scholarly journals On the necessity of Reidemeister move 2 for simplifying immersed planar curves

2014 ◽  
Vol 103 ◽  
pp. 101-110 ◽  
Author(s):  
Tobias Hagge ◽  
Jonathan Yazinski
Keyword(s):  
Reidemeister Move ◽  
Planar Curves

scholarly journals Affine Subspaces of Curvature Functions from Closed Planar Curves

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Leonardo Alese
Keyword(s):  
Arc Length ◽  
Planar Curves ◽  
Affine Subspaces ◽  
Planar Curve ◽  
Real Functions ◽  
Discrete Counterpart ◽  
Equivalent Conditions

AbstractGiven a pair of real functions (k, f), we study the conditions they must satisfy for $$k+\lambda f$$ k + λ f to be the curvature in the arc-length of a closed planar curve for all real $$\lambda $$ λ . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied.

scholarly journals Clothoid fitting and geometric Hermite subdivision

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Ulrich Reif ◽  
Andreas Weinmann
Keyword(s):  
Building Block ◽  
Numerical Results ◽  
Normal Vector ◽  
Subdivision Schemes ◽  
Planar Curves ◽  
Nonlinear Subdivision ◽  
New Strategy ◽  
Vector Information ◽  
Hermite Subdivision

AbstractWe consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision schemes we propose is based on clothoidal averaging, i.e., averaging w.r.t. locally interpolating clothoids, which are curves of linear curvature. To this end, we derive a new strategy to approximate Hermite interpolating clothoids. We employ the proposed approach to define the geometric Hermite analogues of the well-known Lane-Riesenfeld and four-point schemes. We present numerical results produced by the proposed schemes and discuss their features.

scholarly journals Analysis of a Method to Parameterize Planar Curves Immersed In Triangulations

2013 ◽  
Vol 51 (3) ◽  
pp. 1392-1420 ◽  
Author(s):  
Ramsharan Rangarajan ◽  
Adrian J. Lew
Keyword(s):  
Planar Curves

scholarly journals On the curve straightening flow of inextensible, open, planar curves

SeMA Journal ◽  
2011 ◽  
Vol 54 (1) ◽  
pp. 5-24 ◽  
Author(s):  
D. B. Öelz
Keyword(s):  
Planar Curves

Constructive Whitney–Graustein Theorem: Or How to Untangle Closed Planar Curves

1991 ◽  
Vol 20 (4) ◽  
pp. 603-621 ◽  
Author(s):  
Kurt Mehlhorn ◽  
Chee-Keng Yap
Keyword(s):  
Planar Curves

Isoperimetric normalization of planar curves

1994 ◽  
Vol 16 (8) ◽  
pp. 769-777 ◽  
Author(s):  
D. Sinclair ◽  
A. Blake
Keyword(s):  
Planar Curves

Generalized evolutes of planar curves

2021 ◽  
Author(s):  
Yongqiao Wang ◽  
Yuan Chang ◽  
Haiming Liu
Keyword(s):  
Euclidean Plane ◽  
Singular Points ◽  
Moving Frames ◽  
Planar Curves ◽  
Fixed Direction ◽  
Spatial Curves

The evolutes of regular curves in the Euclidean plane are given by the caustics of regular curves. In this paper, we define the generalized evolutes of planar curves which are spatial curves, and the projection of generalized evolutes along a fixed direction are the evolutes. We also prove that the generalized evolutes are the locus of centers of slant circles of the curvature of planar curves. Moreover, we define the generalized parallels of planar curves and show that the singular points of generalized parallels sweep out the generalized evolute. In general, we cannot define the generalized evolutes at the singular points of planar curves, but we can define the generalized evolutes of fronts by using moving frames along fronts and curvatures of the Legendre immersion. Then we study the behaviors of generalized evolutes at the singular points of fronts. Finally, we give some examples to show the generalized evolutes.

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