Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nielson-type transfinite triangular interpolants by means of quadratic
  energy functional optimizations   We generalize the transfinite triangular interpolant of (Nielson, 1987) in
order to generate visually smooth (not necessarily polynomial) local
interpolating quasi-optimal triangular spline surfaces. Given as input a
triangular mesh stored in a half-edge data structure, at first we produce a
local interpolating network of curves by optimizing quadratic energy
functionals described along the arcs as weighted combinations of squared length
variations of first and higher order derivatives, then by optimizing weighted
combinations of first and higher order quadratic thin-plate-spline-like
energies we locally interpolate each curvilinear face of the previous curve
network with triangular patches that are usually only $C^0$ continuous along
their common boundaries. In a following step, these local interpolating optimal
triangular surface patches are used to construct quasi-optimal continuous
vector fields of averaged unit normals along the joints, and finally we extend
the $G^1$ continuous transfinite triangular interpolation scheme of (Nielson,
1987) by imposing further optimality constraints concerning the isoparametric
lines of those groups of three side-vertex interpolants that have to be
convexly blended in order to generate the final visually smooth local
interpolating quasi-optimal triangular spline surface. While we describe the
problem in a general context, we present examples in special polynomial,
trigonometric, hyperbolic and algebraic-trigonometric vector spaces of
functions that may be useful both in computer-aided geometric design and in
computer graphics.

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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: econ