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):  
2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Leonardo Alese

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.


2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Ulrich Reif ◽  
Andreas Weinmann

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.


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

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

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

Author(s):  
Yongqiao Wang ◽  
Yuan Chang ◽  
Haiming Liu

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.


Author(s):  
Ronak R. Mohanty ◽  
Umema H. Bohari ◽  
Vinayak ◽  
Eric Ragan

We present haptics-enabled mid-air interactions for sketching collections of three-dimensional planar curves — 3D curve-soups — as a means for 3D design conceptualization. Haptics-based mid-air interactions have been extensively studied for modeling of surfaces and solids. The same is not true for modeling curves; there is little work that explores spatiality, tangibility, and kinesthetics for curve modeling, as seen from the perspective of 3D sketching for conceptualization. We study pen-based mid air interactions for free-form curve input from the perspective of manual labor, controllability, and kinesthetic feedback. For this, we implemented a simple haptics-enabled workflow for users to draw and compose collections of planar curves on a force-enabled virtual canvas. We introduce a novel force-feedback metaphor for curve drawing, and investigate three novel rotation techniques within our workflow for both controlled and free-form sketching tasks.


Sign in / Sign up

Export Citation Format

Share Document