Edge-Compositions of 3D Surfaces

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Cynthia Sung ◽  
Erik D. Demaine ◽  
Martin L. Demaine ◽  
Daniela Rus
Keyword(s):  
Polynomial Time ◽  
Geometric Approach ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Design Methods ◽  
Robot Design ◽  
Automatic Composition ◽  
Folded Structures ◽  
3D Shapes ◽  
3D Surfaces

Origami-based design methods enable complex devices to be fabricated quickly in plane and then folded into their final 3D shapes. So far, these folded structures have been designed manually. This paper presents a geometric approach to automatic composition of folded surfaces, which will allow existing designs to be combined and complex functionality to be produced with minimal human input. We show that given two surfaces in 3D and their 2D unfoldings, a surface consisting of the two originals joined along an arbitrary edge can always be achieved by connecting the two original unfoldings with some additional linking material, and we provide a polynomial-time algorithm to generate this composite unfolding. The algorithm is verified using various surfaces, as well as a walking and gripping robot design.

Joining Unfoldings of 3-D Surfaces

2013 ◽  
Author(s):  
Cynthia Sung ◽  
Erik D. Demaine ◽  
Martin L. Demaine ◽  
Daniela Rus
Keyword(s):  
Geometric Approach ◽  
Design Methods ◽  
Robot Design ◽  
Automatic Composition ◽  
Folded Structures ◽  
Folded Surfaces

Origami-based design methods enable complex devices to be fabricated quickly in plane and then folded into their final 3-D shapes. So far, these folded structures have been designed manually. This paper presents a geometric approach to automatic composition of folded surfaces, which will allow existing designs to be combined and complex functionality to be produced with minimal human input. We show that given two surfaces in 3-D and their 2-D unfoldings, a surface consisting of the two originals joined along an arbitrary edge can always be achieved by connecting the two original unfoldings with some additional linking material, and we provide an algorithm to generate this composite unfolding. The algorithm is verified using various surfaces, as well as a walking and gripping robot design.

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

A polynomial-time algorithm for designing FIR filters with power-of-two coefficients

2002 ◽  
Vol 50 (8) ◽  
pp. 1935-1941 ◽  
Author(s):  
Dongning Li ◽  
Yong Ching Lim ◽  
Yong Lian ◽  
Jianjian Song
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Fir Filters
Sign in / Sign up

Export Citation Format

Share Document