scholarly journals Intersections With Validated Error Bounds for Building Interval Solid Models

2005 ◽  
Author(s):  
Harish Mukundan ◽  
Kwang Hee Ko ◽  
Nicholas M. Patrikalakis
Keyword(s):  
Interval Arithmetic ◽  
Error Control ◽  
Model Space ◽  
Critical Issue ◽  
Boundary Representation ◽  
Solid Model ◽  
Efficient Computation ◽  
Solid Models ◽  
Bounding Surfaces ◽  
Marching Method

Interval arithmetic has been considered as a step forward to counter numerical robustness problem in geometric and solid modeling. The interval arithmetic boundary representation (B-rep) scheme was developed to tackle this problem. In constructing an interval B-rep solid, robust and efficient computation of intersections between the bounding surfaces of the solid is a critical issue. To address this problem, a marching method based on a validated interval ordinary differential equation (ODE) solver was proposed, motivated by its potential for the interval B-rep model construction. In this paper, we concentrate on the issue of error control in model space using the validated ODE solver, and further explain that the validated ODE solver can be used in the construction of an interval B-rep solid model using such an error control.

Interval Methods for B-Rep Model Verification and Rectification

2000 ◽  
Author(s):  
Guoling Shen ◽  
Takis Sakkalis ◽  
Nicholas M. Patrikalakis
Keyword(s):  
Interval Arithmetic ◽  
Boundary Representation ◽  
Model Verification ◽  
Interval Methods ◽  
Topological Structures ◽  
Numerical Errors ◽  
Solid Models ◽  
Exact Boundary ◽  
Geometric Consistency ◽  
Model Conversion

Abstract Boundary representation (B-rep) models often have geometric specifications inconsistent with their topological structures due to numerical errors. In this paper, we verify the geometric consistency of B-rep models and evaluate existing inconsistencies of such models using interval arithmetic. Moreover, we convert conventional B-rep models into interval solid models to correct them. An interval solid is defined as a collection of non-degenerate boxes whose union covers the intended exact boundary and is guaranteed to be gap-free. An example illustrates our method for model conversion.

Applications of Non-Manifold Topology

1995 ◽  
Author(s):  
William W. Charlesworth ◽  
David C. Anderson
Keyword(s):  
Automatic Generation ◽  
Boundary Representation ◽  
Surface Topology ◽  
Solid Model ◽  
Finite Element Analyses ◽  
Topological Constraints ◽  
Tool Paths ◽  
Solid Models ◽  
New Applications ◽  
Complicated Surface

Abstract It is widely recognized that a solid model based on a non-manifold boundary representation can have a more complicated surface topology than one based on a manifold boundary representation, but non-manifold topology has other capabilities that may be more valuable to the application developer. Non-manifold topology can be put to use in existing application areas in ways that differ significantly from the techniques developed for manifold modeling and it can be put to use in new applications that have not been satisfactorily solved by manifold topology. Several applications of non-manifold topology that would be difficult or impossible to implement using a purely manifold geometric modeler are illustrated: automatic formulation of finite element analyses from solid models, automatic generation of machining tool paths for 2½-dimensional pockets, and construction of geometric models using topological constraints. These applications demonstrate how a non-manifold model partitions the entire space in which an object is embedded, preserves elements of the model that would be discarded by conventional schemes, and permits the implementation of a common merge operation. All three applications have been implemented using a two dimensional non-manifold (non-1-manifold) geometric modeler.

DOMAIN DELAUNAY TETRAHEDRIZATION OF SOLID MODELS

1991 ◽  
Vol 01 (03) ◽  
pp. 299-325 ◽  
Author(s):  
NICKOLAS S. SAPIDIS ◽  
RENATO PERUCCHIO
Keyword(s):  
Delaunay Triangulation ◽  
Boundary Representation ◽  
Solid Model ◽  
Neighborhood Information ◽  
Solid Models

An algorithm is presented for constructing a topologically and geometrically valid Domain Delaunay Tetrahedrization (DDT) of an arbitrarily shaped solid model with quadric curved faces (including objects with holes and nonmanifold objects). The algorithm operates on the boundary representation (B-rep) of the solid, and makes extensive use of properties of the Delaunay triangulation. This algorithm also includes a mechanism for transferring neighborhood information from the solid model to the elements of the tetrahedral model. Neighborhood information is used for identifying tetrahedra to be included in the DDT, and — in combination with geometric criteria — for ensuring that the DDT approximates satisfactorily the curved faces of the solid.

Topological and Geometric Consistency in Boundary Representations of Solid Models of Mechanical Components

1993 ◽  
Vol 115 (4) ◽  
pp. 762-769 ◽  
Author(s):  
A. G. Jablokow ◽  
J. J. Uicker ◽  
D. A. Turcic
Keyword(s):  
Data Exchange ◽  
Solid Modeling ◽  
Boundary Representation ◽  
Solid Model ◽  
Design Data ◽  
Solid Models ◽  
Geometric Consistency ◽  
Boundary Representations ◽  
Mechanical Components ◽  
Manufacturing Applications

This paper describes a method of verifying the consistency (i.e., agreement) between the topology and geometry of boundary representation (B-rep) solid models of mechanical components. This verification is well-suited for implementation as an algorithm and has been implemented as such in a polyhedral boundary representation solid modeling system (Jablokow, 1989). This technique and algorithm is important in the design of mechanical components for design documentation, integration with analysis and manufacturing applications, and design data exchange between solid modeling systems. Information regarding boundary representations has typically divided into the geometry and topology. It is important that the two are consistent for a valid solid model. In this work the genus of a solid model of an object is calculated topologically and geometrically and then compared to verify the consistency of the solid model. The genus of an object gives insight as to the geometric complexity of the object. This is equivalent to verifying the Gauss-Bonnet Theorem for the model, and is discussed in the paper.

Solid Model Databases: Techniques and Empirical Results

2001 ◽  
Vol 1 (4) ◽  
pp. 300-310 ◽  
Author(s):  
David McWherter ◽  
Mitchell Peabody ◽  
William C. Regli ◽  
Ali Shokoufandeh
Keyword(s):  
Metric Spaces ◽  
Boundary Representation ◽  
Management Systems ◽  
Solid Model ◽  
Distance Metrics ◽  
Range Queries ◽  
Solid Models ◽  
Large Databases ◽  
Database Operations ◽  
Relational Database Management

This paper presents techniques for managing solid models in relational database management systems. Our goal is to enable support for traditional database operations (sorting, distance metrics, range queries, nearest neighbors, etc) on large databases of solid models. We introduce an approach to compare models based on shape using information extracted from the model boundary representation into Model Signature Graphs. We show how the Model Signature Graphs can be used to compute topological distances among models and how to use these measures to create metric spaces for indexing and clustering of solid models. We believe this work will begin to bridge the solid modeling and database communities, enabling new paradigms for interrogation of CAD datasets based on the engineering content of solid models.

MMCs and PPCs As Constructs of Curvature Regions for Form Feature Determination

1997 ◽  
Author(s):  
Ratnakar Sonthi ◽  
Rajit Gadh
Keyword(s):  
Feature Recognition ◽  
Geometric Model ◽  
Boundary Representation ◽  
Solid Model ◽  
Cad Model ◽  
Solid Models ◽  
Feature Information ◽  
Primitive Shape ◽  
Region Representation ◽  
Form Feature

Abstract Shape feature information about a part is required to analyze the part for downstream issues such as manufacturability and assemblability. One method of obtaining the feature information is feature recognition from the geometric model. This paper presents an approach called Curvature Region (CR) approach for feature determination in solid models. The CR-approach categorizes features into two primitive shape classes: protrusions and depressions. In the first step, these primitive shape classes are recognized from the solid model. In the next step, the primitive shape classes are analyzed using rules to obtain features. Primitive features are found by first converting the boundary representation (B-Rep) of the CAD model to a higher level of representation called Curvature Region Representation (CR-Rep). Curvature Regions are then grouped together to form Minus-Minus Centers (MMCs) and Plus-Plus Centers (PPCs). Primitive shapes are then defined in terms of these centers.

Reconstruction of B-rep Solid Models From Finite Element Meshes for Design Automation

1993 ◽  
Author(s):  
Andrei G. Jablokow ◽  
Isaac Abraham
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Design Automation ◽  
Boundary Representation ◽  
Finite Element Mesh ◽  
Solid Model ◽  
Element Analysis ◽  
Element Mesh ◽  
Solid Models ◽  
Finite Element Meshes

Abstract This paper presents the integration of Finite Element (FE) techniques with B-rep solid modeling. Algorithms for constructing B-rep solid models from a finite element meshes are presented. The finite element mesh data, which consists of node coordinates and connectivity information, is read in from any standard finite element analysis package (currently SDRC IDEAS and MSC/XL) and then processed to construct a polyhedral non-manifold B-rep solid model of the geometry. Since the finite element mesh of a solid object is essentially a non-manifold object, existing geometric modeling data structures based on two-manifold topologies cannot represent it directly. In this work the non-manifold radial-edge data structure is used for the internal representation of the finite element mesh. The mesh is then processed using non-manifold topology operators to eliminate internal nodes and elements to arrive at the solid model that is a polyhedral boundary representation. The results are useful for design automation through the integration of CAD with finite element analysis, shape optimization, as well as the manufacturing of geometry stored as a finite element mesh.

Topological and Geometric Consistency in Boundary Representations of Solid Models

1990 ◽  
Author(s):  
Andrei G. Jablokow ◽  
John J. Uicker ◽  
David A. Turcic
Keyword(s):  
Solid Modeling ◽  
Boundary Representation ◽  
Solid Model ◽  
Geometric Complexity ◽  
And Topology ◽  
Solid Models ◽  
Geometric Consistency ◽  
Boundary Representations ◽  
Bonnet Theorem

Abstract This paper describes a method of verifying the consistency between the topology and geometry of boundary representation (B-rep) of solid models. This verification is well suited for implementation as an algorithm and has been implemented as such in a polyhedral boundary representation solid modeling system (Jablokow 1989). Information regarding boundary representations is typically divided into the geometry and topology. It is important that the two are consistent for a valid solid model. In this work the genus of an object is calculated topologically and geometrically and then compared to verify the consistency of the solid model. The genus of an object gives insight as to the geometric complexity of the object. This is equivalent to verifying the Gauss-Bonnet Theorem for the model, and is discussed in the paper.

Geometric Assistance for the Construction of Non-Polyhedral Solids From Orthographic Views

1997 ◽  
Author(s):  
Carol Hubbard ◽  
Yong Se Kim
Keyword(s):  
Computer Graphics ◽  
Solid Model ◽  
Geometric Framework ◽  
Mechanical Parts ◽  
Interactive Computer Graphics ◽  
Mechanical Part ◽  
Solid Models ◽  
Spherical Surfaces ◽  
Rapid Construction ◽  
Engineering Drawings

Abstract As the extensive use of solid models becomes widespread, it is important to have a mechanism by which existing engineering drawings can be converted into solid models. Therefore, a geometric assistant which can aid in the construction of solid models is beneficial. In this paper, we present key operations for a system called the Assistant for the Rapid Construction of Solids (ARCS), that provides this assistance given a set of two orthographic views. ARCS is based on the Visual Reasoning Tutor (VRT), a system we developed that provides users with the geometric framework to build polyhedral solids from their orthographic views. However, the geometric domain of ARCS encompasses non-polyhedral solids with cylindrical and spherical surfaces, such as those found in typical mechanical parts. We have devised the Cylindrical and Spherical Warping operations to create cylindrical and spherical surfaces, which use interactive computer graphics that guide a human user to build non-polyhedral faces of a solid. These operations are then illustrated with an example using ARCS to create the solid model of a typical mechanical part from its orthographic projections.

scholarly journals An approach to automatic boundary segmentation of solid models using virtual topology: toward reconstruction of design features

2020 ◽  
Vol 7 (3) ◽  
pp. 367-385
Author(s):  
Yingzhong Zhang ◽  
Yufei Fu ◽  
Jia Jia ◽  
Xiaofang Luo
Keyword(s):  
Design Feature ◽  
Boundary Representation ◽  
Virtual Topology ◽  
Design Features ◽  
Complex Part ◽  
Novel Approach ◽  
Solid Models ◽  
Medium Level ◽  
Feature Based ◽  
Low Dimensional

Abstract Boundary segmentation of solid models is the geometric foundation to reconstruct design features. In this paper, based on the shape evolution analysis for the feature-based modeling process, a novel approach to the automatic boundary segmentation of solid models for reconstructing design features is proposed. The presented approach simulates the designer’s decomposing thinking on how to decompose an existing boundary representation model into a set of design features. First, the modeling traces of design features are formally represented as a set of feature vertex adjacent graphs that use low-dimensional vertex entities and their connection relations. Then, a set of Boolean segmentation loops is searched and extracted from the constructed feature vertex adjacent graphs, which segment the boundary of a solid model into a set of regions with different design feature semantics. In the search process, virtual topology operations are employed to simulate the topological changes resulting from Boolean operations in feature modeling processes. In addition, to realize effective search, search strategies and search algorithms are presented. The segmentation experiments and case study show that the presented approach is feasible and effective for the boundary segmentation of medium-level complex part models. The presented approach lays the foundation for the later reconstruction of design features.

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