Integrals Over Curves and Surfaces

1993 ◽  
pp. 117-138
Author(s):  
Karen Pao ◽  
Frederick Soon
Keyword(s):  
Curves And Surfaces

scholarly journals Motion of curves and surfaces and nonlinear evolution equations in (2+1) dimensions

1998 ◽  
Vol 39 (7) ◽  
pp. 3765-3771 ◽  
Author(s):  
M. Lakshmanan ◽  
R. Myrzakulov ◽  
S. Vijayalakshmi ◽  
A. K. Danlybaeva
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Curves And Surfaces

Digital Jordan Curves and Surfaces with Respect to a Closure Operator

2021 ◽  
Vol 179 (1) ◽  
pp. 59-74
Author(s):  
Josef Šlapal
Keyword(s):  
Direct Product ◽  
Jordan Curve ◽  
Closure Operator ◽  
Jordan Curve Theorem ◽  
Closure Operators ◽  
Ternary Relation ◽  
Digital Space ◽  
Jordan Curves ◽  
Curves And Surfaces ◽  
Digital Plane

In this paper, we propose new definitions of digital Jordan curves and digital Jordan surfaces. We start with introducing and studying closure operators on a given set that are associated with n-ary relations (n > 1 an integer) on this set. Discussed are in particular the closure operators associated with certain n-ary relations on the digital line ℤ. Of these relations, we focus on a ternary one equipping the digital plane ℤ2 and the digital space ℤ3 with the closure operator associated with the direct product of two and three, respectively, copies of this ternary relation. The connectedness provided by the closure operator is shown to be suitable for defining digital curves satisfying a digital Jordan curve theorem and digital surfaces satisfying a digital Jordan surface theorem.

Curvature of singular Bézier curves and surfaces

2011 ◽  
Vol 28 (4) ◽  
pp. 233-244 ◽  
Author(s):  
Thomas W. Sederberg ◽  
Hongwei Lin ◽  
Xin Li
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Curves And Surfaces
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