248,638 research outputs found
Shape Representation Using a Generalized Potential Field Model
Abstract-This paper is concerned with efficient derivation of the medial axis transform of a two-dimensional polygonal region. Instead of using the shortest distance to the region border, a potential field model is used for computational efficiency. The region border is assumed to be charged and the valleys of the resulting potential field are used to estimate the axes for the medial axis transform. The potential valleys are found by following force field, thus, avoiding twodimensional search. The potential field is computed in closed form using the equations of the border segments. The simple Newtonian potential is shown to be inadequate for this purpose. A higher order potential is defined which decays faster with distance than as inverse of distance. It is shown that as the potential order becomes arbitrarily large, the axes approach those computed using the shortest distance to the border. Algorithms are given for the computation of axes, which can run in linear parallel time for part of the axes having initial guesses. Experimental results are presented for a number of examples
Generalized Debye Sources Based EFIE Solver on Subdivision Surfaces
The electric field integral equation is a well known workhorse for obtaining
fields scattered by a perfect electric conducting (PEC) object. As a result,
the nuances and challenges of solving this equation have been examined for a
while. Two recent papers motivate the effort presented in this paper. Unlike
traditional work that uses equivalent currents defined on surfaces, recent
research proposes a technique that results in well conditioned systems by
employing generalized Debye sources (GDS) as unknowns. In a complementary
effort, some of us developed a method that exploits the same representation for
both the geometry (subdivision surface representations) and functions defined
on the geometry, also known as isogeometric analysis (IGA). The challenge in
generalizing GDS method to a discretized geometry is the complexity of the
intermediate operators. However, thanks to our earlier work on subdivision
surfaces, the additional smoothness of geometric representation permits
discretizing these intermediate operations. In this paper, we employ both ideas
to present a well conditioned GDS-EFIE. Here, the intermediate surface
Laplacian is well discretized by using subdivision basis. Likewise, using
subdivision basis to represent the sources, results in an efficient and
accurate IGA framework. Numerous results are presented to demonstrate the
efficacy of the approach
Unified treatment of the Coulomb and harmonic oscillator potentials in dimensions
Quantum mechanical models and practical calculations often rely on some
exactly solvable models like the Coulomb and the harmonic oscillator
potentials. The dimensional generalized Coulomb potential contains these
potentials as limiting cases, thus it establishes a continuous link between the
Coulomb and harmonic oscillator potentials in various dimensions. We present
results which are necessary for the utilization of this potential as a model
and practical reference problem for quantum mechanical calculations. We define
a Hilbert space basis, the generalized Coulomb-Sturmian basis, and calculate
the Green's operator on this basis and also present an SU(1,1) algebra
associated with it. We formulate the problem for the one-dimensional case too,
and point out that the complications arising due to the singularity of the
one-dimensional Coulomb problem can be avoided with the use of the generalized
Coulomb potential.Comment: 18 pages, 3 ps figures, revte
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