Review of Subdivision Schemes and their Applications

Abstract

Background: Subdivision surfaces modeling method and related technology research gradually become a hot spot in the field of computer-aided design(CAD) and computer graphics (CG). In the early stage, research on subdivision curves and surfaces mainly focused on the relationship between the points, thereby failing to satisfy the requirements of all geometric modeling. Considering many geometric constraints is necessary to construct subdivision curves and surfaces for achieving high-quality geometric modeling. Objective: This paper aims to summarize various subdivision schemes of subdivision curves and surfaces, particularly in geometric constraints, such as points and normals. The findings help scholars to grasp the current research status of subdivision curves and surfaces better and to explore their applications in geometric modeling. Methods: This paper reviews the theory and applications of subdivision schemes from four aspects. We first discuss the background and key concept of subdivision schemes. We then summarize the classification of classical subdivision schemes. Next, we show the subdivision surfaces fitting and summarize new subdivision schemes under geometric constraints. Applications of subdivision surfaces are also discussed. Finally, this paper gives a brief summary and future application prospects. Results: Many research papers and patents of subdivision schemes are classified in this review paper. Remarkable developments and improvements have been achieved in analytical computations and practical applications. Conclusion: Our review shows that subdivision curves and surfaces are widely used in geometric modeling. However, some topics need to be further studied. New subdivision schemes need to be presented to meet the requirements of new practical applications.

Geometric Modelling of a Family of 4-Point Ternary Approximating Subdivision Scheme U_φ with Visual Performance

“…Control points or parameters define them. Applications of CAGD are involved in computer graphics, product design and automotive designing [3,4,9,13,18].…”

The Generalized Classes of Linear Symmetric Subdivision Schemes Free from Gibbs Oscillations and Artifacts in the Fitting of Data

“…Later, Zhou et al [14] developed a sufficient condition to test the hypothesis that p-ary subdivision schemes exhibit the Gibbs phenomenon in the limit function at the discontinuous point. Yan et al [15] assembled a collection of surface and curve subdivision schemes.…”