De Casteljau Algorithm and Degree Elevation of Toric Surface Patches

De Casteljau algorithm and degree elevation of Bézier and NURBS curves/surfaces are two important techniques in computer aided geometric design. This paper presents the de Casteljau algorithm and degree elevation of toric surface patches, which include tensor product and triangular rational Bézier surfaces as special cases. Some representative examples of toric surface patches with common shapes are illustrated to verify these two algorithms. Moreover, the authors also apply the degree elevation of toric surface patches to isogeometric analysis. And two more examples show the effectiveness of proposed method.

Enhanced efficiency and stability of triple-cation perovskite solar cells with CsPbI_(x)Br_(3−x)QDs“surface patches”

Perovskite solar cells(PSCs)with a light-harvesting three-dimensional perovskite bulk layer as backbone component have achieved great progress in performance.Nonradiative recombination is one major place to improve efficiency and stability as they cause significant energy loss in PSCs.Additionally,an imperfection in grain boundaries will initiate device degradation.One of the most successful strategies to decrease nonradiative recombination in PSCs is the introduction of reduced dimensional perovskite(e.g.,perovskite quantum wells),benefiting the device's efficiency and stability tremendously.Here,instead of quantum wells,mixed-cation perovskites with ligand-contained CsPbBr_(x)I_(3−x)quantum dots(QDs)are prepared,which is shown to function as perovskite healing“surface patches.”Benefiting from the“surface patches”effect,the QDs-film shows reduced defects and enhancing film quality which lead to the excellent performance of solar cells(enhancing the power conversion efficiency from 19.21%of the control device to 21.71%[22.1%in reverse scan]).

BOUNDING PYRAMIDS AND BOUNDING CONES FOR TRIANGULAR BEZIER SURFACES

This paper describes practical approaches on how to construct bounding pyramids and bounding cones for triangular Bezier surfaces. Examples are provided to illustrate the process of construction and comparison is made between various surface bounding volumes. Furthermore, as a starting point for the construction, we provide a way to compute hodographs of triangular Bezier surfaces and improve the algorithm for computing the bounding cone of a set of vectors. [ABSTRACT FROM AUTHOR]

Curvature-Based r-Adaptive Isogeometric Analysis with Injectivity-Preserving Multi-Sided Domain Parameterization

Inspired by the r-refinement method in isogeometric analysis,in this paper,the authors propose a curvature-based r-adaptive isogeometric method for planar multi-sided computational domains parameterized by toric surface patches.The authors construct three absolute curvature metrics of isogeometric solution surface to characterize its gradient information,which is more straightforward and effective.The proposed method takes the internal weights as optimization variables and the resulting parameterization is analysis-suitable and injectivity-preserving with a theoretical guarantee.Several PDEs are solved over multi-sided computational domains parameterized by toric surface patches to demonstrate the effectiveness and efficiency of the proposed method.