the design, display, and constant-cost query of procedural models of arbitrarily complex lattices.
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    Permutation Classifier
    (Georgia Institute of Technology, 2018-04-24) Zhou, Xinrui ; Guerra, Concettina ; Rossignac, Jarek ; Rossignac-Milon, Leo
    We consider permutations of a given set of n different symbols. We are given two unordered training sets, T1 and T2, of such permutations that are each assumed to contain examples of permutations of the corresponding type, t1 and t2. Our goal is to train a classifier, C(q), by computing a statistical model from T1 and T2, which, when given a candidate permutation, q, decides whether q is of type t1 or t2. We discuss two versions of this problem. The ranking version focuses on the order of the symbols. Our Separation Average Distance Matrix (SADiM) solution expands on previously proposed ranking aggregation formulations. The grouping version focuses on contiguity of symbols and hierarchical grouping. We propose and compare two solutions: (1) The Population Augmentation Ratio (PAR) solution computes a PQ-tree for each training set and uses a novel measure of distance between these and q that is based on ratios of population counts (i.e., of numbers of permutations explained by specific PQ-trees). (2) The Difference of Positions (DoP) solution is computationally less expensive than PAR and is independent of the absolute population counts. Although DoP does not have the simple statistical grounding of PAR, our experiments show that it is consistently effective.
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    Designing and processing parametric models of steady lattices
    ( 2018) Gupta, Ashish ; Kurzeja, Kelsey ; Rossignac, Jarek ; Allen, George ; Kumar, Pranav Srinivas ; Musuvathy, Suraj
    Our 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.
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    RangeFinder: Accelerating ball-interference queries against steady lattices
    (Georgia Institute of Technology, 2018) Kurzeja, Kelsey ; Rossignac, Jarek
    Advances in additive manufacturing techniques are enabling the fabrication of new microstructures and materials. These may often be defined in terms of a set of balls and of beams that each connects two balls. To support application needs, we must support lattices with billions of such elements. To address this problem, we focus on architected and periodic structures in which the connectivity pattern repeats in three directions, and in which the positions and radii of the balls evolve through the structure in a prescribed and steady way that is defined by three similarity transforms. We propose here an algorithm that accelerates the Ball-Interference Query (BIQ), which establishes which elements of the lattice interfere with a query ball Q. Our RangeFinder (RF) solution reduces the asymptotic complexity of BIQs, which, in our tests, reduced the query time by a factor of between 45 and 5500. RF does not use any spatial occupancy data structure and can be trivially parallelized. We demonstrate the effectiveness of RangeFinder through the generation of multi-level lattices that we call Lattice-in-Lattice (LiL).
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    SOT: Compact Representation for Triangle and Tetrahedral Meshes
    (Georgia Institute of Technology, 2010) Rossignac, Jarek ; Gurung, Topraj
    The Corner Table (CT) represents a triangle mesh by storing 6 integer references per triangle (3 vertex references in the Vertex table and 3 references to opposite corners in the Opposite table, which accelerate access to adjacent triangles). The Compact Half Face (CHF) representation extends CT to tetrahedral meshes, storing 8 references per tetrahedron (4 in the Vertex table and 4 in the Opposite table). We use the term Vertex Opposite Table (VOT) to refer to both CT and CHF and propose a sorted variation, SVOT, which is inspired by tetrahedral mesh encoding techniques and which works for both triangle and tetrahedral meshes. The SVOT does not require additional storage and yet provides, for each vertex, a reference to an incident corner from which the star (incident cells) of the vertex may be traversed at a constant cost per visited element. We use the corner operators for querying and traversing the triangle meshes while for tetrahedral meshes, we propose a set of powerful wedge-based operators. Improving on the SVOT, we propose our Sorted Opposite Table (SOT) variation, which eliminates the Vertex table completely and hence reduces storage requirements by 50% to only 3 references per triangle for triangle meshes and 4 references and 9 bits per tetrahedron for tetrahedral meshes, while preserving the vertex-to-incident-corner references and supporting the corner operators and our wedge operators with a constant average cost. The SVOT and SOT representation work on manifold meshes with boundaries.
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    SAM: Steady Affine Motions
    (Georgia Institute of Technology, 2009-11-23) Rossignac, Jarek ; Vinacua, Àlvar
    An affine motion is a continuous map from time value t to an affinity A subscript t. It is a SAM (Steady Affine Motion), when A subscript t = A superscript t. Although the beauty of a motion is subjective, the above equation provides one mathematical characterization and includes the screw ("universal instantaneous") motion and the golden ("mirabilis") spiral. Although a real matrix, A superscript t, may not exist, we show that it does for a dense set of affinities A covering a significant range of rotations and shears around the identity and that it may be computed efficiently and robustly in two and three dimensions using closed form expressions. SAMs have remarkable properties. For example, the velocity of any point remains constant, both in the global (fixed) and local (moving) frames, which facilitates the exact computation of derived entities, such as the envelope surfaces used to define the boundary of a swept volume. We say that a pattern of features F subscript i is steady when there exists an affinity M such that F subscript i = M superscript i F subscript 0. Each M superscript i is a frame of a SAM and may be computed as A superscript (i/n), where A is the afiine relation F subscript n = A F subscript 0 between the first and the last feature. This option makes it possible to edit directly the feature count n or the cumulative transformation A.
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    Open challenges in shape and animation processing
    (Georgia Institute of Technology, 2009-08-28) Rossignac, Jarek
    Jarek Rossignac (IC, http://www.gvu.gatech.edu/~jarek/) will present an overview of his recent research activities (with collaborators and students) and open challenges in shape and animation processing. These include: - SOT: Compact representation of tetrahedral meshes - J-splines: C^4 subdivision curves, surfaces, and animation - SAM: Steady interpolating affine motion - OCTOR: Exceptions in steady patterns - Pearling: Realtime segmentation of tubular structures in images and 3D medical scans - Surgem: Heart surgery planning and optimization based on blood flow simulation - APL: Aquatic Propulsion Lab, tools for designing and simulating swimming strategies - Ball map: Tangent-ball correspondence and compatibility between pairs of shapes - Ball-morph: Interpolation and applications to entertainment and medical surface reconstruction.
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    ITR/PE+SY digital clay for shape input and display
    (Georgia Institute of Technology, 2007-11-30) Book, Wayne J. ; Rossignac, Jarek ; Mynatt, Elizabeth D. ; Allen, Mark G. ; Goldthwaite, John Randall ; Rosen, David W. ; Glezer, Ari
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    Optimized Blist Form (OBF)
    (Georgia Institute of Technology, 2007-05-23) Rossignac, Jarek
    Any Boolean expressions may be converted into positive-form, which has only union and intersection operators. Let E be a positive-form expression with n literals. Assume that the truth-values of the literals are read one at a time. The numbers s(n) of steps (operations) and b(n) of working memory bits (footprint) needed to evaluate E depend on E and on the evaluation technique. A recursive evaluation performs s(n)=n–1 steps but requires b(n)=log(n)+1 bits. Evaluating the disjunctive form of E uses only b(n)=2 bits, but may lead to an exponential growth of s(n). We propose a new Optimized Blist Form (OBF) that requires only s(n)=n steps and b(n)=⌈log2j⌉ bits, where j=⌈log2(2n/3+2)⌉. We provide a simple and linear cost algorithm for converting positive-form expressions to their OBF. We discuss three applications: (1) Direct CSG rendering, where a candidate surfel stored at a pixel is classified against an arbitrarily complex Boolean expression using a footprint of only 6 stencil bits; (2) the new Logic Matrix (LM), which evaluates any positive form logical expression of n literals in a single cycle and uses a matrix of at most n×j wire/line connections; and (3) the new Logic Pipe (LP), which uses n gates that are connected by a pipe of ⌈log2j⌉ lines and when receiving a staggered stream of input vectors produces a value of a logical expression at each cycle.
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    Multiple Object Selection in Pattern Hierarchies
    (Georgia Institute of Technology, 2007) Jang, Justin ; Rossignac, Jarek
    Hierarchies 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.