Several efficient constructions of smooth surfaces following the outlines of a polyhedral mesh are based on three-sided patches. To demonstrate that these constructions arc compatible with existing software based on tensor-product patches, the particular scheme in [3] is expressed in terms of linearly-trimmed bicubic patches. Explicit formulas relating the coefficients of the patches to the ver...

In geometric modeling of curves and surfaces, the overall shape of an individual patch is intuitively governed by the placement of control points, and a patch may be finely tuned by altering the weights of the basis functions—large weights pull the patch towards the corresponding control points. The control points also have a global meaning as the patch lies within the convex hull of the contro...

Abstract We consider geometry theorems whose premises and statement comprise a set of bisector conditions. Each premise the can be represented as rows “bisector matrix”: one with three non zero elements per row, element value -2 others 1. The existence theorem corresponds to rank deficiency in this matrix. Our method discovery starts identification deficient matrices. Some such matrices graphs ...

Option price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating the evolution of the risk-neutral density in time. Our method uses bicubic splines in order to achieve the desired smoothness for the e...

The idea of (combinatorial) Gray codes is to list objects in question in such a way that two successive objects differ in some pre-specified small way. In this paper, we utilize β-description trees to cyclicly Gray code three classes of cubic planar maps, namely, bicubic planar maps, 3-connected cubic planar maps, and cubic non-separable planar maps.

The idea of (combinatorial) Gray codes is to list objects in question in such a way that two successive objects differ in some pre-specified small way. In this paper, we utilize β-description trees to cyclicly Gray code three classes of cubic planar maps, namely, bicubic planar maps, 3-connected cubic planar maps, and cubic non-separable planar maps.

The article proposes the use of bicubic spline interpolation to optimize hydraulic and thermal calculations while processing thermodynamic library data. Research was carried out both in single-phase gas liquid regions, as well two-phase gas-liquid region. accuracy tested for various libraries on multi-component mixtures. Various coordinate systems (P, x), T), H), S) were tested, optimal coordin...

This is a supplement to our paper, “NTIRE 2017 Challenge on Single Image Super-Resolution: Dataset and Study” [1]. We report results for the top challenge methods [10]: SNU CVLab1 [6], SNU CVLab2 [6], Lab402 [2] and HelloSR [10] in comparison with VDSR [5] and A+ [12]. We use the classic setup (bicubic downscaling) of the challenge and report PSNR, SSIM [9], IFC [8], and CORNIA [13] results com...

We present a construction of a visually smooth surface which interpolates to position values and normal vectors of randomly distributed points on a 3D object. The method is local and uses quartic triangular and bicubic quadrilateral patches without splits. It heavily relies on an edge deleting algorithm which, starting from a given triangulation, derives a suitable combination of threeand four ...