Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic Methods for Geometric Modeling via Spherical Decomposition   Analytic methods are emerging in solid and configuration modeling, while
providing new insights into a variety of shape and motion related problems by
exploiting tools from group morphology, convolution algebras, and harmonic
analysis. However, most convolution-based methods have used uniform grid-based
sampling to take advantage of the fast Fourier transform (FFT) algorithm. We
propose a new paradigm for more efficient computation of analytic correlations
that relies on a grid-free discretization of arbitrary shapes as countable
unions of balls, in turn described as sublevel sets of summations of smooth
radial kernels at adaptively sampled 'knots'. Using a simple geometric lifting
trick, we interpret this combination as a convolution of an impulsive skeletal
density and primitive kernels with conical support, which faithfully embeds
into the convolution formulation of interactions across different objects. Our
approach enables fusion of search-efficient combinatorial data structures
prevalent in time-critical collision and proximity queries with analytic
methods popular in path planning and protein docking, and outperforms uniform
grid-based FFT methods by leveraging nonequispaced FFTs. We provide example
applications in formulating holonomic collision constraints, shape
complementarity metrics, and morphological operations, unified within a single
analytic framework.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn