2,363 research outputs found
Smooth quasi-developable surfaces bounded by smooth curves
Computing a quasi-developable strip surface bounded by design curves finds
wide industrial applications. Existing methods compute discrete surfaces
composed of developable lines connecting sampling points on input curves which
are not adequate for generating smooth quasi-developable surfaces. We propose
the first method which is capable of exploring the full solution space of
continuous input curves to compute a smooth quasi-developable ruled surface
with as large developability as possible. The resulting surface is exactly
bounded by the input smooth curves and is guaranteed to have no
self-intersections. The main contribution is a variational approach to compute
a continuous mapping of parameters of input curves by minimizing a function
evaluating surface developability. Moreover, we also present an algorithm to
represent a resulting surface as a B-spline surface when input curves are
B-spline curves.Comment: 18 page
Gn blending multiple surfaces in polar coordinates
International audienceThis paper proposes a method of Gn blending multiple parametric surfaces in polar coordinates. It models the geometric continuity conditions of parametric surfaces in polar coordinates and presents a mechanism of converting a Cartesian parametric surface into its polar coordinate form. The basic idea is first to reparameterize the parametric blendees into the form of polar coordinates. Then they are blended simultaneously by a basis function in the complex domain. To extend its compatibility, we also propose a method of converting polar coordinate blending surface into N NURBS patches. One application of this technique is to fill N-sided holes. Examples are presented to show its feasibility and practicability
Ordinal proportional cost sharing
We consider cost sharing problems with variable demands of heterogeneous goods. We study the compatibility of two axioms imposed on cost sharing methods: ordinality and average cost pricing for homogeneous (ACPH) goods. We generalize the ordinal proportional method (OPM) for the two-agent case, Sprumont [Journal of Economic Theory 81 (1998) 126162] to arbitrary number of agents
Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals
This paper studies nonparametric estimation of conditional moment models in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite dimensional function parameter space. Some of the PSMD procedures use slowly growing finite dimensional sieves with flexible penalties or without any penalty; some use large dimensional sieves with lower semicompact and/or convex penalties. We establish their consistency and the convergence rates in Banach space norms (such as a sup-norm or a root mean squared norm), allowing for possibly non-compact infinite dimensional parameter spaces. For both mildly and severely ill-posed nonlinear inverse problems, our convergence rates in Hilbert space norms (such as a root mean squared norm) achieve the known minimax optimal rate for the nonparametric mean IV regression. We illustrate the theory with a nonparametric additive quantile IV regression. We present a simulation study and an empirical application of estimating nonparametric quantile IV Engel curves.Nonlinear ill-posed inverse, Penalized sieve minimum distance, Modulus of continuity, Convergence rate, Nonparametric additive quantile IV, Quantile IV Engel curves
The INTERNODES method for the treatment of non-conforming multipatch geometries in Isogeometric Analysis
In this paper we apply the INTERNODES method to solve second order elliptic
problems discretized by Isogeometric Analysis methods on non-conforming
multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based
method that, on each interface of the configuration, exploits two independent
interpolation operators to enforce the continuity of the traces and of the
normal derivatives. INTERNODES supports non-conformity on NURBS spaces as well
as on geometries. We specify how to set up the interpolation matrices on
non-conforming interfaces, how to enforce the continuity of the normal
derivatives and we give special attention to implementation aspects. The
numerical results show that INTERNODES exhibits optimal convergence rate with
respect to the mesh size of the NURBS spaces an that it is robust with respect
to jumping coefficients.Comment: Accepted for publication in Computer Methods in Applied Mechanics and
Engineerin
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