A Convergent Convex Decomposition of Polyhedral Objects

1992 ◽  
Vol 114 (3) ◽  
pp. 468-476 ◽  
Author(s):  
Yong Se Kim ◽  
D. J. Wilde
Keyword(s):  
Decomposition Method ◽  
Feature Recognition ◽  
Current Method ◽  
Convex Decomposition ◽  
Object Based ◽  
Geometric Objects ◽  
Polyhedral Objects ◽  
Volumetric Representation ◽  
Boundary Information ◽  
The Given

A convex decomposition method, called Alternating Sum of Volumes (ASV), uses convex hulls and set difference operations. ASV decomposition, however, may not converge, which severely limits the domain of geometric objects that the current method can handle. We investigate the cause of non-convergence and present a remedy; we propose a new convex decomposition called Alternating Sum of Volumes with Partitioning (ASVP) and prove its convergence. ASVP decomposition is a hierarchical volumetric representation which is obtained from the boundary information of the given object based on convexity. As an application, from feature recognition by ASVP decomposition if briefly discussed.

Form Feature Recognition by Convex Decomposition

1991 ◽  
Author(s):  
Yong Se Kim
Keyword(s):  
Decomposition Method ◽  
Feature Recognition ◽  
Convex Hulls ◽  
Convex Decomposition ◽  
Geometric Objects ◽  
Volumetric Representation ◽  
Feature Information ◽  
Form Features ◽  
Form Feature

Abstract A convex decomposition method, called Alternating Sum of Volumes (ASV), uses convex hulls and set difference operations. ASV decomposition may not converge, which severely limits the domain of geometric objects that can be handled. By combining ASV decomposition and remedial partitioning for the non-convergence, we have proposed a convergent convex decomposition called Alternating Sum of Volumes with Partitioning (ASVP). In this article, we describe how ASVP decomposition is used for recognition of form features. ASVP decomposition can be viewed as a hierarchical volumetric representation of form features. Adjacency and interaction between form features are inherently represented in the decomposition in a hierarchical way. Several methods to enhance the feature information obtained by ASVP decomposition are also discussed.

scholarly journals A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Current Method ◽  
Analytical Technique ◽  
Suggested Technique ◽  
Adomian Decomposition ◽  
Novel Method ◽  
The Given

AbstractIn this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

Handling Blending Features in Form Feature Recognition Using Convex Decomposition

1994 ◽  
Author(s):  
Sreekumar Menon ◽  
Yong Se Kim
Keyword(s):  
Feature Recognition ◽  
Boundary Representation ◽  
Recognition Method ◽  
Geometric Information ◽  
Polyhedral Model ◽  
Curved Boundary ◽  
Convex Decomposition ◽  
Geometric Objects ◽  
Form Features ◽  
Form Feature

Abstract Form features intrinsic to the product shape can be recognized using a convex decomposition called Alternating Sum of Volumes with Partitioning (ASVP). However, the domain of geometric objects to which ASVP decomposition can be applied had been limited to polyhedral solids due to the difficulty of convex hull construction for solids with curved boundary faces. We develop an approach to extend the geometric domain to solids having cylindrical and blending features. Blending surfaces are identified and removed from the boundary representation of the solid, and a polyhedral model of the unblended solid is generated while storing the cylindrical geometric information. From the ASVP decomposition of the polyhedral model, polyhedral form features are recognized. Form feature decomposition of the original solid is then obtained by reattaching the stored blending and cylindrical information to the form feature components of its polyhedral model. In this way, a larger domain of solids can be covered by the feature recognition method using ASVP decomposition. In this paper, handling of blending features in this approach is described.

A Convex Decomposition Using Convex Hulls and Local Cause of Its Non-Convergence

1992 ◽  
Vol 114 (3) ◽  
pp. 459-467 ◽  
Author(s):  
Yong Se Kim ◽  
D. J. Wilde
Keyword(s):  
Decomposition Method ◽  
Convex Hulls ◽  
Boolean Combination ◽  
Convex Object ◽  
Convex Decomposition ◽  
Polyhedral Objects

To exploit convexity, a non-convex object can be represented by a boolean combination of convex components. A convex decomposition method of polyhedral objects uses convex hulls and set difference operations. This decomposition, however, may not converge. In this article, we formalize this decomposition method and find local cause of non-convergence.

Augmented Convex Decomposition Using Incremental Update for Recognition of Form Features

1996 ◽  
Author(s):  
Frédéric Parienté ◽  
Yong Se Kim
Keyword(s):  
Feature Recognition ◽  
Feature Representation ◽  
Boundary Representation ◽  
Central Feature ◽  
Decomposition Tree ◽  
Active Components ◽  
Convex Decomposition ◽  
Volumetric Representation ◽  
Incremental Update ◽  
Form Features

Abstract Alternating Sum of Volumes with Partitioning (ASVP) decomposition is a volumetric representation of a part obtained from its boundary representation that organizes faces of the part in an outside-in hierarchy. ASVP decomposition combines Alternating Sum of Volumes (ASV) decomposition, using convex hulls and set difference operations, and remedial partitioning, using cutting operations and concave edges. A Form Feature Decomposition (FFD) which can serve as a central feature representation for various applications is obtained from ASVP decomposition. The incremental update of convex decomposition is achieved by exploiting its hierarchical structure. For a connected incremental design change, the active components that only need to be updated are localized in a subtree of the decomposition tree called active subtree. Then, the new decomposition is obtained by only updating the active subtree in the old decomposition. In this paper, we present a new decomposition, called Augmented Alternating Sum of Volumes with Partitioning (AASVP) decomposition, that is incrementally constructed using ASV incremental update as a local operation on a decomposition tree. AASVP provides an improved feature recognition capability as it localizes the effect of the change in the decomposition tree, avoids excessive remedial partitioning and catches the designer’s intent in feature editing. AASVP differs from ASVP at the remedial-partitioning nodes by partitioning less. The current remedial partitioning method could be improved such that AASVP decomposition can be constructed directly from the solid model.

Local Cause of Non-Convergence in a Convex Decomposition Using Convex Hulls

1989 ◽  
Author(s):  
Y. S.-Kim ◽  
D. J. Wilde
Keyword(s):  
Decomposition Method ◽  
Convex Hulls ◽  
Convex Decomposition ◽  
Polyhedral Objects

Abstract A convex decomposition method of polyhedral objects uses convex hulls and set difference operations. This decomposition may not converge. In this article, we formalize this decomposition method and find local cause of non-convergence.

Conversions in Form Feature Recognition Using Convex Decomposition

1992 ◽  
Author(s):  
Yong Se Kim ◽  
Kenneth D. Roe
Keyword(s):  
Decomposition Method ◽  
Feature Recognition ◽  
Inductive Learning ◽  
The Other ◽  
New Combination ◽  
Convex Decomposition ◽  
Feature Information ◽  
Form Features ◽  
Primal And Dual ◽  
Form Feature

Abstract A convergent convex decomposition method called Alternating Sum of Volumes with Partitioning (ASVP) has been used to recognize volumetric form features intrinsic to the product shape. The recognition process is done by converting the ASVP decomposition into a form feature decomposition by successively applying combination operations on ASVP components. In this paper, we describe a method to generate new combination operations through inductive learning from conversion processes of primal and dual ASVP decompositions when one decomposition produces more desirable form feature information than the other.

Feature Recognition by Volume Decomposition Using Half-Space Partitioning

1994 ◽  
Author(s):  
Yan Shen ◽  
Jami J. Shah
Keyword(s):  
Half Space ◽  
Decomposition Method ◽  
Feature Recognition ◽  
Boundary Representation ◽  
Solid Model ◽  
Space Partitioning ◽  
Machining Features ◽  
Convex Decomposition ◽  
Volume Decomposition ◽  
Convex Cell

Abstract A volume decomposition method called minimum convex decomposition by half space partitioning has been developed to recognize machining features from the boundary representation of the solid model. First, the total volume to be removed by machining is obtained by subtracting the part from the stock. This volume is decomposed into minimum convex cells by half space partitioning at every concave edge. A method called maximum convex cell composition is developed to generate all alternative volume decompositions. The composing sub volumes are classified based on degree of freedom analysis. This paper focuses on the first part of our system, i.e., the volume decomposition. The other part of the work will be submitted for publication at a leter date.

Approach to spatial modeling of networks and groups of objects on the basis of the weighted graph construction procedure

2020 ◽  
Vol 964 (10) ◽  
pp. 49-58
Author(s):  
V.I. Bilan ◽  
A.N. Grigor’ev ◽  
G.G. Dmitrikov ◽  
E.A. Dudin
Keyword(s):  
Spatial Configuration ◽  
Weighted Graph ◽  
Edge Length ◽  
Buffer Zones ◽  
Typical Structure ◽  
Spatial Graph ◽  
Object Based ◽  
Complementary Graph ◽  
Spatial Parameters ◽  
The Given

The direction of research on the development of a scientific and methodological tool for the analysis of spatial objects in order to determine their generalized spatial parameters was selected. An approach to the problem of modeling networks and groups of objects based on the synthesis of a weighted graph is proposed. The spatial configuration of objects based on the given conditions is described by a weighted graph, the edge length of which is considered as the weight of the edges. A generalization to the typical structure of a spatial graph is formulated; its essence is representation of nodal elements as two-dimensional (polygonal) objects. To take into account the restrictions on the convergence of the vertices described by the buffer zones, a complementary graph is formed. An algorithm for constructing the implementation of a spatial object based on the sequential determination of vertices that comply with the given conditions is proposed. Using the software implementation of the developed algorithm, an experiment was performed to evaluate the spatial parameters of the simulated objects described by typical graph structures. The following parameters were investigated as spatial ones

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