On the variance of the number of extreme points of a random convex hull

1999 ◽  
Vol 44 (2) ◽  
pp. 123-130 ◽  
Author(s):  
Bruno Massé
Keyword(s):  
Convex Hull ◽  
Extreme Points ◽  
Random Convex

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.

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.

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.

On the LLN for the number of vertices of a random convex hull

2000 ◽  
Vol 32 (03) ◽  
pp. 675-681 ◽  
Author(s):  
Bruno Massé
Keyword(s):  
Convex Hull ◽  
Law Of Large Numbers ◽  
Large Numbers ◽  
General Conjecture ◽  
Common Parent ◽  
Random Convex

For several common parent laws, the number of vertices of a sample convex hull follows a kind of law of large numbers. We exhibit an example of a parent law which contradicts a general conjecture about this matter.

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.

Random convex hulls: a variance revisited

2004 ◽  
Vol 36 (04) ◽  
pp. 981-986
Author(s):  
Steven Finch ◽  
Irene Hueter
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Convex Hull ◽  
Asymptotic Variance ◽  
Circular Disk ◽  
Exact Expression ◽  
Convex Hulls ◽  
Asymptotic Constant ◽  
Uniform Sample ◽  
Random Convex

An exact expression is determined for the asymptotic constant c 2 in the limit theorem by P. Groeneboom (1988), which states that the number of vertices of the convex hull of a uniform sample of n random points from a circular disk satisfies a central limit theorem, as n → ∞, with asymptotic variance 2πc 2 n 1/3.

Coverage problems and random convex hulls

1982 ◽  
Vol 19 (3) ◽  
pp. 546-561 ◽  
Author(s):  
Nicholas P. Jewell ◽  
Joseph P. Romano
Keyword(s):  
Convex Hull ◽  
Finite Number ◽  
Random Sample ◽  
Bivariate Distribution ◽  
Convex Hulls ◽  
Coverage Problem ◽  
Coverage Problems ◽  
Random Convex

Consider the placement of a finite number of arcs on the circle of circumference 2π where the midpoint and length of each arc follows an arbitrary bivariate distribution. In the case where each arc has lengthπ, the probability that the circle is completely covered is equal to the probability that the convex hull of a finite random sample of points, chosen according to a certain bivariate distribution in the plane contains the origin. In general, we show that evaluating the probability that the random convex hull contains a fixed disc is equivalent to solving the general coverage problem where the midpoint and length of each arc follows an arbitrary bivariate distribution. Exact formulae for the above probabilities are obtained and some examples are considered.

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