TITLE:
Study of Second-Order Continuities of a Composite Surface
AUTHORS:
Yukun Liu, Yong Yue
KEYWORDS:
Parametric Continuities, Geometric Continuities, Composite Surface, Bending Rate, Normal Section Curvature
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.10 No.1,
January
16,
2020
ABSTRACT: There are two classes of continuities, parametric continuities and geometric continuities, which are used to illuminate the smoothness of a composite surface in surface construction and reconstruction in computer graphics (CG) and computer aided design (CAD). A parametric continuity is more stiff than its corresponding geometric continuity of the same order. This paper uncovers the geometric properties of parametric and geometric continuities less than and equal to second order and presents the proofs for the corresponding propositions. These propositions can be applied to the existent or promising schemes of surface construction or reconstruction, which can provide a convincing theory for researchers to establish their schemes in surface construction. Three examples are used in this paper to show the applications of these propositions.