Weiyin Ma

NURBS curve and surface fitting for reverse engineering

Reverse engineering is an approach for constructing a computer-aided design (CAD) model from a physical part through dimensional measurement and surface modelling. This paper presents alternatives for reverse engineering of free-form parts using Non-Uniform Rational B-Spline (NURBS) surfaces. A two-step linear approach is employed for fitting NURBS curves and surfaces using the measured points. During the first step, the weights of the control points are identified from a homogeneous system using symmetric eigenvalue decomposition. The control points are further processed in a way similar to B-spline curve and surface fitting. Some examples are presented to illustrate both the steps of reverse engineering and the process of NURBS curve and surface fitting.

Conceptual design of fuzzy object‐oriented databases using extended entity‐relationship model

Entity‐relationship–extended entity‐relationship models play a crucial role in the conceptual design of relational databases as well as object‐oriented databases. Recently, several approaches have been proposed to enhance object‐oriented databases (OODBs) using fuzzy set theory. In this paper, we introduce a fuzzy extended entity‐relationship model to cope with imperfect as well as complex objects in the real world at a conceptual level. In particular, we provide the formal approach to mapping a fuzzy extended entity‐relationship model to a fuzzy object‐oriented database schema. © 2001 John Wiley & Sons, Inc.

NURBS-based adaptive slicing for efficient rapid prototyping

Abstract This paper presents slicing algorithms for efficient model prototyping. The algorithms directly operate upon a non-uniform rational B-spline surface model. An adaptive slicing algorithm is developed to obtain an accurate and smooth part surface. A selective hatching strategy is employed to further reduce the build time by solidifying the kernel regions of a part with the maximum allowable thick layers while solidifying the skin areas with adaptive thin layers to obtain the required surface accuracy. In addition, it provides a generalization to the containment problem with mixed tolerances for slicing a part. The article also developed a direct method for computing skin contours for all tolerance requirements. Some case studies are presented to illustrate the developed algorithms and the selective hatching and adaptive slicing strategy. The developed algorithms have been implemented and tested on a fused deposition modeling rapid prototyping machine. Both the implementation and test results are discussed in the paper.

A direct approach for subdivision surface fitting from a dense triangle mesh

Abstract This article presents a new and direct approach for fitting a subdivision surface from an irregular and dense triangle mesh of arbitrary topological type. All feature edges and feature vertices of the original mesh model are first identified. A topology- and feature-preserving mesh simplification algorithm is developed to further simplify the dense triangle mesh into a coarse mesh. A subdivision surface with exactly the same topological structure and sharp features as that of the simplified mesh is finally fitted from a subset of vertices of the original dense mesh. During the fitting process, both the position masks and subdivision rules are used for setting up the fitting equation. Some examples are provided to demonstrate the proposed approach.

B-spline surface local updating with unorganized points

This paper presents an approach to update a local area of a B-spline surface based on a set of locally distributed and unorganized points in three-dimensional space. The region of the original surface to be updated is first identified. The control points affecting these regions are further extracted or registered. The original B-spline surface is then updated by modifying part or all of the registered control points through a local fitting process. Surface local updating can be done either with or without affecting the neighboring patches of the region being updated. Depending on the number of patches involved in a region to be updated and whether the neighboring patches of a region are allowed for alteration, additional knots may need to be inserted in the corresponding patches before surface local updating. If the shape of a region is likely to become more complex after updating, additional knots may also need to be inserted in this region in order to obtain better fitting between the final updated surface and the locally distributed points. B-spline surface local updating is particularly useful for free-form surface design and shape modification based on physical mockups.

Subdivision surfaces for CAD-an overview

Subdivision surfaces refer to a class of modelling schemes that define an object through recursive subdivision starting from an initial control mesh. Similar to B-splines, the final surface is defined by the vertices of the initial control mesh. These surfaces were initially conceived as an extension of splines in modelling objects with a control mesh of arbitrary topology. They exhibit a number of advantages over traditional splines. Today one can find a variety of subdivision schemes for geometric design and graphics applications. This paper provides an overview of subdivision surfaces with a particular emphasis on schemes generalizing splines. Some common issues on subdivision surface modelling are addressed. Several key topics, such as scheme construction, property analysis, parametric evaluation and subdivision surface fitting, are discussed. Some other important topics are also summarized for potential future research and development. Several examples are provided to highlight the modelling capability of subdivision surfaces for CAD applications.

A hierarchically structured and constraint-based data model for intuitive and precise solid modeling in a virtual reality environment

Abstract This article proposes a hierarchically structured and constraint-based data model for intuitive and precise solid modeling in a virtual reality (VR) environment. The data model integrates a high level constraint-based model for intuitive and precise manipulation, a middle level solid model for complete and precise representation and a low-level polygon mesh model for real-time interactions and visualization in a VR environment. The solid model is based on a hybrid B-rep/CSG data structure. Constraints are embedded in the solid model and are organized at hierarchical levels as feature constraints among internal feature elements, part constraints among internal features and assembly constraints between individual parts. In addition to providing a complete and precise model representation and the support for real-time visualization, the proposed data model permits intuitive and precise interaction through constraint-based manipulations for solid modeling in a VR environment. This is a critical issue for product design in a VR environment due to the limited resolutions of todays VR input and output devices.

Seed-growing segmentation of 3-D surfaces from CT-contour data

The article presents a layer-based seed-growing technique for the segmentation of 3-D surfaces from computed tomography (CT) contour data. It falls in an area called reverse engineering for creating a computer aided design (CAD) model of an industrial or medical object using CT-scanners for dimensional measurement. After pre-processing, a layer-based 3-D contour model is obtained from the 2-D raw CT-images. A seed-growing technique is developed for extracting user-interested surface features from the CT-contour data. After entering a seed contour on an interested layer, contour points belonging to the same surface or feature as the seed contour are segmented from others by growing the seed contour layer by layer, the so called seed-growing segmentation. The seed contour can be either a closed contour or an open contour depending on the characteristics of the surface feature to be extracted. For a complex object, the segmentation can be performed in two steps. A composite surface is first segmented from the raw CT-contour data. Individual surface features are further segmented from the extracted composite surface contours. An elastic spline and an optimization algorithm are used in the growing process. A 2-D feature point recognition algorithm is incorporated in the open contour growing process.

2 Subdivision for quadrilateral meshes

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Semantic measure of fuzzy data in extended possibility-based fuzzy relational databases

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