Eigenanalysis and Artifacts of Subdivision Curves and Surfaces

2002 ◽  
pp. 69-92 ◽  
Author(s):  
Malcolm Sabin
Keyword(s):  
Curves And Surfaces ◽  
Subdivision Curves

scholarly journals A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 66 ◽  
Author(s):  
Aamir Shahzad ◽  
Faheem Khan ◽  
Abdul Ghaffar ◽  
Ghulam Mustafa ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Numerical Algorithm ◽  
Subdivision Schemes ◽  
Practical Applications ◽  
Curves And Surfaces ◽  
Geometrical Shapes ◽  
Subdivision Depth ◽  
Subdivision Curves

Subdivision schemes are extensively used in scientific and practical applications to produce continuous geometrical shapes in an iterative manner. We construct a numerical algorithm to estimate subdivision depth between the limit curves/surfaces and their control polygons after k-fold subdivisions. In this paper, the proposed numerical algorithm for subdivision depths of binary subdivision curves and surfaces are obtained after some modification of the results given by Mustafa et al in 2006. This algorithm is very useful for implementation of the parametrization.

Review of Subdivision Schemes and their Applications

2021 ◽  
Vol 16 ◽  
Author(s):  
Yan Liu ◽  
Huahao Shou ◽  
Kangsong Ji
Keyword(s):  
Computer Aided Design ◽  
Geometric Modeling ◽  
Hot Spot ◽  
Geometric Constraints ◽  
Future Application ◽  
Subdivision Surfaces ◽  
Subdivision Schemes ◽  
Practical Applications ◽  
Curves And Surfaces ◽  
Subdivision Curves

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.

scholarly journals Semi-sharp Creases on Subdivision Curves and Surfaces

2014 ◽  
Vol 33 (5) ◽  
pp. 217-226 ◽  
Author(s):  
J. Kosinka ◽  
M. A. Sabin ◽  
N. A. Dodgson
Keyword(s):  
Curves And Surfaces ◽  
Subdivision Curves

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.

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