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has been cited by the following article:

• 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.