A Review of T-spline Surfaces

Background: Curved modeling technology originated from the geometric lofting and design of aircrafts, automobiles and ships. The control points of the traditional B-spline mesh should be placed regularly in whole rows and columns. A T-spline surface is a B-spline surface that allows T-junctions. It can overcome the limitations of traditional B-mesh topology and has its own advantages in surface splicing, surface fining, surface simplification, etc. T-spline has wide application prospects in product modeling, art design, animation production, numerical control machining, volume data expression, and other aspects. Objective: The objective of this paper is to summarize the properties, algorithms, and applications of T-splines. It helps scholars in determining the research status of T-splines and in further exploring the theories related to the applications of T-splines. Methods: This paper reviews the theories on T-splines and their applications from four aspects. First, we discuss the development of the concept, properties, and algorithms of T-splines and the Tspline reconstruction. Then, we conducted an isogeometric analysis using T-splines. Next, we demonstrate the applications of T-splines in actual scenarios. Finally, we present a brief summary of the paper and expectations for the future. Results: The paper provides a brief introduction to the relevant papers on T-splines. The research on T-spline technology is currently active, and there are many studies on T-spline theories and applications. Among these, the spline theory on T-mesh has aroused widespread interest in engineering, especially in Computer-Aided Geometric Design (CAGD) and computer graphics. Conclusion: The T-spline surface is the most important new spline surface in the CADG field since the creation of the B-spline surface and non-uniform rational B-spline surface. Although the surface modeling technology based on the T-spline surface is developing rapidly, there are still some problems that need to be further studied.