Intersections of planar convex curves

1984 ◽  
Vol 267 (2) ◽  
pp. 145-159 ◽  
Author(s):  
P. R. Goodey
Keyword(s):  
Convex Curves ◽  
Planar Convex

scholarly journals Helly-type theorems for homothets of planar convex curves

2002 ◽  
Vol 131 (3) ◽  
pp. 921-932 ◽  
Author(s):  
Konrad J. Swanepoel
Keyword(s):  
Convex Curves ◽  
Planar Convex

On a Class of Generalized Curve Flows for Planar Convex Curves

2021 ◽  
Vol 42 (3) ◽  
pp. 367-382
Author(s):  
Huaqiao Liu ◽  
Li Ma
Keyword(s):  
Convex Curves ◽  
Planar Convex ◽  
Curve Flows

On evolutoids of planar convex curves II

2015 ◽  
Vol 89 (6) ◽  
pp. 1433-1447 ◽  
Author(s):  
V. A. Aguilar-Arteaga ◽  
R. Ayala-Figueroa ◽  
I. González-García ◽  
J. Jerónimo-Castro
Keyword(s):  
Convex Curves ◽  
Planar Convex

On evolutoids of planar convex curves

2013 ◽  
Vol 88 (1-2) ◽  
pp. 97-103 ◽  
Author(s):  
Jesús Jerónimo-Castro
Keyword(s):  
Convex Curves ◽  
Planar Convex

scholarly journals A robotic grasping approach with elliptical cone-based potential fields under disturbed scenes

2021 ◽  
Vol 18 (1) ◽  
pp. 172988142098573
Author(s):  
Wenjie Geng ◽  
Zhiqiang Cao ◽  
Zhonghui Li ◽  
Yingying Yu ◽  
Fengshui Jing ◽  
...  
Keyword(s):  
Principal Component ◽  
Major Axis ◽  
Target Object ◽  
Potential Fields ◽  
Single Shot ◽  
Robotic Grasping ◽  
Vertical Projection ◽  
Convex Curves ◽  
Functional Representation ◽  
Continuous Potential

Vision-based grasping plays an important role in the robot providing better services. It is still challenging under disturbed scenes, where the target object cannot be directly grasped constrained by the interferences from other objects. In this article, a robotic grasping approach with firstly moving the interference objects is proposed based on elliptical cone-based potential fields. Single-shot multibox detector (SSD) is adopted to detect objects, and considering the scene complexity, Euclidean cluster is also employed to obtain the objects without being trained by SSD. And then, we acquire the vertical projection of the point cloud for each object. Considering that different objects have different shapes with respective orientation, the vertical projection is executed along its major axis acquired by the principal component analysis. On this basis, the minimum projected envelope rectangle of each object is obtained. To construct continuous potential field functions, an elliptical-based functional representation is introduced due to the better matching degree of the ellipse with the envelope rectangle among continuous closed convex curves. Guided by the design principles, including continuity, same-eccentricity equivalence, and monotonicity, the potential fields based on elliptical cone are designed. The current interference object to be grasped generates an attractive field, whereas other objects correspond to repulsive ones, and their resultant field is used to solve the best placement of the current interference object. The effectiveness of the proposed approach is verified by experiments.

scholarly journals Maximizing the overlap of two planar convex sets under rigid motions

2007 ◽  
Vol 37 (1) ◽  
pp. 3-15 ◽  
Author(s):  
Hee-Kap Ahn ◽  
Otfried Cheong ◽  
Chong-Dae Park ◽  
Chan-Su Shin ◽  
Antoine Vigneron
Keyword(s):  
Convex Sets ◽  
Planar Convex ◽  
Rigid Motions

A $\operatorname{log}$-type non-local flow of convex curves

2021 ◽  
Vol 29 (5) ◽  
pp. 1157-1182
Author(s):  
Laiyuan Gao ◽  
Shengliang Pan ◽  
Ke Shi
Keyword(s):  
Local Flow ◽  
Convex Curves ◽  
Non Local

On the Fourier transforms of distribution on convex curves

1936 ◽  
Vol 2 (4) ◽  
pp. 712-721
Author(s):  
E. K. Haviland ◽  
Aurel Wintner
Keyword(s):  
Fourier Transforms ◽  
Convex Curves

Area properties associated with a convex plane curve

2017 ◽  
Vol 24 (3) ◽  
pp. 429-437
Author(s):  
Dong-Soo Kim ◽  
Young Ho Kim ◽  
Hyeong-Kwan Ju ◽  
Kyu-Chul Shim
Keyword(s):  
Characteristic Property ◽  
Plane Curve ◽  
Characterization Theorem ◽  
Convex Curve ◽  
Convex Plane ◽  
Convex Curves ◽  
Necessary And Sufficient ◽  
Locally Convex

AbstractArchimedes knew that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area of the region bounded by the parabola X and chord AB is four thirds of the area of the triangle {\bigtriangleup ABP}. Recently, the first two authors have proved that this fact is the characteristic property of parabolas.In this paper, we study strictly locally convex curves in the plane {{\mathbb{R}}^{2}}. As a result, generalizing the above mentioned characterization theorem for parabolas, we present two conditions, which are necessary and sufficient, for a strictly locally convex curve in the plane to be an open arc of a parabola.

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