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.

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.

Verification of Boundary Representations of Solid Models

1994 ◽  
Vol 116 (2) ◽  
pp. 666-668
Author(s):  
A. G. Jablokow ◽  
J. J. Uicker ◽  
D. A. Turcic
Keyword(s):  
Design Automation ◽  
Solid Modeling ◽  
Solid Model ◽  
Object Model ◽  
Application Program ◽  
Solid Models ◽  
Verification Algorithms ◽  
Boundary Representations ◽  
Object Models

Verification of polyhedral boundary representations (B-reps) of solid models through the use of an algorithm is addressed here. The validity conditions for B-rep models are presented in a format which leads directly to a set of verification algorithms. The validity verification algorithms are intended for design automation through execution after each solid modeling operation, after localized geometry modification, on imported object model databases, prior to storage of object models, or prior to execution of an application program on the solid model.

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.

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.

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.

Solid Modeling of In-Process Workpiece Geometry for Hole Milling

2012 ◽  
Author(s):  
Jue Wang ◽  
Derek Yip-Hoi
Keyword(s):  
Cutting Forces ◽  
Tool Path ◽  
Solid Modeling ◽  
Solid Model ◽  
Virtual Machining ◽  
Solid Models ◽  
Milling Operation ◽  
Swept Volumes ◽  
Swept Volume ◽  
Physics Based Simulation

Capturing the in-process workpiece geometry generated during machining is an important part of tool path verification and increasingly the physics-based simulation of cutting forces used in Virtual Machining. Swept volume generation is a key supporting methodology that is necessary for generating these in-process states. Hole milling is representative of one class of milling operation where the swept volume is continuously intersecting. Due to this it is impossible to decompose the tool path into non-intersecting regions which is typically the approach used in solid model based swept volume generation. In this paper an approach to generating NURBS based solid models for self-intersecting swept volumes generated during hole milling is presented. NURB surfaces are generated that compactly represent the surfaces of the swept volume. This utilizes the geometry of the helical curve as opposed to a linearly interpolated tool path that is used for more generic approaches to generating swept volumes. Examples applying the approach to various types of cutter geometries used in milling are presented.

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.

Sheet Modeling and Thickening Operations Based on Non-Manifold Boundary Representations

2001 ◽  
Author(s):  
Sang Hun Lee ◽  
Hyun-Soo Kim
Keyword(s):  
Boundary Representation ◽  
Metal Parts ◽  
Sheet Metal Parts ◽  
Solid Models ◽  
Boundary Representations ◽  
Thin Walled ◽  
Topological Framework ◽  
Manifold Models ◽  
Definition Of ◽  
Euler Operators

Abstract This paper describes sheet modeling and thickening operations based on a non-manifold topological representation for efficient solid modeling of thin-walled plastic or sheet metal parts. Since the existing methods have adopted boundary representations for solid models, it is difficult to represent the exact adjacency relations between topological entities in a sheet model, and to describe a mixture of wireframe and sheet objects that appear in the intermediate steps of sheet modeling operations. Accordingly, it is difficult to devise and implement the algorithms for sheet modeling and thickening operations. To solve these problems, we introduce a non-manifold boundary representation as a topological framework and propose a sheet thickening algorithm by presenting variations to a general non-manifold offset algorithm that is based on the mathematical definition of offsets. In addition, to facilitate sheet modeling operations, not only a set of generalized Euler operators for non-manifold models are provided, but also sheet modeling capabilities, including adding, bending, and punching functions with two-dimensional curve editors.

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