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Deep learning based methods have penetrated many image processing problems and become dominant solutions to these problems. A natural question raised here is "Is there any space for conventional methods on these problems?" In this paper,…
In this study, we investigate and compare formulations for computing shape derivatives in bi-material level-set optimization with precise modeling of the interface. The level-set function is parameterized using B-splines, whose coordinates…
This paper derives strong relations that boundary curves of a smooth complex of patches have to obey when the patches are computed by local averaging. These relations restrict the choice of reparameterizations for geometric continuity. In…
This paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and…
Multi-sided surfaces are often defined by side interpolants (also called ribbons), i.e. the surface has to connect to the ribbons with a prescribed degree of smoothness. The I-patch is such a family of implicit surfaces capable of…
We present a learning-based method for interpolating and manipulating 3D shapes represented as point clouds, that is explicitly designed to preserve intrinsic shape properties. Our approach is based on constructing a dual encoding space…
Interpolation and smoothing using cubic and generalized splines are fundamental tools in data analysis and statistical modeling. Recently, fast computational algorithms were developed for natural $L$-splines of order four, which arise as…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
In this short note we describe a simple adaptation of biharmonic surfaces to interpolate boundary cross-derivatives given in ribbon form, and compare with the recently proposed Generalized B-spline patches.
Porous structures are widely used in various industries because of their excellent properties. Porous surfaces have no thickness and should be thickened to sheet structures for further fabrication. However, conventional methods for…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a…
In this paper, we focus on model reduction of large-scale bilinear systems. The main contributions are threefold. First, we introduce a new framework for interpolatory model reduction of bilinear systems. In contrast to the existing methods…
Shell analysis is a well-established field, but achieving optimal higher-order convergence rates for such simulations is a difficult challenge. We present an isogeometric Kirchhoff-Love shell framework that treats every numerical aspect in…
Generating continuous surfaces from discrete point cloud data is a fundamental task in several 3D vision applications. Real-world point clouds are inherently noisy due to various technical and environmental factors. Existing data-driven…
In this paper, the construction of $C^{1}$ cubic quasi-interpolants on a three-direction mesh of $\RR^{2}$ is addressed. The quasi-interpolating splines are defined by directly setting their Bernstein-B\'{e}zier coefficients relative to…
Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or…
Porous structures are intricate solid materials with numerous small pores, extensively used in fields like medicine, chemical engineering, and aerospace. However, the design of such structures using computer-aided tools is a time-consuming…
Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects…
The exponential B-spline basis function set is used to develop a collocation method for some initial boundary value problems (IBVPs) to the Gardner equation. The Gardner equation has two nonlinear terms, namely quadratic and cubic ones. The…