A Survey of CAD Model Simplification Techniques for Physics-based Simulation Applications
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paper_title: A small feature suppression/unsuppression system for preparing B-rep models for analysis

paper_content:

CAD technology plays an ever more central role in today's multidisciplinary simulation environments. While this has enabled highly complex and detailed models to be used earlier in the design process it has brought with it difficulties for simulation specialists. Most notably CAD models now contain many details which are irrelevant to simulation disciplines. CAD systems have feature trees which record feature creation but unfortunately this does not capture which features are relevant to which analysis discipline. Many features of little significance to an analysis only emerge during the construction of the model. The ability to selectively suppress and reinstate features while maintaining an audit trail of changes is required to facilitate the control of the idealisation process. Features suppressed for one analysis can be retrieved for use in another.This work uses combinatorial topology concepts to outline the necessary conditions so that CAD model simplification operations can be designed as continuous transformations. Irrelevant features can then be suppressed and subsequently reinstated, within defined limitations, independently from the order in which they were suppressed. The implementation of these concepts provides analysts with a mechanism for generating analysis models with different levels of detail, without having to repeat the simplification process from the original CAD geometry. Most importantly, the information recorded during the suppress operations forms an essential audit trail of the idealisation process and can be presented in a feature-tree like structure allowing analysts to review their modelling decisions retrospectively. The approach also facilitates the generation of local, detailed models encapsulating a feature of interest. The proposed system follows a Find and Fix paradigm; where different algorithms for feature finding and fixing can be utilised in a common cellular modelling framework.
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paper_title: Fast collision detection between massive models using dynamic simplification

paper_content:

We present a novel approach for collision detection between large models composed of tens of millions of polygons. Each model is represented as a clustered hierarchy of progressive meshes (CHPM). The CHPM is a dual hierarchy of the original model: it serves both as a multiresolution representation of the original model, as well as a bounding volume hierarchy. We use the cluster hierarchy of a CHPM to perform coarse-grained selective refinement and the progressive meshes for fine-grained local refinement. We present a novel conservative error metric to perform collision queries based on the multiresolution representation. We use this error metric to perform dynamic simplification for collision detection. Our approach is conservative in that it may overestimate the set of colliding regions, but never misses any collisions. Furthermore, we are able to generate these hierarchies and perform collision queries using out-of-core techniques on all triangulated models. We have applied our algorithm to perform conservative collision detection between massive CAD and scanned models, consisting of millions of triangles at interactive rates on a commodity PC.
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paper_title: Topology Simplification for Polygonal Virtual Environments

paper_content:

We present a topology simplifying approach that can be used for genus reductions, removal of protuberances, and repair of cracks in polygonal models in a unified framework. Our work is complementary to the existing work on geometry simplification of polygonal datasets and we demonstrate that using topology and geometry simplifications together yields superior multiresolution hierarchies than is possible by using either of them alone. Our approach can also address the important issue of repair of cracks in polygonal models, as well as for rapid identification and removal of protuberances based on internal accessibility in polygonal models. Our approach is based on identifying holes and cracks by extending the concept of /spl alpha/-shapes to polygonal meshes under the L/sub /spl infin// distance metric. We then generate valid triangulations to fill them using the intuitive notion of sweeping an L/sub /spl infin// cube over the identified regions.
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paper_title: Modelling requirements for finite-element analysis

paper_content:

Abstract Efficient modelling of many problems in the finite-element analysis of structural and other continuum problems requires substantial simplification of the design geometry. Tools are needed for the efficient transformation of the detailed design geometry into an appropriate analysis model. It is argued that the medial axis and surface transform of geometric models provide an alternative representation that has many attractive properties for analysis feature recognition and simplification. Strategies for identifying possible idealizations, controlling their application, and estimating the associated errors appear feasible. Some requirements for geometric-modelling tools are identified.
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paper_title: Voxel based object simplification

paper_content:

Presents a simple, robust and practical method for object simplification for applications where gradual elimination of high-frequency details is desired. This is accomplished by sampling and low-pass filtering the object into multi-resolution volume buffers and applying the marching cubes algorithm to generate a multi-resolution triangle-mesh hierarchy. Our method simplifies the genus of objects and can also help existing object simplification algorithms achieve better results. At each level of detail, a multi-layered mesh can be used for an optional and efficient antialiased rendering.
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paper_title: Meshing Complexity of Single Part CAD Models

paper_content:

This paper proposes a method for predicting the complexity of meshing Computer Aided Design (CAD) geometries with unstructured, hexahedral, finite elements. Meshing complexity refers to the relative level of effort required to generate a valid finite element mesh on a given CAD geometry. A function is proposed to approximate the meshing complexity for single part CAD models. The function is dependent on a user defined element size as well as on data extracted from the geometry and topology of the CAD part. Several geometry and topology measures are proposed which both characterize the shape of the CAD part and detect configurations that complicate mesh generation. Based on a test suite of CAD models the function is demonstrated to be accurate within a certain range of error. The solution proposed here is intended to provide managers and users of meshing software a method of predicting the difficulty in meshing a CAD model. This will enable them to make decisions about model simplification and analysis approaches prior to mesh generation.
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paper_title: A Comparison of mesh simplification algorithms

paper_content:

Abstract In many applications the need for an accurate simplification of surface meshes is becoming more and more urgent. This need is not only due to rendering speed reasons, but also to allow fast transmission of 3D models in network-based applications. Many different approaches and algorithms for mesh simplification have been proposed in the last few years. We present a survey and a characterization of the fundamental methods. Moreover, the results of an empirical comparison of the simplification codes available in the public domain are discussed. Five implementations, chosen to give a wide spectrum of different topology preserving methods, were run on a set of sample surfaces. We compared empirical computational complexities and the approximation accuracy of the resulting output meshes.
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paper_title: Computing bounding volume hierarchies using model simplification

paper_content:

This paper presents a framework that uses the outputs of model simplification to guide the construction of bounding volume hierarchies for use in, for example, collision detection. Simplified models, besides their application to multiresolution rendering, can provide clues to the object’s shape. These clues help in the partitioning of the object’s model into components that may be more tightly bounded by simple bounding volumes. The framework naturally employs both the bottom-up and the topdown approaches of hierarchy building, and thus can have the advantages of both approaches. Experimental results show that our method built on top of the framework can indeed improve the bounding volume hierarchy, and as a result, significantly speedup the collision detection.
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paper_title: Automated mixed dimensional modelling for the finite element analysis of swept and revolved CAD features

paper_content:

Thin-walled aerospace structures can be idealised as dimensionally reduced shell models. These models can be analysed in a fraction of the time required for a full 3D model yet still provide remarkably accurate results. The disadvantages of this approach are the time taken to derive the idealised model, though this is offset by the ease and rapidity of design optimisation with respect to parameters such as shell thickness, and the fact that the stresses in the local 3D details can not be resolved.A process for automatically creating a mixed dimensional idealisation of a component from its CAD model is outlined in this paper. It utilises information contained in the CAD feature tree to locate the sketches associated with suitable features in the model. Suitable features are those created by carrying out dimensional addition operations on 2D sketches, in particular sweeping the sketch along a line to create an extruded solid, or revolving the sketch around an axis to create an axisymetric solid. Geometric proximity information provided by the 2D Medial Axis Transform is used to determine slender regions in the sketch suitable for dimensional reduction. The slender regions in the sketch are used to create sheet bodies representing the thin regions of the component, into which local 3D solid models of complex details are embedded. Analyses of the resulting models provide accurate results in a fraction of the run time required for the 3D model analysis.Also discussed is a web service implementation of the process which automatically dimensionally reduces 2D planar sketches in the STEP format.
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paper_title: A small feature suppression/unsuppression system for preparing B-rep models for analysis

paper_content:

CAD technology plays an ever more central role in today's multidisciplinary simulation environments. While this has enabled highly complex and detailed models to be used earlier in the design process it has brought with it difficulties for simulation specialists. Most notably CAD models now contain many details which are irrelevant to simulation disciplines. CAD systems have feature trees which record feature creation but unfortunately this does not capture which features are relevant to which analysis discipline. Many features of little significance to an analysis only emerge during the construction of the model. The ability to selectively suppress and reinstate features while maintaining an audit trail of changes is required to facilitate the control of the idealisation process. Features suppressed for one analysis can be retrieved for use in another.This work uses combinatorial topology concepts to outline the necessary conditions so that CAD model simplification operations can be designed as continuous transformations. Irrelevant features can then be suppressed and subsequently reinstated, within defined limitations, independently from the order in which they were suppressed. The implementation of these concepts provides analysts with a mechanism for generating analysis models with different levels of detail, without having to repeat the simplification process from the original CAD geometry. Most importantly, the information recorded during the suppress operations forms an essential audit trail of the idealisation process and can be presented in a feature-tree like structure allowing analysts to review their modelling decisions retrospectively. The approach also facilitates the generation of local, detailed models encapsulating a feature of interest. The proposed system follows a Find and Fix paradigm; where different algorithms for feature finding and fixing can be utilised in a common cellular modelling framework.
---
paper_title: Topology-reducing surface simplification using a discrete solid representation

paper_content:

This paper presents a new approach for generating coarse-level approximations of topologically complex models. Dramatic topology reduction is achieved by converting a 3D model to and from a volumetric representation. Our approach produces valid, error-bounded models and supports the creation of approximations that do not interpenetrate the original model, either being completely contained in the input solid or bounding it. Several simple to implement versions of our approach are presented and discussed. We show that these methods perform significantly better than other surface-based approaches when simplifying topologically-rich models such as scene parts and complex mechanical assemblies.
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paper_title: Decomposition of complex models for manufacturing

paper_content:

This work presents a feature recognition (FR) technique that separates protrusions bounded by freeform surface geometry. The method can also generate complementary male/female assembly features at the interface between components. A heuristic that uses edge curvature continuity is applied to direct the search and the construction of protrusion boundaries. The result is represented as a cellular model. The objective is to manufacture complex prototype assemblies on multiaxis machining centres. After describing the algorithm and presenting some examples of its application the paper concludes by discussing the approach's limitations.
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paper_title: Representation and management of feature information in a cellular model

paper_content:

Many limitations in current feature modelling systems are inherited from the geometric representation they use for the product model. Both a very rigid and a very extensive representation are unsuitable for feature applications, at least if no convenient support is provided to manage the data. This paper describes a cellular representation for feature models that contains all the relevant information to effectively solve a variety of current problems in feature modelling. Much benefit is gained from a coherent integration between shapes of a feature model and cells in the cellular model. Every feature shape has an explicit volumetric representation in terms of cells. Specific subsets of its boundary are also distinguished in terms of cell faces and edges. Feature interactions are maintained in attributes of cells, cell faces and cell edges. Methods for modifying and querying the cellular model are presented, and their application is illustrated for feature validity maintenance, feature interaction management, feature conversion between multiple views, and feature visualization.
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paper_title: Geometric and Solid Modeling: An Introduction

paper_content:

It is the view of the author that the streams of geometric and solid modeling are converging, and that as the importance of this convergence is anticipated and recognized, the need for the development of techniques to bridge the gap between the two becomes critical. This book is devoted to filling that need. "Geometric and Solid Modeling" deals with the concepts and tools needed to design and implement solid-modeling systems and their infrastructure and substrata, making this information remarkably accessible--to the novice as well as to the experienced designer. The essential algorithms and the underlying theory needed to design these systems are given primary emphasis. Techniques for the study and implementation of geometric algorithms are taken from computer science, numerical analysis, and symbolic computation, among other areas. Special attention is given to geometric investigations of implicit and parametric surfaces, with the focal point being the possible integration of geometric and solid modeling.
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paper_title: Voxel based object simplification

paper_content:

Presents a simple, robust and practical method for object simplification for applications where gradual elimination of high-frequency details is desired. This is accomplished by sampling and low-pass filtering the object into multi-resolution volume buffers and applying the marching cubes algorithm to generate a multi-resolution triangle-mesh hierarchy. Our method simplifies the genus of objects and can also help existing object simplification algorithms achieve better results. At each level of detail, a multi-layered mesh can be used for an optional and efficient antialiased rendering.
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paper_title: A CAD-CAE integration approach using feature-based multi-resolution and multi-abstraction modelling techniques

paper_content:

In spite of the widespread use of CAD systems for design and CAE systems for analysis, the two processes are not well integrated because CAD and CAE models inherently use different types of geometric models and there currently exists no generic, unified model that allows both design and analysis information to be specified and shared. In this paper, a new approach called the CAD/CAE-integrated approach is proposed and implemented by a feature-based non-manifold modelling system. The system creates and manipulates a single master model containing different types of all of the geometric models required for CAD and CAE. Both a solid model (for CAD) and a non-manifold model (for CAE) are immediately extracted from the master model through a selection process. If a design change is required, the master model is modified by the feature modelling capabilities of the system. As a result, the design and analysis models are modified simultaneously and maintained consistently. This system also supports feature-based multi-resolution and multi-abstraction modelling capabilities providing the CAD model at different levels of detail and the CAE model at various levels of abstraction.
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paper_title: Boundary representation deformation in parametric solid modeling

paper_content:

One of the major unsolved problems in parametric solid modeling is a robust update (regeneration) of the solid's boundary representation, given a specified change in the solid's parameter values. The fundamental difficulty lies in determining the mapping between boundary representations for solids in the same parametric family. Several heuristic approaches have been proposed for dealing with this problem, but the formal properties of such mappings are not well understood. We propose a formal definition for boundary representation. (BR-)deformation for solids in the same parametric family, based on the assumption of continuity: small changes in solid parameter values should result in small changes in the solid's boundary reprentation, which may include local collapses of cells in the boundary representation. The necessary conditions that must be satisfied by any BR-deforming mappings between boundary representations are powerful enough to identify invalid updates in many (but not all) practical situations, and the algorithms to check them are simple. Our formulation provides a formal criterion for the recently proposed heuristic approaches to “persistent naming,” and explains the difficulties in devising sufficient tests for BR-deformation encountered in practice. Finally our methods are also applicable to more general cellular models of pointsets and should be useful in developing universal standards in parametric modeling.
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paper_title: A cellular topology-based approach to generating progressive solid models from feature-centric models

paper_content:

Abstract Progressive mesh representation and generation have become one of the most important issues in network-based computer graphics. However, current researches are mostly focused on triangular mesh models. On the other hand, solid models are widely used in industry and are applied to advanced applications such as product design and virtual assembly. Moreover, as the demand to share and transmit these solid models over the network is emerging, how to effectively stream the solid models has been considered as one of the major research issues. In this paper, we present a cellular topology-based approach to generating progressive solid models (PSM) from feature-based models. The proposed approach introduces a new scheme for storing and transmitting solid models over the network. The cellular topology (CT) approach makes it possible to effectively generate PSMs and to efficiently transmit the models over the network with compact model size. Thus, an arbitrary solid model SM designed by a set of design features is stored as a much coarser solid model SM 0 together with a sequence of n detail records that indicate how to incrementally refine SM 0 exactly back into the original solid model SM=SM n .
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paper_title: Dimensional Reduction of Surface Models for Analysis

paper_content:

This paper describes a set of procedures by which an analyst can idealise slender 2D shell structures for linear static analysis using reduced-dimensional beam finite elements. The first step is the development of the topological operations that are necessary to achieve the desired dimensionally reduced representation. Next, the automatic derivation of necessary geometric and physical properties of the reduced dimensional entities are described, together with the application of appropriate coupling constraints between dimensions. Dimensional reduction of shell models involves finding areas of the geometric model whose dimensions are such that this region may be represented in an analysis model with a 1D beam. Using the medial axis transform, geometric measures are defined for identifying such areas in the geometric model. However, topological features of the model and its medial axis were also identified as significant in the automation of dimensional reduction. The application of the medial axis transform to automatic dimensional reduction is described and example models given.
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paper_title: Surface simplification using quadric error metrics

paper_content:

Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models. The algorithm uses iterative contractions of vertex pairs to simplify models and maintains surface error approximations using quadric matrices. By contracting arbitrary vertex pairs (not just edges), our algorithm is able to join unconnected regions of models. This can facilitate much better approximations, both visually and with respect to geometric error. In order to allow topological joining, our system also supports non-manifold surface models. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—surface and object representations
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paper_title: Intelligent Form Feature Interaction Management in a Cellular Modeling Scheme

paper_content:

Form features present a rather attractive building block in computer-aided design environments for a variety of applications, providing the embodiment of engineering semantics in specific part shape. In this paper we address the issue of volume feature behaviour throughout interaction phenomena. First, the fundamental concept of form feature as expression of the morphology of a model, is presented. A description of the feature properties, attributes and general constraints that are relevant for our purpose is attempted. In order to develop sound validity conditions for the various classes of form features, feature definitional entities are also introduced. A comprehensive definition of interaction among features is given that encompasses both adjacent and intersecting features. We use a structured cellular modeling scheme to capture both the morphology of features and the interactions among them. Within this framework, a thorough analysis of feature interactions is performed that explores the accessibility of feature definitional entities in order to assist feature-based model editing and validation. Operations that create or modify features often interfere with pre-existing ones, producing unanticipated effects that can corrupt or, at least, modify desired feature semantics and/or morphology. On the other hand, valid features can be obtained that exhibit non-standard or disconnected topology as a result of interactions caused by such operations. Systematic management of feature interactions is explored in both cases, from an object-oriented point of view, encapsulating interaction detection methods in feature class definition. This approach is shown to be quite adequate to handle complex interactions among several features. Reasoning mechanisms may, thereafter, be required to handle each situation identified.
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paper_title: Elimination of the adverse effects of small model features by the local modification of automatically generated meshes

paper_content:

Issues related to the automated identification and elimination of the adverse influence of small geometric model features on the quality of automatically generated meshes, using local mesh modification operators, are addressed. The definition of mesh validity with respect to the geometric model is extended to include multiple mesh entity classifications. Checks based on mesh topology are used to ensure no dimensional reductions in the locally modified mesh. Example geometric models of varied complexity containing small geometric features are used to demonstrate the ability of presented procedures to improve mesh quality in terms of aspect ratio and small angle metrics.
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paper_title: Face Clustering of a Large-scale CAD Model for Surface Mesh Generation

paper_content:

A detailed CAD model needs manual clean-up, or simplifying operations, before a finite element mesh can be automatically generated because such a model consists of hundreds or thousands of faces many of which may be smaller than a desired mesh element size. We propose an automated face clustering method used as a pre-process of surface mesh generation. By decomposing a model into face clusters so that each region can be projected onto a simple parametric surface such as a plane, we obtain a final mesh as an aggregate of sub-meshes for respective clusters without time-consuming manual preparation work. The projection onto a surface realises re-parameterisation as well as suppression of small details. The main contribution of this work is the integration of (1) a greedy algorithm for combining faces into clusters, and (2) geometric indices that reflect various aspects of a preferable shape for a cluster. The validity of the approach is demonstrated with results of clustering and mesh generation for a realistic-scale CAD model.
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paper_title: Shape preserving polyhedral simplification with bounded error

paper_content:

Abstract A new approach is introduced to reduce the number of nodes of a polyhedral model according to several conditions which allow to produce high quality simplified geometries. The simplified polyhedron must satisfy everywhere a geometric restoration criterion based on an error zone assigned to each node of its initial model. These error zones can be specified by the user or automatically set up using the accuracy characteristics of the digitizing device. Moreover, specific criteria are used to preserve the shape of the object during the simplification process both from geometric and topologic points of view. Indeed, the uses of such polyhedra require a good geometric quality without topologic and geometric singularities. The simplification process is based on a node removal method. A new strategy is developed to produce the simplified polyhedron using front propagations and multiple remeshing schemes which take into account the discrete curvature characteristics of the object. Such an approach allows to increase the node reduction of the initial polyhedron and produces a smoothing effect on the simplified geometry. The front propagation technique also leads to a better preservation of the shape of the object. Examples illustrate the behaviour of the simplification algorithm in terms of data reduction, quality of the simplified geometry and shape preservation of objects.
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paper_title: A small feature suppression/unsuppression system for preparing B-rep models for analysis

paper_content:

CAD technology plays an ever more central role in today's multidisciplinary simulation environments. While this has enabled highly complex and detailed models to be used earlier in the design process it has brought with it difficulties for simulation specialists. Most notably CAD models now contain many details which are irrelevant to simulation disciplines. CAD systems have feature trees which record feature creation but unfortunately this does not capture which features are relevant to which analysis discipline. Many features of little significance to an analysis only emerge during the construction of the model. The ability to selectively suppress and reinstate features while maintaining an audit trail of changes is required to facilitate the control of the idealisation process. Features suppressed for one analysis can be retrieved for use in another.This work uses combinatorial topology concepts to outline the necessary conditions so that CAD model simplification operations can be designed as continuous transformations. Irrelevant features can then be suppressed and subsequently reinstated, within defined limitations, independently from the order in which they were suppressed. The implementation of these concepts provides analysts with a mechanism for generating analysis models with different levels of detail, without having to repeat the simplification process from the original CAD geometry. Most importantly, the information recorded during the suppress operations forms an essential audit trail of the idealisation process and can be presented in a feature-tree like structure allowing analysts to review their modelling decisions retrospectively. The approach also facilitates the generation of local, detailed models encapsulating a feature of interest. The proposed system follows a Find and Fix paradigm; where different algorithms for feature finding and fixing can be utilised in a common cellular modelling framework.
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paper_title: Adaptation of CAD model topology for finite element analysis

paper_content:

The preparation of a Finite Element Analysis (FEA) model from a Computer Aided Design (CAD) model is still a difficult task since its Boundary Representation (B-Rep) is often composed of a large number of faces, some of which may be narrow or feature short edges that are smaller than the desired FE size (for mesh generation). Consequently, these faces and edges are considered as geometric artefacts that are irrelevant for the automatic mesh generation process. Such inconsistencies often cause either poorly-shaped elements or meshes that are locally over-densified. These inconsistencies not only slow down the solver (using too many elements) but also produce poor or inappropriate simulation results. In this context, we propose a ''Mesh Constraint Topology'' (MCT) model with automatic adaptation operators aimed at transforming a CAD model boundary decomposition into a FE model, featuring only mesh-relevant faces, edges and vertices, i.e., an explicit data model that is intrinsically adapted to the meshing process. We provide a set of criteria that can be used to transform CAD model boundary topology using MCT transformations, i.e., edge deletion, vertex deletion, edge collapsing, and merging of vertices. The proposed simplification criteria take into account a size map, a discretization error threshold and boundary conditions. Applications and results are presented through the adaptation of CAD models using the proposed simplification criteria.
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paper_title: A cellular topology-based approach to generating progressive solid models from feature-centric models

paper_content:

Abstract Progressive mesh representation and generation have become one of the most important issues in network-based computer graphics. However, current researches are mostly focused on triangular mesh models. On the other hand, solid models are widely used in industry and are applied to advanced applications such as product design and virtual assembly. Moreover, as the demand to share and transmit these solid models over the network is emerging, how to effectively stream the solid models has been considered as one of the major research issues. In this paper, we present a cellular topology-based approach to generating progressive solid models (PSM) from feature-based models. The proposed approach introduces a new scheme for storing and transmitting solid models over the network. The cellular topology (CT) approach makes it possible to effectively generate PSMs and to efficiently transmit the models over the network with compact model size. Thus, an arbitrary solid model SM designed by a set of design features is stored as a much coarser solid model SM 0 together with a sequence of n detail records that indicate how to incrementally refine SM 0 exactly back into the original solid model SM=SM n .
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paper_title: Topology-reducing surface simplification using a discrete solid representation

paper_content:

This paper presents a new approach for generating coarse-level approximations of topologically complex models. Dramatic topology reduction is achieved by converting a 3D model to and from a volumetric representation. Our approach produces valid, error-bounded models and supports the creation of approximations that do not interpenetrate the original model, either being completely contained in the input solid or bounding it. Several simple to implement versions of our approach are presented and discussed. We show that these methods perform significantly better than other surface-based approaches when simplifying topologically-rich models such as scene parts and complex mechanical assemblies.
---
paper_title: Voxel based object simplification

paper_content:

Presents a simple, robust and practical method for object simplification for applications where gradual elimination of high-frequency details is desired. This is accomplished by sampling and low-pass filtering the object into multi-resolution volume buffers and applying the marching cubes algorithm to generate a multi-resolution triangle-mesh hierarchy. Our method simplifies the genus of objects and can also help existing object simplification algorithms achieve better results. At each level of detail, a multi-layered mesh can be used for an optional and efficient antialiased rendering.
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paper_title: Feature-based multiresolution techniques for product design

paper_content:

Abstract3D computer-aided design (CAD) systems based on feature-based solid modelling technique have been widely spread and used for product design. However, when part models associated with features are used in various downstream applications, simplified models in various levels of detail (LODs) are frequently more desirable than the full details of the parts. In particular, the need for feature-based multiresolution representation of a solid model representing an object at multiple LODs in the feature unit is increasing for engineering tasks. One challenge is to generate valid models at various LODs after an arbitrary rearrangement of features using a certain LOD criterion, because composite Boolean operations consisting of union and subtraction are not commutative. The other challenges are to devise proper topological framework for multiresolution representation, to suggest more reasonable LOD criteria, and to extend applications. This paper surveys the recent research on these issues.
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paper_title: Feature-based multiresolution modeling of solids

paper_content:

Recently, three-dimensional CAD systems based on feature-based solid modeling techniques have been widely used for product design. However, when part models associated with features are used in various downstream applications, simplified models at various levels of detail (LODs) are frequently more desirable than the full details of the parts. One challenge is to generate valid models at various LODs after an arbitrary rearrangement of features using a certain LOD criterion, because composite Boolean operations consisting of union and subtraction are not commutative. This article proposes an algorithm for feature-based multiresolution solid modeling based on the effective volumes of features. This algorithm guarantees the same resulting shape and the reasonable intermediate LOD models for an arbitrary rearrangement of the features, regardless of whether feature types are additive or subtractive. This characteristic enables various LOD criteria to be used for a wide range of applications including computer-aided design and analysis.
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paper_title: A CAD-CAE integration approach using feature-based multi-resolution and multi-abstraction modelling techniques

paper_content:

In spite of the widespread use of CAD systems for design and CAE systems for analysis, the two processes are not well integrated because CAD and CAE models inherently use different types of geometric models and there currently exists no generic, unified model that allows both design and analysis information to be specified and shared. In this paper, a new approach called the CAD/CAE-integrated approach is proposed and implemented by a feature-based non-manifold modelling system. The system creates and manipulates a single master model containing different types of all of the geometric models required for CAD and CAE. Both a solid model (for CAD) and a non-manifold model (for CAE) are immediately extracted from the master model through a selection process. If a design change is required, the master model is modified by the feature modelling capabilities of the system. As a result, the design and analysis models are modified simultaneously and maintained consistently. This system also supports feature-based multi-resolution and multi-abstraction modelling capabilities providing the CAD model at different levels of detail and the CAE model at various levels of abstraction.
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paper_title: B-Rep model simplification by automatic fillet/round suppressing for efficient automatic feature recognition

paper_content:

Abstract The CAD models of real-world mechanical parts usually have many fillets and rounds that are essentially important to ensure the manufacturability and assembability. In feature-based modeling, fillets and rounds are often referred as secondary features that are used to modify the local details of the primary features such as holes, slots and pockets. Although the major shape of the primary features may not be affected, fillets and rounds can greatly change the geometric and topological patterns of the primary features. The geometric and topological variations can result in inefficient feature semantics classification in feature recognition. When feature interactions occur, it may become even worse to identify the regular patterns of the primary features. In addition, the fillets and rounds consist of no-linear surfaces such as cylindrical surfaces, spherical surfaces and toroidal surfaces, which bring the difficulties in volumetric feature extraction by half-space partition. In order to facilitate volumetric feature extraction and feature semantics classification, we pre-process the input B-Rep models by suppressing fillets and rounds before the feature recognition. Thus the input B-Rep models can be simplified without altering the major shapes of primary features, the targets of the feature recognition. The B-Rep simplification can be viewed as the reverse process of the edge blending in feature-based design. In this paper, several issues on fillet/round suppressing are discussed and a relatively general and robust approach is proposed to suppress blendings in B-Rep models of mechanical parts before the surface feature recognition and volumetric feature extraction.
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paper_title: Removal of blends from boundary representation models

paper_content:

This paper reports an algorithm for deletion of blends (or fillets) from Boundary Representation (B-rep) solid models. Blend deletion is usually performed as the first step in feature recognition since it simplifies the model for recognition of volumetric features. The algorithm handles several blend types that include face-face, face-edge and vertex blends. It also handles interactions of blends with other blends and/or volumetric features. The main feature of our approach is the usage of the underlying blend structure in predicting the final topology. This results in fewer intersections and greater predictability than earlier face-deletion approaches, especially for large blend networks. Another unique feature of our algorithm is the recreation of new faces in certain situations of blend deletion.
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paper_title: An integrated approach to realize multi-resolution of B-rep model

paper_content:

It is becoming a common trend that many designers work on a very complex assembly together in a collaborative environment. In this environment, every designer should be able to see the whole assembly in a full detail or in a rough shape at least. Even though the hardware technology is being improved very rapidly, it is very difficult to display a very complex assembly at a speed to allow smooth interactions for designers. This problem could be solved if a designer could manipulate his portion of the assembly in a full resolution while the remaining portion of the assembly is displayed in a rough resolution. It is also desired that the remaining portion is converted to the full resolution when needed. To realize this environment, the capabilities to simplify the portions of an assembly and to reset to the original resolution should be added to the current CAD systems. Thus operators realizing multi-resolution on B-rep are proposed in this paper, They are: wrap-around, smooth-out, and thinning operator. Through appropriately applying these operators sequentially, an assembly model of any desired resolution can be easily generated. Of course, the assembly can go back to the finer resolution. In this paper, the data structures and the processes to realize these operators are described and a prototype modeling system with these operators is also demonstrated.
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paper_title: Wrap-around operation to make multi-resolution model of part and assembly

paper_content:

Abstract When a single computer or network deals with large and complex assembly, a special method to compress or simplify the assembly is needed. One method is the use of a multi-resolution modeler, for which many approaches have been tried to obtain multi-solutions. Some of these approaches have considered triangular mesh compression, while some have considered features and topologies. This paper proposes a method for simplifying boundary representation models, in which the wrapping of products using the plastic wrap in the kitchen has been imitated. In wrapping, the plastic wrap hides the details of a product. This method is composed of two steps. The first step is the part level wrap-around operation. In this step, a convex inner loop is used as a clue to find concave space and fill this space by removing the convex inner loop. After filling the concave space, the faces that cannot be seen from outside the model are removed. The level of detail in our model was defined using a set composed of convex inner loop and faces that are removed with the convex inner loop. The second step is assembly level wrap-around operation. As a result of first step, an overlap between parts exists and faces that cannot be seen from outside of the model exist. These faces are deleted in the second step. Graph traverse method used to find these faces is presented. The proposed method is implemented using Parasolid kernel V12.1 and allows arbitrary movement to coarser and finer resolution.
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paper_title: Reconstruction of feature volumes and feature suppression

paper_content:

This paper describes a systematic algorithm for reconstructing the feature volume from a set of faces in a solid model. This algorithm serves a dual purpose. Firstly, the algorithm generates the feature volume by extending or contracting the neighboring faces of the set of faces. Secondly, the algorithm may also be used to remove (or suppress) the face-set from the model. The algorithm uses a divide-and-conquer strategy and geometric cues to identify the correct topology. It robustly handles a wide class of feature volumes with complex topology and geometry. A simplified version of the algorithm has also been presented to handle volumes resulting from 2.5D features.
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paper_title: Wrap-around Operation for Multi-resolution CAD Model

paper_content:

AbstractIn the design of a very complex product, the multi-resolution modeling technique plays an important role for the real time operation of the model on computers. There are many previous works to simplify or compress the geometric data to obtain a multi-resolution model from the original shape. But, most of them focused on the generation of multi-resolution model for facetbased models, not for B-rep models. The facet model is good enough for rendering purpose, but is not the basis model for many commercial CAD systems. A new multi-resolution algorithm for the B-rep model is needed to improve the interactivity in dealing with a large assembly model generated by CAD systems. We propose a new modeling operation, called wrap-around, to simplify a B-rep model. With this operation, a part model and an assembly can be simplified efficiently to yield multi-resolution models. Also, applying the reverse wrap-around operation can recover the original un-simplified model. In this paper, the structures and the pr...
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paper_title: Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration

paper_content:

Visualization is one of the most active and exciting areas of Mathematics and Computing Science, and indeed one which is only beginning to mature. Current visualization algorithms break down for very large data sets. While present approaches use multi-resolution ideas, future data sizes will not be handled that way. New algorithms based on sophisticated mathematical modeling techniques must be devised which will permit the extraction of high-level topological structures that can be visualized. For these reasons a workshop was organized at the Banff International Research Station, focused specifically on mathematical issues. A primary objective of the workshop was to gather together a diverse set of researchers in the mathematical areas relevant to the recent advances in order to discuss the research challenges facing this field in the next several years. The workshop was organized into five different thrusts: - Topology and Discrete Methods; - Signal and Geometry Processing; - Partial Differential Equations; - Data Approximation Techniques; - Massive Data Applications. This book presents a summary of the research ideas presented at this workshop.
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paper_title: Homotopy-Preserving Medial Axis Simplification

paper_content:

We present a novel algorithm to compute a simplified medial axis of a polyhedron. Our simplification algorithm tends to remove unstable features of Blum's medial axis. Moreover, our algorithm preserves the topological structure of the original medial axis and ensures that the simplified medial axis has the same homotopy type as Blum's medial axis. We use the separation angle formed by connecting a point on the medial axis to closest points on the boundary as a measure of the stability of the medial axis at the point. The medial axis is decomposed into its parts that are the sheets, seams and junctions. We present a stability measure of each part of the medial axis based on separation angles and examine the relation between the stability measures of adjacent parts. Our simplification algorithm uses iterative pruning of the parts based on efficient local tests. We have applied the algorithm to compute a simplified medial axis of complex models with tens of thousands of triangles and complex topologies.
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paper_title: Dimensional Reduction of Surface Models for Analysis

paper_content:

This paper describes a set of procedures by which an analyst can idealise slender 2D shell structures for linear static analysis using reduced-dimensional beam finite elements. The first step is the development of the topological operations that are necessary to achieve the desired dimensionally reduced representation. Next, the automatic derivation of necessary geometric and physical properties of the reduced dimensional entities are described, together with the application of appropriate coupling constraints between dimensions. Dimensional reduction of shell models involves finding areas of the geometric model whose dimensions are such that this region may be represented in an analysis model with a 1D beam. Using the medial axis transform, geometric measures are defined for identifying such areas in the geometric model. However, topological features of the model and its medial axis were also identified as significant in the automation of dimensional reduction. The application of the medial axis transform to automatic dimensional reduction is described and example models given.
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paper_title: Automatic solid decomposition and reduction for non-manifold geometric model generation

paper_content:

Abstract Oftentimes the level of complexity of a structure requires the analyst to idealize the finite element model, so that a solution may be obtained within a reasonable time scale. This paper describes some operations that have been defined and implemented which allow the user to reduce the dimensionality of geometric models automatically using a novel decomposition and reduction method. The model is first decomposed into simpler solids, and these solids undergo a reduction process to extract their midsurfaces. In some cases, not every part of the model can be reduced and thus, a non-manifold geometric model, suitable for mixed finite element modeling, is generated.
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Title: A Survey of CAD Model Simplification Techniques for Physics-based Simulation Applications

Section 1: Introduction
Description 1: Introduce the significance of physics-based simulations in the product realization process and outline the challenges caused by complex CAD models in simulations.

Section 2: Terminology
Description 2: Define the basic terminology and model representations used in CAD model simplification, including boundary representation, constructive solid geometry, and features.

Section 3: Techniques Based on Surface Entities
Description 3: Present techniques that simplify a model's surface entities, such as low pass filtering, face cluster-based simplification, and size-based entity decimation.

Section 4: Techniques Based on Volumetric Entities
Description 4: Discuss simplification techniques that operate on volumetric entities, including voxel-based simplification and effective volume-based simplification.

Section 5: Techniques Based on Explicit Features
Description 5: Describe methods that recognize and simplify explicit application features like prismatic features, blends, and arbitrary-shaped features.

Section 6: Techniques based on Dimension Reduction
Description 6: Explain dimension reduction methods that simplify models by reducing their dimensionality, such as medial axis transform and mid-surface abstraction.

Section 7: Discussion
Description 7: Analyze the taxonomy of model simplification techniques, comparing their application domains, types of features handled, and other critical factors for selection.

Section 8: Conclusions
Description 8: Summarize the key findings from the survey, highlight open research issues, and emphasize the need for further advancements in CAD model simplification techniques for physics-based simulations.