Person:
Rossignac, Jarek

Associated Organization(s)
Organizational Unit
School of Interactive Computing
School established in 2007
ORCID
ArchiveSpace Name Record

Publication Search Results

Now showing 1 - 10 of 66
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SAM: Steady Affine Motions

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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Optimized Blist Form (OBF)

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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Pressing: Smooth Isosurfaces with Flats from Binary Grids

2007 , Chica, Antonio , Williams, Jason , Andujar, Carlos , Brunet, Pere , Navazo, Isabel , Rossignac, Jarek , Vinacua, Alvar

We explore the automatic recovery of solids from their binary volumetric discretizations. In particular, we propose an approach, called Pressing, for smoothing isosurfaces extracted from binary volumes while recovering their large planar regions (flats). Pressing yields a surface that is guaranteed to contain the samples of the volume classified as interior and exclude those classified as exterior. It uses global optimization to identify flats and constrained bilaplacian smoothing to eliminate sharp features and high-frequencies from the rest of the isosurface. It recovers sharp edges between flat regions and between flat and smooth regions. Hence, the resulting isosurface is usually a very accurate approximation of the original solid. Furthermore, the segmentation of the isosurface into flat and curved faces and the sharp/smooth labelling of their edges may be valuable for shape recognition, simplification, compression, and various reverse engineering and manufacturing applications.

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Ball-map: Homeomorphism Between Compatible Surfaces

2006 , Chazal, Frederic , Lieutier, Andre , Rossignac, Jarek , Whited, Brian

We introduce the ball-map, BM [subscript S],[subscript T], between two manifolds, S and T. It maps each point x of S to a point x = BM[subscript S],[subscript T](x) of T. Its inverse is BM[subscript T],[subscript S]. We define conditions for BM[subscript S],[subscript T] to be a homeomorphism. We show that they hold when the minimum feature size of each surface exceeds their Hausdorff distance. We show that, when S and T are C[superscript k] (n-1)-manifolds in R[superscript n], BM[subscript T],[subscript S] is a C[superscript k-1] diffeomorphism and defines a C[superscript k-1] ambient isotopy that smoothly morphs between S to T. In practice, the ball-map yields an excellent map for transferring parameterizations and textures between ball compatible curves or surfaces. Furthermore, it may be used to define a morph, during which each point x of S travels to the corresponding point y of T along a circular arc that is normal to S at x and to T at y.

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Open challenges in shape and animation processing

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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Simulation of Bubbles in Foam With The Volume Control Method

2007 , Kim, Byungmoon , Liu, Yingjie , Llamas, Ignacio , Jiao, Xiangmin , Rossignac, Jarek

Liquid and gas interactions often produce bubbles that stay for a long time without bursting on the surface, making a dry foam structure. Such long lasting bubbles simulated by the level set method can suffer from a small but steady volume error that accumulates to a visible amount of volume change. We propose to address this problem by using the volume control method. We track the volume change of each connected region, and apply a carefully computed divergence that compensates undesired volume changes. To compute the divergence, we construct a mathematical model of the volume change, choose control strategies that regulate the modeled volume error, and establish methods to compute the control gains that provide robust and fast reduction of the volume error, and (if desired) the control of how the volume changes over time.

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Ringing Js refinements

2007 , Schaefer, Scott , Rossignac, Jarek

Both the four-point and the uniform cubic B-spline refinement (i.e. subdivision) schemes double the number of vertices of a closed-loop polygonal curve jP and respectively produce sequences of vertices fk and bk. The Js refinement proposed here produces vertices vk=(1-s)fk+sbk. Iterative applications of Js yield a family of curves parameterized by s. It includes the four-point curve (J0), the uniform cubic B-spline (J8/8), and the quintic B-spline (J12/8). Iterating Js converges to a C2 curve for 0[less than]s[less than]1, to a C3 curve for 1[less than or equal to]s[less than]3/2, and to a C4 curve for s=S3/2. J3/8 tends to reduce the error between consecutive refinements and is useful to reduce popping when switching levels-of-detail in multi-resolution rendering. J4/8 produces the Jarek curve, which, in 2D, encloses a surface area that is usually very close to the area enclosed by the original control polygon 0P. We propose model-dependent and model-independent optimizations for these parameter values. As other refinement schemes, the Js approach extends trivially to open curves, animations, and surfaces. To reduce memory requirements when evaluating the final refined curve, surface, or animation, we introduce a new evaluation technique, called Ringing. It requires a footprint of only 5 points per subdivision level for each curve and does not introduce any redundant calculations.

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ITR/PE+SY digital clay for shape input and display

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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Multiple Object Selection in Pattern Hierarchies

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.

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CST: Constructive Solid Trimming for Rendering BReps and CSG

2006 , Hable, John , Rossignac, Jarek

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, which 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.