scholarly journals The Voronoi Diagram of Two-Dimensional Shape with Algebraic Curve Boundary

2011 ◽  
Vol 01 (02) ◽  
pp. 39-43
Author(s):  
华好 寿
Keyword(s):  
Voronoi Diagram ◽  
Algebraic Curve ◽  
Curve Boundary ◽  
Two Dimensional ◽  
Dimensional Shape

scholarly journals Surface energies emerging in a microscopic, two-dimensional two-well problem

2017 ◽  
Vol 147 (5) ◽  
pp. 1041-1089 ◽  
Author(s):  
Georgy Kitavtsev ◽  
Stephan Luckhaus ◽  
Angkana Rüland
Keyword(s):  
Surface Energy ◽  
Two Dimensional ◽  
Direct Control ◽  
First Order ◽  
Surface Energies ◽  
Energy Scaling ◽  
Continuous Analogue ◽  
Dimensional Shape ◽  
Set Up ◽  
Microscopic Modelling

In this paper we are interested in the microscopic modelling of a two-dimensional two-well problem that arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on the surface energy scaling regime and further analyse the Hamiltonian that was introduced by Kitavtsev et al. in 2015. It turns out that this class of Hamiltonians allows for a direct control of the discrete second-order gradients and for a one-sided comparison with a two-dimensional spin system. Using this and relying on the ideas of Conti and Schweizer, which were developed for a continuous analogue of the model under consideration, we derive a (first-order) continuum limit. This shows the emergence of surface energy in the form of a sharp-interface limiting model as well the explicit structure of the minimizers to the latter.

scholarly journals Development of Android-Based Appy Pie Learning Media on Mathematics in Elementary School

2020 ◽  
Vol 8 (2) ◽  
pp. 81
Author(s):  
Inas Sayyida Latifa ◽  
Aan Subhan Pamungkas ◽  
Trian Pamungkas Alamsyah ◽  
Indhira Asih Vivi Yandari
Keyword(s):  
Elementary School ◽  
3D Model ◽  
Fourth Grade ◽  
Average Score ◽  
Two Dimensional ◽  
Design And Development ◽  
Fourth Grade Students ◽  
Dimensional Shape ◽  
Expert Validation

This research aimed to develop Android-based Appy Pie learning media in mathematics subjects, especially two-dimensional shape material. Moreover, to determine the validity level of the android-based Appy Pie learning media developed and to determine the students' responses after using android-based Appy Pie learning media. This research uses the 3D model (define, design, and development) as the modification result of the 4D model by Thiagarajan. The subjects of this research were 45 fourth-grade students of SDN Rawu. The result of this research is the average score of media experts validation is 91.11% which included in the “very feasible” category, the average score of material expert validation is 98.33% which included in the “very feasible” category. The average score of the students response is 91.11% that included in the “very good” category, so it can be concluded that the Android-based Appy Pie learning media is feasible to use in the two-dimensional shape material of fourth-grade.

Parallel kNN Queries for Big Data Based on Voronoi Diagram Using MapReduce

2015 ◽  
pp. 392-414
Author(s):  
Wei Yan
Keyword(s):  
Big Data ◽  
Voronoi Diagram ◽  
Spatial Databases ◽  
Nearest Neighbor ◽  
Programming Model ◽  
Dimensional Space ◽  
Data Sets ◽  
Two Dimensional ◽  
K Nearest Neighbor ◽  
K Nearest Neighbors

In cloud computing environments parallel kNN queries for big data is an important issue. The k nearest neighbor queries (kNN queries), designed to find k nearest neighbors from a dataset S for every object in another dataset R, is a primitive operator widely adopted by many applications including knowledge discovery, data mining, and spatial databases. This chapter proposes a parallel method of kNN queries for big data using MapReduce programming model. Firstly, this chapter proposes an approximate algorithm that is based on mapping multi-dimensional data sets into two-dimensional data sets, and transforming kNN queries into a sequence of two-dimensional point searches. Then, in two-dimensional space this chapter proposes a partitioning method using Voronoi diagram, which incorporates the Voronoi diagram into R-tree. Furthermore, this chapter proposes an efficient algorithm for processing kNN queries based on R-tree using MapReduce programming model. Finally, this chapter presents the results of extensive experimental evaluations which indicate efficiency of the proposed approach.

TWO-DIMENSIONAL RANGE SEARCH BASED ON THE VORONOI DIAGRAM

2005 ◽  
Vol 15 (02) ◽  
pp. 151-166
Author(s):  
TAKESHI KANDA ◽  
KOKICHI SUGIHARA
Keyword(s):  
Voronoi Diagram ◽  
Dimensional Space ◽  
Search Problem ◽  
Two Dimensional ◽  
Worst Case ◽  
Average Case ◽  
Range Search ◽  
Almost All ◽  
Set Of Points ◽  
Dimensional Range

This paper studies the two-dimensional range search problem, and constructs a simple and efficient algorithm based on the Voronoi diagram. In this problem, a set of points and a query range are given, and we want to enumerate all the points which are inside the query range as quickly as possible. In most of the previous researches on this problem, the shape of the query range is restricted to particular ones such as circles, rectangles and triangles, and the improvement on the worst-case performance has been pursued. On the other hand, the algorithm proposed in this paper is designed for a general shape of the query range in the two-dimensional space, and is intended to accomplish a good average-case performance. This performance is actually observed by numerical experiments. In these experiments, we compare the execution time of the proposed algorithm with those of other representative algorithms such as those based on the bucketing technique and the k-d tree. We can observe that our algorithm shows the better performance in almost all the cases.

The effect of particle orientation and/or position on two-dimensional shape measurements

2001 ◽  
Vol 12 (3) ◽  
pp. 413-426 ◽  
Author(s):  
Toshiaki Miyajima ◽  
Ken-Ichi Yamamoto ◽  
Masunori Sugimoto
Keyword(s):  
Particle Orientation ◽  
Two Dimensional ◽  
Dimensional Shape

Design of a Two-Piece Brassiere Cup From its Data Points Toward its Automation

2020 ◽  
Author(s):  
Kotaro Yoshida ◽  
Hidefumi Wakamatsu ◽  
Eiji Morinaga ◽  
Takahiro Kubo
Keyword(s):  
Three Dimensional ◽  
Developable Surface ◽  
Two Dimensional ◽  
Trial And Error ◽  
Design Efficiency ◽  
Developable Surfaces ◽  
Data Points ◽  
Dimensional Shape ◽  
The Given ◽  
Three Dimensional Shape

Abstract A method to design the two-dimensional shapes of patterns of two piece brassiere cup is proposed when its target three-dimensional shape is given as a cloud of its data points. A brassiere cup consists of several patterns and their shapes are designed by repeatedly making a paper cup model and checking its three-dimensional shape. For improvement of design efficiency of brassieres, such trial and error must be reduced. As a cup model for check is made of paper not cloth, it is assumed that the surface of the model is composed of several developable surfaces. When two lines that consist in the developable surface are given, the surface can be determined. Then, the two-piece brassiere cup can be designed by minimizing the error between the surface and given data points. It was mathematically verified that the developable surface calculated by our propose method can reproduce the given data points which is developable surface.

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