##
Person:
Rossignac,
Jarek

Rossignac,
Jarek

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## Publication Search Results

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1 - 10 of 66

Item

#### 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.

Item

#### 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.

Item

#### 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.

Item

#### Boundary of the Volume Swept By a Free-form Solid in Screw Motion

2006
,
Rossignac, Jarek
,
Kim, J. J.
,
Song, S. C.
,
Suh, K. C.
,
Joung, C. B.

The swept volume of a moving solid provides an excellent aid for path and accessibility planning in robotics and for simulating various manufacturing operations. To compute the boundary of the swept volume, we approximate the motion by a polyscrew (continuous, piecewise-screw), generate candidate faces, compute the two-cells of their arrangement, and use a new point-in-sweep test to select the correct cells whose union forms the boundary of the swept volume.

Item

#### 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.

Item

#### 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.

Item

#### 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.

Item

#### 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.

Item

#### Simulation of Bubbles and Liquid Films

2006
,
Kim, Byungmoon
,
Liu, Yingjie
,
Llamas, Ignacio
,
Rossignac, Jarek

Liquid 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.