{"title":"4-8 factorization of quadrilateral subdivision","authors":"L. Velho","doi":"10.1145/376957.376993","DOIUrl":"https://doi.org/10.1145/376957.376993","url":null,"abstract":"Mesh structures traditionally used for subdivision are derived from regular triangular or quadrilateral tilings. In contrast, the 4–8 mesh is based on the Laves tilings of type [4:8], which is a triangulated quadrangulation. The semi-regular 4–8 mesh is a hierarchical structure for subdivision surfaces that has powerful adaptation capabilities. In this work, we show how to construct Catmull-Clark and Doo-Sabin surfaces, using 4–8 mesh refinement. We decompose the associated subdivision schemes into rules that are compatible with the underlying 4–8 mesh structure. Our motivation for developing such methods is to incorporate the power of 4–8 meshes into the above classical subdivision surfaces. The refinement of 4–8 meshes is composed of two binary subdivision steps. In the first step, the mesh is refined in the horizontal and vertical directions, while in the second step, the mesh is refined in the two diagonal directions. The principle for decomposing the Catmull-Clark subdivision scheme using 4–8 meshes is to distribute the rules at the appropriate steps of 4–8 refinement. According to this principle, face and corner rules are applied at even steps, while the edge rule is applied at odd steps. The associated masks are shown below: 1_ 4 1_ 4 1_ 4 1_ 4 (a) face 1_ 16 _ 1 2 1_ 16 1_ 16 1_ 16 1_ 16","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129376594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Geometric constraint solver using multivariate rational spline functions","authors":"G. Elber, Myung-Soo Kim","doi":"10.1145/376957.376958","DOIUrl":"https://doi.org/10.1145/376957.376958","url":null,"abstract":"We present a new approach to building a solver for a set of geometric constraints represented by multivariate rational functions. The constraints are formulated using inequalities as well as equalities. When the solution set has dimension larger than zero, we approximate it by fitting a hypersurface to discrete solution points. We also consider a variety of constraint solving problems common in geometric modeling. These include computing ray-traps, bisectors, sweep envelopes, and regions accessible during 5-axis machining.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122388146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reconstructing occlusal surfaces of teeth using a genetic algorithm with simulated annealing type selection","authors":"V. Savchenko, L. Schmitt","doi":"10.1145/376957.376962","DOIUrl":"https://doi.org/10.1145/376957.376962","url":null,"abstract":"In this paper, we present an application of numerical optimization for surface reconstruction (more precisely: reconstruction of missing parts of a real geometric object represented by volume data) by employing a specially designed genetic algorithm to solve a problem concerning computer-aided design in dentistry. Using a space mapping technique the surface of a given model tooth is fitted by a shape transformation to extrapolate (or reconstruct) the remaining surface of a patient's tooth with occurring damage such as a “drill hole.” Thereby, the genetic algorithm minimizes the error of the approximation by optimizing a set of control points that determine the coefficients for spline functions, which in turn define a space transformation. The fitness function to be minimized by the genetic algorithm is the error between the transformed occlusal surface of the model tooth and the remaining occlusal surface of the damaged (drilled) tooth. The algorithm, that is used, is based upon a proposal by Mahfoud and Goldberg. It uses a simulated-annealing type selection scheme, which is applied sequentially (pair-wise, or one-by-one) to the members in the parent generation and their respective offspring generated by mutation-crossover. We outline a proof of convergence for this algorithm. The algorithm is parallel in regard to computing the fitness-values of creatures.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"355 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122799022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
B. Mills, F. Langbein, A. Marshall, Ralph Robert Martin
{"title":"Approximate symmetry detection for reverse engineering","authors":"B. Mills, F. Langbein, A. Marshall, Ralph Robert Martin","doi":"10.1145/376957.376985","DOIUrl":"https://doi.org/10.1145/376957.376985","url":null,"abstract":"The authors are developing an automated reverse engineering system for reconstructing the shape of simple mechanical parts. B-rep models are created by fitting surfaces to point clouds obtained by scanning an object using a 3D laser scanner. The resulting models, although valid, are often not suitable for purposes such as redesign because expected regularities and constraints are not present. This information is lost because each face of the model is determined independently. A global approach is required, in particular one that is capable of finding symmetries originally present. This paper describes a practical algorithm for finding global symmetries in suitable B-rep models built from planes, spheres, cylinders, cones and tori. It has been implemented and used to determine approximate symmetries of models with up to about 200 vertices in reasonable time. The time performance of the algorithm in the worst case is bounded by O(n 3.5 log4 n), and a justification is given that on common engineering objects it takes about O(n2 log4 n), making it a practical tool for use in a reverse engineering package. Details of the algorithm are given, along with some results from a number of illustrative test runs.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126659154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Three dimensional threaded fastener meshing algorithm","authors":"Paul Kinney, D. Strenski","doi":"10.1145/376957.376967","DOIUrl":"https://doi.org/10.1145/376957.376967","url":null,"abstract":"Understanding the stresses in the root of a thread of a bolt has never been easy. Ideally one would like to put a strain gage right at the root and measure them directly, but the placement of the gage and its wires are impossible without changing the insitu environment. Engineers then turned to analytical models, but soon discovered that two dimensional models where not giving the correct results because the geometry is not axis symmetric and three dimensional models where too difficult to mesh with today's CAD tools. A team consisting of Ford engineers and computer programers developed a program that will automatically generate a full three dimensional model of a thread fastener and mating threaded block by using a combination of cylindrical meshing techniques and a method of revolving “profiles” in a helical coordinate system. The bolt meshing program is able to input parameters about the thread fastener and block: diameter, pitch, length, etc., and output a complete three dimensional model in the form of an ABAQUS or NASTRAN finite element input deck. This model can then run through the ABAQUS finite element program and the resulting stress field computed. This paper will focus on the algorithm used to generate the mesh.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115090226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jun Huang, Satyandra K. Gupta, S. Dhaliwal, Malay Kumar
{"title":"A geometric algorithm for automated design of multi-piece sacrificial molds","authors":"Jun Huang, Satyandra K. Gupta, S. Dhaliwal, Malay Kumar","doi":"10.1145/376957.376996","DOIUrl":"https://doi.org/10.1145/376957.376996","url":null,"abstract":"Molds are required in a large number of manufacturing operations such as metal casting, die making, injection molding, ceramic and polymer processing etc. Molded and cast parts are used extensively because they produce net-shape parts that require minimal secondary operations. On the basis of the number of pieces in a mold, molds can be divided into two piece molds and multi-piece molds. Multi-piece molds refer to molds having more than two pieces. These molds can produce complex parts that cannot be made using two-piece molds. They enable the use of molding for making parts that were previously manufactured using other processes. Since they have more than two pieces, multi-piece molds have more than one parting surface. This enables the mold to be decomposed along different directions and thus can be used to make geometrically complex parts.\u0000Sacrificial molds refer to molds that can be destroyed after the part has been produced. They are generally made of low melting point materials such as wax or ABS and are typically destroyed by heating the mold-part assembly. Moreover, the wax molds can be easily machined making them very easy to manufacture at high production rates. Therefore, sacrificial molds can be used to circumvent the disassembly problems that arise in permanent mold casting. Sacrificial multi-piece molds find use in several manufacturing domains. Examples include manufacture of polymer parts and gelcasting of ceramic parts.\u0000Our algorithm for automated design of multi-piece sacrificial molds uses a three-step approach. The gross mold is created by subtracting the part from a large rectangular block that completely encloses the part. The three steps of the mold design algorithm are listed below.\u0000Decomposition to Solve Accessibility Problems: First, a feature-based decomposition of the mold is done to generate individual mold components for each of the primitives constituting the part. All decompositions are performed along planar faces. Second, once the feature-based decomposition is completed, some of the individual mold components are further decomposed to eliminate concave edges that are not accessible to non-zero diameter milling tools.\u0000Combining Mold Components to Reduce Manufacturing Cost: Once the decomposition has been completed, some of the individual mold components may be combined if the resulting mold component is completely accessible. The list of candidate combinations consists of all pairs of mold components that share a common planar face. Among them, only valid combinations are performed. The validation check is guided by a set of rules to ensure the accessibility of the composite mold components resulting from combinations.\u0000Addition of Assembly Features: Once the mold combination is completed, assembly features are added to the mold components in the mold assembly.\u0000There are a number of potential benefits of automating the design of multi-piece molds. The principal benefits are enumerated below.\u0000Mold design is a labor","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126308034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Is this a quadrisected mesh?","authors":"G. Taubin","doi":"10.1145/376957.376987","DOIUrl":"https://doi.org/10.1145/376957.376987","url":null,"abstract":"In this paper we introduce a fast and efficient linear time and space algorithm to detect and reconstruct uniform Loop subdivision structure, or triangle quadrisection, in irregular triangular meshes. Instead of a naive sequential traversal algorithm, and motivated by the concept of covering surface in Algebraic Topology, we introduce a new algorithm based on global connectivity properties of the covering mesh. We consider two main applications for this algorithm. The first one is to enable interactive modelling systems that support Loop subdivision surfaces, to use popular interchange file formats which do not preserve the subdivision structure, such as VRML, without loss at information. The second application is to improve the compression efficiency of existing lossless connectivity compression schemes, by optimally compressing meshes with Loop subdivision connectivity. Extensions to other popular uniform subdivision schemes such as Catmull-Clark and Doo-Sabin, are relatively straightforward but will be studied elsewhere.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129493931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Representation of temporal change in solid models","authors":"Erik E. Hayes, J. Sevy, W. Regli","doi":"10.1145/376957.377001","DOIUrl":"https://doi.org/10.1145/376957.377001","url":null,"abstract":"Solid models are static entities, usually defined by a boundary representation model as a set of enclosing surfaces. Constructive Solid Geometry and existing feature-based computer-aided design environments create procedural descriptions of 3D objects as history or CSG trees. These representations are temporally fixed, i.e., they describe the state of a 3D object at a particular point in time.\u0000This paper describes a method to represent and capture the temporal evolution of solid models—what we call the model process history of an object. We define the process history to be the total set of states the model goes through during the design process—the search space of the detailed design process. This paper presents our work to develop a representational formalism we call model process graphs (MPGs). We use MPGs to integrate a traditional 3D solid model's BRep and feature-based descriptions with a model of the temporal changes that occur during the design process. We believe that MPG representations can have valuable application for many design and manufacturing problems. The paper briefly defines our MPGs that will (1) create a record of the design process; (2) store process-based design rationale; (3) represent in-process shapes for machined artifacts. We anticipate that MPG-like representations will find application in other design and manufacturing problems in which important process knowledge is embodied by temporal changes that occur as models evolve to their final forms.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129691270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"FRONTIER: fully enabling geometric constraints for feature-based modeling and assembly","authors":"J. Oung, Meera Sitharam, Brandon Moro, A. Arbree","doi":"10.1145/376957.376995","DOIUrl":"https://doi.org/10.1145/376957.376995","url":null,"abstract":"In the full paper [1], we discuss the functionality and implementation challenges of the Frontier geometric constraint engine, designed to address the main reasons for the underutilization of geometric constraints in today's 3D design and assembly systems. Here, we motivate the full paper by outlining the advantages of Frontier.\u0000Frontier fully enables both (a) the use of complex, cyclic, spatial constraint structures as well as (b) feature-based design. To deal with Issue (a), Frontier relies on the efficient generation of a close-to-optimal decomposition and recombination (DR) plan for completely general variational constraint systems (see Figure 1). A serious bouleneck in constraint solving is the exponential time dependence on the size of the largest system that is simultaneously solved by the algebraic-numeric solver. In most naturally occurring cases, Frontier's DR-plan is guaranteed in minimize this size (to within a small constant factor). To deal with Issue (b), Frontier's DR-plan admits the independent and local manipulation of features and sub-assemblies in one or more underlying feature hierarchies that are input (Figures 1 and 2). A DR-plan satisfying the above requirements is generated by the new Frontsier vertex Algorithm (FA): the DR problem and its significance as well as FA and its performance with respect to several relevant and newly formalized abstract measures are described in [2, 3].\u0000Frontier employs a crucial representation of the DR-plan's subsystems or clusters, their hierarchy and their interaction This representation merges network flow information, as well as other geometric and combinatorial information in a natural manner. Some of this information is obtained from an efficient flow-based algorithm for detecting small rigid sub-systems presented in [4]. The clarity of this representation is crucial in the concrete realization of FA's formal performance. More significantly, this representation allows Frontier to take advantage of its DR-plan in surprising and unsuspected ways listed below.\u0000","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123279691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Volumetric multi-texturing for functionally gradient material representation","authors":"Seok-Min Park, R. Crawford, J. Beaman","doi":"10.1145/376957.376982","DOIUrl":"https://doi.org/10.1145/376957.376982","url":null,"abstract":"Solid Freeform Fabrication (SFF) methods have demonstrated the potential to manufacture parts from Functionally Gradient Materials (FGM). One of the keys to success is an accurate and systematic represention of varying material distributions in the geometry. This paper introduces a method called Volumetric Multi-Texturing (VMT) to represent a three dimensional density gradient. The scheme originates from volumetric rendering by texturing, which is used in computer graphics to create fuzzy objects such as clouds and smoke. By analogy, FGM design is envisaged as creating material clouds in a confined geometric space in a structured and controllable manner. Another motivation for pursuing this approach is that, based on our research into expected applications, material gradients will be emphasized near the surface of a part. Our method exploits procedural and implicit schemes to design and acquire density information. The implicit procedural approach, as opposed to an input database, allows a user to interactively create and modify the design patterns without explicitly changing the individual values in the database. Further, it promises convenience in process planning, and efficiency in data storage and computation time. The material gradient modeler is applied to a boundary representation (B-rep) model of the part. Therefore, this scheme can be easily integrated most commercial solid modelers. The theoretical approach, design procedure, and tool path generation for fabricating example parts are presented in the paper.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"623 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124108678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}