28,517 research outputs found
L-systems in Geometric Modeling
We show that parametric context-sensitive L-systems with affine geometry
interpretation provide a succinct description of some of the most fundamental
algorithms of geometric modeling of curves. Examples include the
Lane-Riesenfeld algorithm for generating B-splines, the de Casteljau algorithm
for generating Bezier curves, and their extensions to rational curves. Our
results generalize the previously reported geometric-modeling applications of
L-systems, which were limited to subdivision curves.Comment: In Proceedings DCFS 2010, arXiv:1008.127
Index Information Algorithm with Local Tuning for Solving Multidimensional Global Optimization Problems with Multiextremal Constraints
Multidimensional optimization problems where the objective function and the
constraints are multiextremal non-differentiable Lipschitz functions (with
unknown Lipschitz constants) and the feasible region is a finite collection of
robust nonconvex subregions are considered. Both the objective function and the
constraints may be partially defined. To solve such problems an algorithm is
proposed, that uses Peano space-filling curves and the index scheme to reduce
the original problem to a H\"{o}lder one-dimensional one. Local tuning on the
behaviour of the objective function and constraints is used during the work of
the global optimization procedure in order to accelerate the search. The method
neither uses penalty coefficients nor additional variables. Convergence
conditions are established. Numerical experiments confirm the good performance
of the technique.Comment: 29 pages, 5 figure
A Bayesian Approach to Manifold Topology Reconstruction
In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated
Discrete denoising of heterogenous two-dimensional data
We consider discrete denoising of two-dimensional data with characteristics
that may be varying abruptly between regions.
Using a quadtree decomposition technique and space-filling curves, we extend
the recently developed S-DUDE (Shifting Discrete Universal DEnoiser), which was
tailored to one-dimensional data, to the two-dimensional case. Our scheme
competes with a genie that has access, in addition to the noisy data, also to
the underlying noiseless data, and can employ different two-dimensional
sliding window denoisers along distinct regions obtained by a quadtree
decomposition with leaves, in a way that minimizes the overall loss. We
show that, regardless of what the underlying noiseless data may be, the
two-dimensional S-DUDE performs essentially as well as this genie, provided
that the number of distinct regions satisfies , where is the total
size of the data. The resulting algorithm complexity is still linear in both
and , as in the one-dimensional case. Our experimental results show that
the two-dimensional S-DUDE can be effective when the characteristics of the
underlying clean image vary across different regions in the data.Comment: 16 pages, submitted to IEEE Transactions on Information Theor
Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Holder constants
In this paper, the global optimization problem with
being a hyperinterval in and satisfying the Lipschitz condition
with an unknown Lipschitz constant is considered. It is supposed that the
function can be multiextremal, non-differentiable, and given as a
`black-box'. To attack the problem, a new global optimization algorithm based
on the following two ideas is proposed and studied both theoretically and
numerically. First, the new algorithm uses numerical approximations to
space-filling curves to reduce the original Lipschitz multi-dimensional problem
to a univariate one satisfying the H\"{o}lder condition. Second, the algorithm
at each iteration applies a new geometric technique working with a number of
possible H\"{o}lder constants chosen from a set of values varying from zero to
infinity showing so that ideas introduced in a popular DIRECT method can be
used in the H\"{o}lder global optimization. Convergence conditions of the
resulting deterministic global optimization method are established. Numerical
experiments carried out on several hundreds of test functions show quite a
promising performance of the new algorithm in comparison with its direct
competitors.Comment: 26 pages, 10 figures, 4 table
Physical bounds and radiation modes for MIMO antennas
Modern antenna design for communication systems revolves around two extremes:
devices, where only a small region is dedicated to antenna design, and base
stations, where design space is not shared with other components. Both imply
different restrictions on what performance is realizable. In this paper
properties of both ends of the spectrum in terms of MIMO performance is
investigated. For electrically small antennas the size restriction dominates
the performance parameters. The regions dedicated to antenna design induce
currents on the rest of the device. Here a method for studying fundamental
bound on spectral efficiency of such configurations is presented. This bound is
also studied for -degree MIMO systems. For electrically large structures the
number of degrees of freedom available per unit area is investigated for
different shapes. Both of these are achieved by formulating a convex
optimization problem for maximum spectral efficiency in the current density on
the antenna. A computationally efficient solution for this problem is
formulated and investigated in relation to constraining parameters, such as
size and efficiency
Semi-Automated SVG Programming via Direct Manipulation
Direct manipulation interfaces provide intuitive and interactive features to
a broad range of users, but they often exhibit two limitations: the built-in
features cannot possibly cover all use cases, and the internal representation
of the content is not readily exposed. We believe that if direct manipulation
interfaces were to (a) use general-purpose programs as the representation
format, and (b) expose those programs to the user, then experts could customize
these systems in powerful new ways and non-experts could enjoy some of the
benefits of programmable systems.
In recent work, we presented a prototype SVG editor called Sketch-n-Sketch
that offered a step towards this vision. In that system, the user wrote a
program in a general-purpose lambda-calculus to generate a graphic design and
could then directly manipulate the output to indirectly change design
parameters (i.e. constant literals) in the program in real-time during the
manipulation. Unfortunately, the burden of programming the desired
relationships rested entirely on the user.
In this paper, we design and implement new features for Sketch-n-Sketch that
assist in the programming process itself. Like typical direct manipulation
systems, our extended Sketch-n-Sketch now provides GUI-based tools for drawing
shapes, relating shapes to each other, and grouping shapes together. Unlike
typical systems, however, each tool carries out the user's intention by
transforming their general-purpose program. This novel, semi-automated
programming workflow allows the user to rapidly create high-level, reusable
abstractions in the program while at the same time retaining direct
manipulation capabilities. In future work, our approach may be extended with
more graphic design features or realized for other application domains.Comment: In 29th ACM User Interface Software and Technology Symposium (UIST
2016
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