Optimal Inscribed Polygons in Convex Curves

1989 ◽  
Vol 96 (10) ◽  
pp. 886 ◽  
Author(s):  
John S. Lew ◽  
Donald A. Quarles
Keyword(s):  
Convex Curves ◽  
Inscribed Polygons

Optimal Inscribed Polygons in Convex Curves

1989 ◽  
Vol 96 (10) ◽  
pp. 886-902 ◽  
Author(s):  
John S. Lew ◽  
Donald A. Quarles
Keyword(s):  
Convex Curves ◽  
Inscribed Polygons

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.

84.55 Perpendiculars and Inscribed Polygons

2000 ◽  
Vol 84 (501) ◽  
pp. 502 ◽  
Author(s):  
Larry Hoehn
Keyword(s):  
Inscribed Polygons

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.

scholarly journals A Curated Cacophony: Implementing an Intangible

2021 ◽  
Author(s):  
◽  
Oliver Wright
Keyword(s):  
Architectural Design ◽  
Flat Surfaces ◽  
The North ◽  
Architectural Element ◽  
Convex Curves ◽  
The Relationship ◽  
Effective Design ◽  
Target Design ◽  
Acoustic Measure

<p>This research investigates a progression away from acoustics formed by spaces and towards spaces that are driven by target acoustics. Despite architecture and acoustics’ shared consideration of form, materiality and inhabitation, too often acoustics is neglected from design and so is treated remedially, nullifying creativity. A case study project was undertaken to investigate the opportunities and limitations of two parametric tools, Galapagos (a generative solver) and Pachyderm (an acoustic simulation tool), to develop acoustic qualities in early architectural design. Yet, what are these acoustic qualities and how could they be measured? Testing of cafes in the Wellington CBD was undertaken to investigate these questions.  Six cafes were acoustically tested and five patrons from each of these completed a subjective survey. The café testing suggested that Reverberation Time (RT) could be an effective acoustic measure to direct architectural design. The café with the lowest patron enjoyment rating also recorded the longest RT and highest Sound Pressure Level (SPL), reinforcing the relationship between these three elements. Through these findings, patron enjoyment was concluded to be dependent on SPL and SPL was concluded to be dependent on RT (Whitlock and Dodd, 424). In order to increase patron enjoyment, Galapagos was utilised to explore possible forms that met a target design RT of 0.7 seconds. An RT of 0.7 seconds was chosen as it was shorter than the AS/NZS 2107 (2000) maximum and was comparable to the cafés with the two highest subjective enjoyment ratings.  Through a parametric and analogue design methodology, Galapagos and Pachyderm were used to investigate how acoustic goals could shape a café design. The case study project produced a design that not only meets this acoustic criterion but harnesses form to sculpt sound. Instead of applying absorption to flat surfaces, the convex curves on the north and east facades disperse sound, producing both a diffuse environment and an engaging architectural element. This integrated investigation demonstrated that a parametric and analogue design process can be implemented to create a acoustically and architecturally effective design.</p>

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 Integral points on convex curves

2020 ◽  
Vol 53 (2) ◽  
pp. 399-422
Author(s):  
Jean-Marc Deshouillers ◽  
Adrián Ubis
Keyword(s):  
Integral Points ◽  
Convex Curves

scholarly journals Note on convex curves on the hyperbolic plane

1945 ◽  
Vol 51 (6) ◽  
pp. 405-413 ◽  
Author(s):  
L. A. Santaló
Keyword(s):  
Hyperbolic Plane ◽  
Convex Curves
Sign in / Sign up

Export Citation Format

Share Document