Showing papers in "Computer-aided Design in 2006"

Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids

Abstract: This paper introduces a method to extract 'Shape-DNA', a numerical fingerprint or signature, of any 2d or 3d manifold (surface or solid) by taking the eigenvalues (i.e. the spectrum) of its Laplace-Beltrami operator. Employing the Laplace-Beltrami spectra (not the spectra of the mesh Laplacian) as fingerprints of surfaces and solids is a novel approach. Since the spectrum is an isometry invariant, it is independent of the object's representation including parametrization and spatial position. Additionally, the eigenvalues can be normalized so that uniform scaling factors for the geometric objects can be obtained easily. Therefore, checking if two objects are isometric needs no prior alignment (registration/localization) of the objects but only a comparison of their spectra. In this paper, we describe the computation of the spectra and their comparison for objects represented by NURBS or other parametrized surfaces (possibly glued to each other), polygonal meshes as well as solid polyhedra. Exploiting the isometry invariance of the Laplace-Beltrami operator we succeed in computing eigenvalues for smoothly bounded objects without discretization errors caused by approximation of the boundary. Furthermore, we present two non-isometric but isospectral solids that cannot be distinguished by the spectra of their bodies and present evidence that the spectra of their boundary shells can tell them apart. Moreover, we show the rapid convergence of the heat trace series and demonstrate that it is computationally feasible to extract geometrical data such as the volume, the boundary length and even the Euler characteristic from the numerically calculated eigenvalues. This fact not only confirms the accuracy of our computed eigenvalues, but also underlines the geometrical importance of the spectrum. With the help of this Shape-DNA, it is possible to support copyright protection, database retrieval and quality assessment of digital data representing surfaces and solids. A patent application based on ideas presented in this paper is pending.

Ontology-based assembly design and information sharing for collaborative product development

Abstract: To realize a truly collaborative product design and development process, effective communication among design collaborators is a must. In other words, the design intent that is imposed in a product design should be seized and interpreted properly; heterogeneous modeling terms should be semantically processed both by design collaborators and intelligent systems. Ontologies in the Semantic Web can explicitly represent semantics and promote integrated and consistent access to data and services. Thus, if an ontology is used in a heterogeneous and distributed design collaboration, it will explicitly and persistently represent engineering relations that are imposed in an assembly design. Design intent can be captured by reasoning, and, in turn, as reasoned facts, it can be propagated and shared with design collaborators. This paper presents a new paradigm of ontology-based assembly design. In the framework, an assembly design (AsD) ontology serves as a formal, explicit specification of assembly design so that it makes assembly knowledge both machine-interpretable and to be shared. An Assembly Relation Model (ARM) is enhanced using ontologies that represent engineering, spatial, assembly, and joining relations of assembly in a way that promotes collaborative assembly information-sharing environments. In the developed AsD ontology, implicit AsD constraints are explicitly represented using OWL (Web Ontology Language) and SWRL (Semantic Web Rule Language). This paper shows that the ability of the AsD ontology to be reasoned can capture both assembly and joining intents by a demonstration with a realistic mechanical assembly. Finally, this paper presents a new assembly design information-sharing framework and an assembly design browser for a collaborative product development.

Developing an engineering shape benchmark for CAD models

Abstract: Three-dimensional shape retrieval is a problem of current interest in several different fields, especially in the mechanical engineering domain. There exists a large body of work in developing representations for 3D shapes. However, there has been limited work done in developing domain-dependent benchmark databases for 3D shape searching. We propose a benchmark database for evaluating shape-based search methods relevant to the mechanical engineering domain. Twelve different shape descriptors belonging to three categories, namely: (1) feature vector-based, (2) histogram-based, and (3) view-based, are compared using the benchmark database. The main contributions of this paper are the development of a new engineering shape benchmark and an understanding of the effectiveness of different shape representations for classes of engineering parts. Overall, it was found that view-based representations yielded better retrieval results for a majority of shape classes, while no single method performed best for all shape categories.

Sub-part correspondence by structural descriptors of 3D shapes

Abstract: To fully exploit the valuable knowledge embedded in repositories of digital models, it is crucial to devise search engines capable of expressing high-level and advanced queries, which can effectively support the re-use of CAD models. The retrieval mechanism should be able to return not only global similarity measures among objects, but it should also be coupled with methods for the automatic identification of similar sub-parts in the query and retrieved models, possibly highlighting automatically the object differences. This paper describes a method for partial shape-matching able to recognize similar sub-parts of objects represented as 3D polygonal meshes. The geometry and the structure of the shapes are coupled in a descriptor that provides a flexible coding, grounded on solid mathematical theories, and that can be adapted to the user’s needs and to the context of applications. The matching framework for sub-part correspondence is achieved through a graph-matching technique, which builds the common sub-graphs between the two shapes and highlights the maximal sub-parts having similar structure and similar space distribution.

Semantic interoperability in building design: Methods and tools

Abstract: Semantic interoperability is a crucial element to make building information models understandable and model data sharable across multiple design disciplines and heterogeneous computer systems. This paper presents a new approach and its software implementation for the development of building design objects with semantics of interoperable information to support semantic interoperability in building designs. The novelty of the approach includes its incorporation of building design domain ontology, object-based CAD information modeling, and interoperability standard to make building information models and model data semantically interoperable. A set of methods are proposed to address the issues of object-based building information representation compliant with the Industrial Foundation Classes (IFC); extension of IFC models with the supplementary information; and semantic annotation of the interoperable and extensible information sets. The prototype implementation of these methods provides a set of Web-enabled software tools for effectively generating, managing, and reusing the semantically interoperable building objects in design applications of architectural CAD, structural analysis, and building code conformance checking.

Generation of functional tolerancing based on positioning features

Abstract: The aim behind applying functional tolerancing to a mechanism is to widen the tolerances used in parts manufacturing according to the effective functional properties of the product. This step may be performed using CAD systems and geometrical specifications defined by ISO standards. The present paper will describe the complete process involved in functional tolerancing. The CLIC tolerancing method has been implemented within an Excel software environment. CAD models for parts have been imported via a STEP interface. According to this approach, the designer describes the assembly process; the CLIC system then determines the functional requirements corresponding to the joints between parts and generates all datum reference frames and tolerancing of set-up surfaces in compliance with ISO standards. CLIC also determines both the geometrical conditions of minimum distances in order to avoid interference between parts and the conditions for assembling small standard components. The designer next adds other functional requirements. For each such requirement, a tolerancing process creates location and orientation specifications for influential parts using datum reference frames derived during the previous stage. Excel formulae focusing on the sum of tolerances are generated using a three-dimensional statistical approach. Moreover, the tolerance database allows optimizing the tolerances and nominal dimensions of parts.

On visual similarity based 2D drawing retrieval

Abstract: A large amount of 2D drawings have been produced in engineering fields. To reuse and share the available drawings efficiently, we propose two methods in this paper, namely 2.5D spherical harmonics transformation and 2D shape histogram, to retrieve 2D drawings by measuring their shape similarity. The first approach represents a drawing as a spherical function by transforming it from a 2D space into a 3D space. Then a fast spherical harmonics transformation is employed to get a rotation invariant descriptor. The second statistics-based approach represents the shape of a 2D drawing using a distance distribution between two randomly sampled points. To allow users to interactively emphasize certain local shapes that they are interested in, we have adopted a flexible sampling strategy by specifying a bias sampling density upon these local shapes. The two proposed methods have many valuable properties, including transform invariance, efficiency, and robustness. In addition, their insensitivity to noise allows for the user's causal input, thus supporting a freehand sketch-based retrieval user interface. Experiments show that a better performance can be achieved by combining them together using weights.

Local feature extraction and matching partial objects

Abstract: A primary shortcoming of existing techniques for hree-dimensional (3D) model matching is the reliance on global information of the model’s structure. Models are matched in their entirety, depending on overall topology and geometry information. A currently open challenge is how to perform partial matching. Partial matching is important for finding similarities across part models with different global shape properties and for the segmentation and matching of data acquired from 3D scanners. This paper presents a Scale–Space feature extraction technique based on recursive decomposition of polyhedral surfaces into surface patches. The experimental results presented in this paper suggest that this technique can potentially be used to perform matching based on local model structure. In our previous work, Scale–Space decomposition has been used successfully to extract features from mechanical artifacts. Scale–Space techniques can be parameterized to generate decompositions that correspond to manufacturing, assembly or surface features relevant to mechanical design. One application of these technique is to support matching and content-based retrieval of solid models. This paper shows how a Scale–Space technique can extract features that are invariant with respect to the global structure of the model as well as small perturbations that 3D laser scanning process introduce. In order to accomplish this, we introduce a new distance function defined on triangles instead of points. We believe this technique offers a new way to control the feature decomposition process, which results in the extraction of features that are more meaningful from an engineering viewpoint. The new technique is computationally practical for use in indexing large models. Examples are provided that demonstrate effective feature extraction on 3D laser scanned models. In addition, a simple sub-graph isomorphism algorithm was used to show that the feature adjacency graphs, obtained through feature extraction, are meaningful descriptors of 3D CAD objects. All of the data used in the experiments for this work is freely available at: http://www.designrepository.org/datasets/ .

Feature-based reverse modeling strategies

Abstract: We presented two integrated solution schemes, sectional feature based strategy and surface feature based strategy, for modeling industrial components from point cloud to surfaces without using triangulation. For the sectional feature based strategy, slicing, curve feature recognition and constrained fitting are introduced. This strategy emphasizes the advanced feature architecture patterns from 2D to 3D in reverse engineering. The surface feature based strategy relies on differential geometric attributes estimation and diverse feature extraction techniques. The methods and algorithms such as attributes estimation based on 4D Shepard surface, symmetry plane extraction, quadric surface recognition and optimization, extruded and rotational surface extraction, and blend feature extraction with probability and statistic theory are proposed. The reliable three-dimensional feature fabricated the valid substratum of B-rep model faultlessly. All the algorithms are implemented in RE-SOFT, a reverse engineering software developed by Zhejiang University. The proposed strategies can be used to capture the original design intention accurately and to complete the reverse modeling process conveniently. Typical industrial components are used to illustrate the validation of our feature-based strategies.

An image evaluation approach for parameter-based product form and color design

Abstract: The parameter-based technique provides an efficient and valid means of constructing 3-D geometric models in many CAD software systems. However, its use is generally restricted to the design of mechanical components with regular configurations, and it is not ideally suited to product form and color design. This paper proposes a rapid conceptual design approach, which creates color-rendered forms and combines parameter-based features with fuzzy neural network theorems and gray theory to predict their image evaluation. Two evaluation models (Evaluation Model I and Evaluation Model II) are developed and applied in a case study of an electronic door lock design. Model I uses a fuzzy neural network to predict the overall image, while Model II uses a gray clustering operation for the color image evaluation and two fuzzy neural networks for the form image evaluation and the overall image evaluation. The results show that the image prediction capability of Model II is superior to that of Model I (RMSE: 0.062 versus 0.105). Furthermore, the overall image evaluation is dominated by the door lock's color rather than by its form (RMSE: 0.071 versus 0.162). The dominance of color in determining the image evaluation may be due to the specified image words, form evolution restrictions, or the membership grade ranges of the test color samples and the test form samples, etc. Having established the superiority of Model II, it is applied to develop a consultative design interface integrated with a professional CAD system in order to demonstrate the effectiveness of the proposed product design and image evaluation approach. The design system presented in this study enables a designer to predict the likely image tendencies of a designed product without the need to create and test a prototype model. Hence, he or she can make any design parameter modifications necessary to ensure that the finished product meets its specified image goals.

Finding feasible mold parting directions using graphics hardware

Abstract: We present new programmable graphics hardware accelerated algorithms to test the 2-moldability of geometric parts and assist with part redesign. These algorithms efficiently identify and graphically display undercuts as well as minimum and insufficient draft angles. Their running times grow only linearly with respect to the number of facets in the solid model, making them efficient subroutines for our algorithms that test whether a tessellated CAD model can be manufactured in a two-part mold. We have developed and implemented two such algorithms to choose candidate directions to test for 2-moldability using accessibility analysis and Gauss maps. The efficiency of these algorithms lies in the fact that they identify groups of candidate directions such that if any one direction in the group is undercut-free, all are, or if any one is not undercut-free, none are. We examine trade-offs between the algorithms' speed, accuracy, and whether they guarantee that an undercut-free direction will be found for a part if one exists.

Real-time NURBS interpolation using FPGA for high speed motion control

Abstract: Modern motion control adopts NURBS (Non-Uniform Rational B-Spline) interpolation for the purpose of achieving high-speed and high-accuracy performance. However, in conventional control architectures, the computation of the basis functions of a NURBS curve is very time-consuming due to serial computing constraints. In this paper, a novel FPGA (Field Programmable Gate Array) based motion controller utilizing its high-speed parallel computing power is proposed to realize the Cox-de Boor algorithm for second and higher degrees NURBS interpolation. The motion control algorithm is also embedded in the FPGA chip to implement real-time control and NURBS interpolation simultaneously for multi-axis servo systems. The proposed FPGA-based motion controller is capable of performing the Cox-de Boor algorithm and the IIR (Infinite Impulse Response) control algorithm in about 46 clock cycles, as compared to the 1303 clock cycles by the traditional approach. Numerical simulations and experimental tests using an X-Y table verify the outstanding computation performance of the FPGA-based motion controller. The result indicates that shorter sampling time (10 @ms) can be achieved for NURBS interpolation which is highly critical to the success of high-speed and high-accuracy motion control.

Quasi-triangulation and interworld data structure in three dimensions

Abstract: It is well-known that the Voronoi diagram of points and the power diagram for weighted points, such as spheres, are cell complexes, and their respective dual structures, i.e. the Delaunay triangulation and the regular triangulation, are simplicial complexes. Hence, the topologies of these diagrams are usually stored in their dual complexes using a very compact data structure of arrays. The topology of the Voronoi diagram of three-dimensional spheres in the Euclidean distance metric, on the other hand, is stored in a radial edge data structure which is not as compact as the data structure used for the Voronoi diagram of points and the power diagram for weighted points. In this paper, we define a dual structure of the Voronoi diagram of three-dimensional spheres called a quasi-triangulation and present its important properties. Based on the properties of a quasi-triangulation, we propose a data structure, called an interworld data structure, based on arrays to compactly store the topology of the quasi-triangulation with a guaranteed query performance.

Similarity comparison of mechanical parts to reuse existing designs

Abstract: In actual practice, many new mechanical parts are designed by modifying existing ones In this way, time and effort can be saved by not having to design parts from scratch Design time would be further reduced if there were an efficient way to search for existing similar designs Furthermore, a new part design can be very efficiently generated by modifying the dimensions on the features of the existing part if a part with a similar feature set and the corresponding modeling history can be easily searched from the existing part library In this paper, a two-step similarity comparison method for B-rep files is proposed Overall appearances are compared first, and then detailed features are compared In this way, existing parts with similar feature set in addition to similar overall shape can be identified from the part library Once the similar part is identified, its modeling history can also be used for parametric modeling if the existing part was designed by a feature-based modeler

A public fragile watermarking scheme for 3D model authentication

Abstract: A public fragile watermarking scheme based on the sensitivity of vertex geometry is proposed for 3D model authentication. In the 3D fragile watermarking embedding, slightly perturbing the positions of a subset of vertices is usually needed to keep them in some predefined relationship with their neighboring vertices. Two problems frequently arise in the embedding stage: the causality problem and the convergence problem. The causality problem arises while the neighboring relationship of a former processed vertex is influenced by the perturbing of its latter processed neighboring vertices. The convergence problem means that the original model has been heavily distorted before some vertices reach the predefined relationship. In this paper, we propose a multi-function vertex embedding method and an adjusting-vertex method to overcome these two problems. The proposed method does not need the original model and watermarks for authentication; moreover, the key for extracting watermarks is relatively smaller than that of previous works. For some artistic or technical models, sometimes it is very important to control the distortion ratio caused by watermark embedding. Our method can control the average distortion by the keys used in watermark embedding. Experimental and analytic results on various kinds of 3D models show the effectiveness of the scheme.

Trimming local and global self-intersections in offset curves/surfaces using distance maps

Abstract: A robust and efficient algorithm for trimming both local and global self-intersections in offset curves and surfaces is presented Our scheme is based on the derivation of a rational distance map between the original curve or surface and its offset By solving a bivariate polynomial equation for an offset curve or a system of three polynomial equations for an offset surface, all local and global self-intersection regions in offset curves or surfaces can be detected The zero-set of polynomial equation(s) corresponds to the self-intersection regions These regions are trimmed by projecting the zero-set into an appropriate parameter space The projection operation simplifies the analysis of the zero-set, which makes the proposed algorithm numerically stable and efficient Furthermore, in a post-processing step, a numerical marching method is employed, which provides a highly precise scheme for self-intersection elimination in both offset curves and surfaces The effectiveness of our approach is demonstrated using several experimental results

Machining feature-based similarity assessment algorithms for prismatic machined parts

Abstract: This paper presents algorithms for identifying machined parts in a database that are similar to a given query part based on machining features. In this paper we only consider parts that are machined on 3-axis machining centers. We utilize reduced feature vectors consisting of machining feature access directions, feature types, feature volumes, feature dimensional tolerances and feature group cardinality as a basis for assessing shape similarity. We have defined a distance function between two sets of reduced feature vectors to assess the similarity between them from the machining effort point of view. To assess the similarity between the two parts, one set of reduced feature vectors is transformed in space using rigid body transformations with respect to the other set such that the distance between them is minimized. The distance between the two sets of aligned reduced feature vectors is used as a measure of similarity between the two parts. The existing machined parts are rank ordered based on the value of the distance with respect to the query part. The cost of previously machined parts that have a very small distance from the query part can be used as a basis for estimating the cost of machining the new part.

STEP-compliant CNC system for turning: Data model, architecture, and implementation

Abstract: STEP-NC, a new data model for CAD-CAM-CNC chain, is expected to encompass the whole scope of e-manufacturing. The new data model formalized as ISO 14649 is under development by ISO TC184 SC1 and SC4 for the replacement of the old standard so-called G&M codes, formalized as ISO 6983 which has been used since the 1950s. As the new data model is being established, development and implementation of STEP-compliant CAD/CAM/CNC system based on the new data model is drawing worldwide attention. Several systems have been reported in such international conventions as the ISO Expert Committee Meeting. Up to the present time, all the STEP-CNC systems are intended for milling operation. In this paper, the authors first present STEP-compliant CNC system for turning system including the data model, followed by a generic architecture and functionality. Implementation results obtained from a prototype system called TurnSTEP have been provided. Based on the results, the authors are convinced of the validity of the STEP-NC data model together with the effectiveness of the STEP-CNC system for turning.

Capturing aesthetic intention during interactive evolution

Abstract: Interactive Evolutionary Systems (IES) are capable of generating and evolving large numbers of alternative designs. When using such systems, users are continuously required to interact with the system by making evaluations and selections of the designs that are being generated and evolved. The evolutionary process is therefore led by the visual aesthetic intentions of the user. However, due to the limited size of the computer screen and fuzzy nature of aesthetic evaluations, evolution is usually a mutation-driven and divergent process. The convergent mechanisms typically found in standard Evolutionary Algorithms are more difficult to achieve with IES. To address this problem, this paper presents a computational framework that creates an IES with a higher level of convergence without requiring additional actions from the user. This can be achieved by incorporating a Neural Network based learning mechanism, called a General Regression Neural Network (GRNN), into an IES. GRNN analyses the user's aesthetic evaluations during the interactive evolutionary process and is thereby able to approximate their implicit aesthetic intentions. The approximation is a regression of aesthetic appeals conditioned on the corresponding designs. This learning mechanism allows the framework to infer which designs the users may find desirable. For the users, this reduces the tedious work of evaluating and selecting designs. Experiments have been conducted using the framework to support the process of parametric tuning of facial characters. In this paper we analyze the performance of our approach and discuss the issues that we believe are essential for improving the usability and efficiency of IES.

Standardization and modularization driven by minimizing overall process effort

Abstract: Faster product development is a major goal for companies in competitive markets. Product platform architectures support planning for addressing diverse markets and fulfilling future market desires. Applying standardization or modularization on product platform components leverages current product design effort across future products. This work introduces a method-SMDP (standardization and modularization driven by process effort)-for focusing engineering effort when applying standardization or modularization on product platform components. SMDP calculates the total design effort from current to future generations of the platform following standardization or modularization of components. By comparing the total design cost of different simulations, we can direct the design team to standardization or modularization opportunities. The contribution of this work is in using an estimation of design effort as the basis for decision in contrast to commonly used static measures of components' interactions. Such a computational approach allows conducting sensitivity studies that address the subjective nature of various estimations needed for exercising SMDP. SMDP is illustrated in a product platform design of an external-drum plate-setter for the digital prepress printing market.

Three-dimensional beta shapes

Abstract: The Voronoi diagram of a point set has been extensively used in various disciplines ever since it was first proposed. Its application realms have been even further extended to estimate the shape of point clouds when Edelsbrunner and Mucke introduced the concept of @a-shape based on the Delaunay triangulation of a point set. In this paper, we present the theory of @b-shape for a set of three-dimensional spheres as the generalization of the well-known @a-shape for a set of points. The proposed @b-shape fully accounts for the size differences among spheres and therefore it is more appropriate for the efficient and correct solution for applications in biological systems such as proteins. Once the Voronoi diagram of spheres is given, the corresponding @b-shape can be efficiently constructed and various geometric computations on the sphere complex can be efficiently and correctly performed. It turns out that many important problems in biological systems such as proteins can be easily solved via the Voronoi diagram of atoms in proteins and @b-shapes transformed from the Voronoi diagram.

Region-expansion for the Voronoi diagram of 3D spheres

Abstract: Given a set of spheres in 3D, constructing its Voronoi diagram in Euclidean distance metric is not easy at all even though many mathematical properties of its structure are known This Voronoi diagram has been known for many important applications from science and engineering In this paper, we characterize the Voronoi diagram of spheres in three-dimensional Euclidean space, which is also known as an additively weighted Voronoi diagram, and propose an algorithm to construct the diagram Starting with the ordinary Voronoi diagram of the centers of the spheres, the proposed region-expansion algorithm constructs the desired diagram by expanding the Voronoi region of each sphere, one after another We also show that the whole Voronoi diagram of n spheres can be constructed in O(n^3) time in the worst case

Internal architecture design and freeform fabrication of tissue replacement structures

Abstract: Modeling, design and fabrication of tissue scaffolds with intricate architecture, porosity and pore size for desired tissue properties presents a challenge in tissue engineering. This paper will present the details of our development in the design and fabrication of the interior architecture of scaffolds using a novel design approach. The interior architecture design (IAD) approach seeks to generate layered scaffold freeform fabrication tool path without forming complicated 3D CAD scaffold models. This involves: applying the principle of layered manufacturing to determine the scaffold individual layered process planes and layered contours; defining the 2D characteristic patterns of the scaffold building blocks (unit cells) to form the Interior Scaffold Pattern; and the generating the process tool path for freeform fabrication of these scaffolds with the specified interior architecture. Feasibility studies applying the IAD algorithm to example models with multi-interior architecture and the generation of fabrication planning instructions will also be presented.

Meta-ontology for automated information integration of parts libraries

Abstract: Seamless integration of digital parts libraries or electronic parts catalogs for e-procurement is impeded by semantic heterogeneity. The utilization of ontologies as metadata descriptions of the information sources is a possible approach to providing an integrated view of multiple parts libraries. However, in order to integrate ontologies, the mismatches between them should be resolved. In this paper, we propose meta-concepts with which the ontology developers describe the domain concepts of parts libraries. The meta-concepts have explicit ontological semantics, so that they help to identify domain concepts consistently and structure them systematically. Consequently, our method ensures that the mismatches between parts library ontologies are confined to manageable mismatches which a software program can resolve automatically. Modeling ontologies of real mold and die parts libraries is taken as an example task to show how to use the meta-concepts. We also demonstrate how easily a computer system can merge the resultant well-established ontologies.

Machining feature recognition and tool-path generation for 3-axis CNC milling

Abstract: This study develops an effective method for identifying machining features. While recognizing features, the workpiece is sliced at some assigned positions. The sectional curves of the workpiece faces and slicing plane constitute the feature profiles. Not only the isolated machining features but also the intersecting machining features can be identified by the information from these intersection profiles. Moreover, the recognized machining features can be employed for scheduling the manufacturing sequence. Different kinds of tool paths can be automatically generated for various machining features to improve the cutting efficiency.

A C-tree decomposition algorithm for 2D and 3D geometric constraint solving

Abstract: In this paper, we propose a method which can be used to decompose a 2D or 3D constraint problem into a C-tree. With this decomposition, a geometric constraint problem can be reduced into basic merge patterns, which are the smallest problems we need to solve in order to solve the original problem in certain sense. Based on the C-tree decomposition algorithm, we implemented a software package MMP/Geometer. Experimental results show that MMP/Geometer finds the smallest decomposition for all the testing examples efficiently.

A curvature estimation for pen input segmentation in sketch-based modeling

Abstract: A proper segmentation of pen marking enhances shape recognition and enables a natural interface for sketch-based modeling from simple line drawing tools to 3D solid modeling applications; user input is otherwise restricted to draw only one segment per one stroke. In general, the pen marking segmentation is achieved by detecting the points of high curvature-called, segmenting points-and splitting the pen marking at those points. This paper presents a curvature estimation method, which considers only local shape information. The proposed method can therefore estimate curvature on-the-fly while user is drawing on a pen-input display, such as tablet PCs.

A sweepline algorithm for Euclidean Voronoi diagram of circles

Abstract: Presented in this paper is a sweepline algorithm to compute the Voronoi diagram of a set of circles in a two-dimensional Euclidean space. The radii of the circles are non-negative and not necessarily equal. It is allowed that circles intersect each other, and a circle contains others. The proposed algorithm constructs the correct Voronoi diagram as a sweepline moves on the plane from top to bottom. While moving on the plane, the sweepline stops only at certain event points where the topology changes occur for the Voronoi diagram being constructed. The worst-case time complexity of the proposed algorithm is O((n+m)log n), where n is the number of input circles, and m is the number of intersection points among circles. As m can be O(n^2), the presented algorithm is optimal with O(n^2 log n) worst-case time complexity.

Constrained 3D shape reconstruction using a combination of surface fitting and registration

Abstract: We investigate 3D shape reconstruction from measurement data in the presence of constraints. The constraints may fix the surface type or set geometric relations between parts of an object's surface, such as orthogonality, parallelity and others. It is proposed to use a combination of surface fitting and registration within the geometric optimization framework of squared distance minimization (SDM). In this way, we obtain a quasi-Newton like optimization algorithm, which in each iteration simultaneously registers the data set with a rigid motion to the fitting surface and adapts the shape of the fitting surface. We present examples to show the applicability of our method to constrained 3D shape fitting for reverse engineering of CAD models and to high accuracy fitting with kinematic surfaces, which include surfaces of revolution (reconstructed from fragments of archeological pottery) and spiral surfaces, which are fitted to 3D measurement data of shells. Our optimization algorithm can combine registration of multiple scans of an object and model fitting into a single optimization process which is shown to be superior to the traditional procedure, which first registers the data and then fits a model to it.

P-smart—a virtual system for clothing thermal functional design

Abstract: This paper presents a virtual CAD system developed for clothing thermal functional design and simulation. It allows designers and engineers in virtual space to design and preview the thermal functional performance of clothing and gives feedback to improve the design iteratively. The system provides designers with an effective tool for designing and engineering clothing to achieve superior thermal functional performance.