Digital Modeling and Movement Resolution of Rubber Band Analogy for 2D Packing Problem

2012 ◽  
Vol 220-223 ◽  
pp. 2466-2470 ◽  
Author(s):  
Jun Yan Ma ◽  
Xiao Ping Liao ◽  
Juan Lu ◽  
Hong Yao
Keyword(s):  
Convex Hull ◽  
Extreme Points ◽  
Packing Problem ◽  
Rubber Band ◽  
Scanning Method ◽  
Resultant Vector ◽  
Digital Modeling ◽  
Volume Decrease ◽  
Modeling Algorithm

Packing problem is how to arrange the components in available spaces to make the layout compact. This paper adopts a digital modeling algorithm to establish a novel rubber band convex hull model to solve this problem. A ray scanning method analogy QuickHull algorithm is presented to get extreme points of rubber band convex hull. A plural vector expression approach is adopted to movement resolution,which calculate the resultant vector to translate, rotate and slide the subbody to make the volume decrease. An experiment proved this digital modeling algorithm effective.

Digital Modeling and Movement Resolution of Rubber Ballon Analogy for 3D Packing Problem

2013 ◽  
Vol 753-755 ◽  
pp. 1670-1674
Author(s):  
Jun Yan Ma ◽  
Feng Ying Long ◽  
Xiao Ping Liao ◽  
Biao Chen ◽  
Juan Lu ◽  
...  
Keyword(s):  
Convex Hull ◽  
Extreme Points ◽  
Packing Problem ◽  
Maximum Distance ◽  
Distance Method ◽  
Resultant Vector ◽  
Digital Modeling ◽  
3D Packing ◽  
Volume Decrease ◽  
Modeling Algorithm

Packing problem is how to arrange the components in available spaces to make the layout compact. This paper adopts a digital modeling algorithm to establish a novel rubber ballon convex hull model to solve this problem. A visible point puls maximum distance method analogy QuickHull algorithm is presented to get extreme points of rubber ballon convex hull. Movement resolution aim at force analyze and calculate the resultant vector to translate, rotate and slide the component to make the volume decrease in detail. An experiment proved this digital modeling algorithm effective.

Modeling of 2D Layout Design System Based on Convex Hull Plus Rubber Band Analog

2012 ◽  
Vol 215-216 ◽  
pp. 1219-1223 ◽  
Author(s):  
Xiao Ping Liao ◽  
Juan Lu ◽  
Jun Yan Ma ◽  
Jia Hai Xue ◽  
Xiao Mo Yu
Keyword(s):  
Convex Hull ◽  
Data Processing ◽  
Collision Detection ◽  
Rubber Band ◽  
Layout Design ◽  
Boolean Logic ◽  
Design System ◽  
Scanning Method ◽  
Modeling Methods ◽  
Novel Approach

This paper introduces a novel approach to develop a 2D layout system based on the convex hull plus rubber band analogy. The data processing of convex hull and the rubber band analogy modeling methods are elaborated practically; The rubber band simulating model is built quickly by using the ray scanning method; Collision detection by area algorithm based on Boolean logic is processed; The practical cases of developing 2D layout system are demonstrated to illustrate that the proposed approaches are effective.

Packing Optimisation Using a Rubberband Analogy

2001 ◽  
Author(s):  
Georges M. Fadel ◽  
Avijit Sinha ◽  
Todd McKee
Keyword(s):  
Convex Hull ◽  
Relative Position ◽  
Dimensional Space ◽  
Packing Problem ◽  
Rubber Band ◽  
Single Component ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Optimal Packing ◽  
3 Dimensional

Abstract Packing is a topic of interest in many fields. During our research on the underhood-packing problem, we observed that to bring components together — without switching their relative position — one could use the analogy of a rubber object stretched around the artifacts. In two-dimensional space, that object is a rubber band, and in three-dimensions, it is a balloon. Using this analogy, the convex hull can be used to determine the direction of forces applied to a single component, and a motion can result from the application of such forces. The objects can then be moved until contact occurs, at which point the forces become moments, and the objects can rotate with respect to each other. This technique can guarantee locally optimal packing, and displays a very intuitive behavior that might lead to further advances in optimization. This paper introduces the methodology for optimizing the packing of 2-dimensional geometric entities (polygons) in a plane and of 3-dimensional objects in space using the Rubber band Analogy.

The Min-Max Load Criteria as a Measure of Machining Fixture Performance

1994 ◽  
Vol 116 (4) ◽  
pp. 500-507 ◽  
Author(s):  
E. C. DeMeter
Keyword(s):  
Convex Hull ◽  
Linear Model ◽  
Model Validation ◽  
Contact Region ◽  
Extreme Points ◽  
Simulation Experiments ◽  
Machining Operations ◽  
The Impact ◽  
External Loads ◽  
The Continuum

Spherical-tipped locators and clamps are often used for the restraint of castings during machining. For structurally rigid castings, contact region deformation and micro-slippage are the predominant modes of workpiece displacement. In turn contact region deformation and micro-slippage are heavily influenced by contact region loading. This paper presents a linear model for predicting the impact of locator and clamp placement on workpiece displacement throughout a series of machining operations. It illustrates how the continuum of external loads exerted on a workpiece during machining can be bounded within a convex hull, and how the extreme points of this hull are used within the model. Finally it describes the simulation experiments which were used for model validation.

scholarly journals Some results on isometric composition operators on Lipschitz spaces

2021 ◽  
Author(s):  
Abraham Rueda Zoca
Keyword(s):  
Convex Hull ◽  
Composition Operator ◽  
Metric Spaces ◽  
Composition Operators ◽  
Extreme Points ◽  
Necessary Condition ◽  
Closed Convex Hull ◽  
Lipschitz Spaces ◽  
Complete Characterisation

AbstractGiven two metric spaces M and N we study, motivated by a question of N. Weaver, conditions under which a composition operator $$C_\phi :{\mathrm {Lip}}_0(M)\longrightarrow {\mathrm {Lip}}_0(N)$$ C ϕ : Lip 0 ( M ) ⟶ Lip 0 ( N ) is an isometry depending on the properties of $$\phi $$ ϕ . We obtain a complete characterisation of those operators $$C_\phi $$ C ϕ in terms of a property of the function $$\phi $$ ϕ in the case that $$B_{{\mathcal {F}}(M)}$$ B F ( M ) is the closed convex hull of its preserved extreme points. Also, we obtain necessary condition for $$C_\phi $$ C ϕ being an isometry in the case that M is geodesic.

Development of youth diplomacy on the example of modeling international organizations

2021 ◽  
Author(s):  
N.N. Popova ◽  
A.I. Potapkina
Keyword(s):  
International Relations ◽  
United Nations ◽  
International Organizations ◽  
Digital Technologies ◽  
Youth Movement ◽  
Digital Modeling ◽  
The United Nations ◽  
Foreign Ministry ◽  
Modeling Algorithm

The article highlights the importance of the youth movement and international organizations as one of the practical areas of implementation of youth diplomacy. The authors describe the development of the International Youth Model of the UN in the Diplomatic Academy of the Russian Foreign Ministry. Special attention is paid to the transformation of the traditional modeling algorithm in the context of the development of digital technologies. The development of a new stage of the youth model movement in the fi eld of international relations — digital modeling of the United Nations-was announced.

The number of extreme points in the convex hull of a random sample

1991 ◽  
Vol 28 (02) ◽  
pp. 287-304 ◽  
Author(s):  
David J. Aldous ◽  
Bert Fristedt ◽  
Philip S. Griffin ◽  
William E. Pruitt
Keyword(s):  
Convex Hull ◽  
Random Sample ◽  
Limit Distribution ◽  
Extreme Points ◽  
Radial Component ◽  
Limiting Distribution ◽  
Precise Information ◽  
Mean And Variance ◽  
The Mean

Let {Xk} be an i.i.d. sequence taking values in ℝ2with the radial and spherical components independent and the radial component having a distribution with slowly varying tail. The number of extreme points in the convex hull of {X1, · ··,Xn} is shown to have a limiting distribution which is obtained explicitly. Precise information about the mean and variance of the limit distribution is obtained.

Collision Detection Analysis of 2D Layout Based on Convex Hull Plus Rubber Band Simulation

2014 ◽  
Vol 488-489 ◽  
pp. 1480-1484
Author(s):  
Juan Lu ◽  
Jia Xun Wei ◽  
Wei Xia ◽  
Jun Yan Ma ◽  
Li Ying ◽  
...  
Keyword(s):  
Convex Hull ◽  
Collision Detection ◽  
Design Method ◽  
Rubber Band ◽  
Digital Design ◽  
Detection Methods ◽  
Movement Model ◽  
Model Based ◽  
Collision Response ◽  
Optimized Model

It is an innovative design method in physics that product layout design is abstracted into convex hull plus rubber band simulation layout mode by setting up the optimized model. Based on the physics model of Newtons Second Law, this paper analyzed collision detection methods during the process of realizing reasonable layout, and it is founded that real-time collision detection and collision response during movement, produced components within the given beat, appeared to be the key content of resolving digital model design. In this paper, Area Difference method was adopted to detect when the collision occurred during component movement and what kind of state the component tended to be in collision. At the same time, it also determined the interference degree, solved critical point pose for collision response as well as its generation time and related torque and force, which can confirm the components continued movement model of rotation and sliding. Meanwhile, it employed the Judgment Matrix method to analyze collision response so as to confirm the collision interference relationship and collision action state, movement possessing mode (rotation, sliding and retraction, etc.) within the remaining time after collision with given beat during the layout process. All these provided with a practical solution for digital design of optimized model based on convex hull plus rubber band simulation compact layout.

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