Dimensions of Biquadratic and Bicubic Spline Spaces over Hierarchical T-meshes

This paper discusses the dimensions of biquadratic C1 spline spaces and bicubic C2 spline spaces over hierarchical T-meshes using the smoothing cofactor-conformality method. We obtain the dimension formula of biquadratic C1 spline spaces over hierarchical T-meshes in a concise way. In addition, we provide a dimension formula for bicubic C2 spline spaces over hierarchical T-mesh with fewer restrictions than that in the previous literature. A dimension formula for bicubic C2 spline spaces over a new type hierarchical T-mesh is also provided.Comment: 21 pages, 19 figure

The Mask of Odd Points n

We present an explicit formula for the mask of odd points n-ary, for any odd n⩾3, interpolating subdivision schemes. This formula provides the mask of lower and higher arity schemes. The 3-point and 5-point a-ary schemes introduced by Lian, 2008, and (2m+1)-point a-ary schemes introduced by, Lian, 2009, are special cases of our explicit formula. Moreover, other well-known existing odd point n-ary schemes including the schemes introduced by Zheng et al., 2009, can easily be generated by our formula. In addition, error bounds between subdivision curves and control polygons of schemes are computed. It has been noticed that error bounds decrease when the complexity of the scheme decreases and vice versa. Also, as we increase arity of the schemes the error bounds decrease. Furthermore, we present brief comparison of total absolute curvature of subdivision schemes having different arity with different complexity. Convexity preservation property of scheme is also presented

Design of Lingnan Cultural Gene Implantation Cultural and Creative Products Based on Virtual Reality Technology

With the development of virtual reality technology, people are increasingly aware that the combination of virtual reality technology and product design can enable companies to obtain stable profits and maintain long-term competitive advantages. And design evaluation plays a pivotal role in a large number of important decisions in product development. This article takes Lingnan culture and cultural products as an example, combining virtual reality technology with the design of Lingnan cultural and creative products, verifies the effectiveness and rationality of the virtual evaluation system of Lingnan cultural products through the evaluation of examples of Lingnan cultural products, and proposes amendments to the evaluation case. This paper constructs a product design evaluation system based on virtual reality technology and designs a theoretical model VR, which is the application of virtual reality technology in product design evaluation. The PDES system expounds the idea and method of constructing the system model. This paper studies the evaluation object, evaluation content, evaluation method, evaluation platform, and manifestation of evaluation results of the Lingnan cultural product virtual evaluation system and builds the framework of the Lingnan cultural product virtual evaluation system. This paper studies the product display method based on virtual reality technology and realizes the three-dimensional display of products on the Internet and the design of user interaction in virtual reality. In this paper, the two algorithms BRSK and SURF are used together, and the multiscale expression characteristics of BRISK in space and the rotation invariant characteristics of SURF are used. Experimental research shows that, compared with the pure BRISK algorithm, the rotation performance of the method in this paper can be seen through the experimental results in this paper to have better accuracy. The method in this paper ensures the accuracy and accuracy of matching as much as possible