{"title":"An algorithm for deciding similarities of 3-D objects","authors":"Shinji Mukai, S. Furukawa, M. Kuroda","doi":"10.1145/566282.566334","DOIUrl":"https://doi.org/10.1145/566282.566334","url":null,"abstract":"A new algorithm for deciding the similarity of polyhedral objects is presented. The method consists of the following five sub-procedures.A polyhedron is decomposed into only convex components and represented as a hierarchical tree structure with those convex components, which has already been developed by the authors.From the tree structure, a new data structure called two layer structure, which consists of convex components separated into two layers, i.e., the first layer includes only positive convex components to be added and the second layer represents negative convex components to be subtracted from positive ones, is constructed.The two layer structure of an object is compared with that of another object.Each component of an object is compared with the corresponding convex component of the other object.Similarity of those two polyhedral objects is decided. In addition, similar and dissimilar parts can be recognized, even if two objects are totally not similar..The algorithm is implemented in C language and numerical similarities are calculated for various concave polyhedrons, and the correlation coefficient between numerical similarities and our feeling is calculated. The result is over 0.8. This means that the numerical similarities closely match our expectation.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126819585","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}
V. Adzhiev, E. Kartasheva, T. Kunii, A. Pasko, B. Schmitt
{"title":"Cellular-functional modeling of heterogeneous objects","authors":"V. Adzhiev, E. Kartasheva, T. Kunii, A. Pasko, B. Schmitt","doi":"10.1145/566282.566311","DOIUrl":"https://doi.org/10.1145/566282.566311","url":null,"abstract":"The paper presents an approach to modeling heterogeneous objects as multidimensional point sets with multiple attributes (hypervolumes). A theoretical framework is based on a hybrid model of hypervolumes combining a cellular representation and a constructive representation using real-valued functions. This model allows for independent but unifying representation of geometry and attributes, and makes it possible to represent dimensionally non-homogeneous entities and their cellular decompositions. Hypervolume model components such as objects, operations and relations are introduced and outlined. The framework's inherent multidimensionality allowing, in particular, to deal naturally with time dependence promises to model complex dynamic objects composed of different materials with constructive building of their geometry and attributes. Attributes given at each point can represent properties of arbitrary nature (material, photometric, physical, statistical, etc.). To demonstrate a particular application of the proposed framework, we present an example of multimaterial modeling - a multilayer geological structure with cavities and wells. Another example illustrating the treatment of attributes other than material distributions is concerned with time-dependent adaptive mesh generation where function representation is used to describe object geometry and density of elements in the cellular model of the mesh. The examples have been implemented by using a specialized modeling language and software tools being developed by the authors.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124514409","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":"A new solid subdivision scheme based on box splines","authors":"Yu-Sung Chang, K. T. McDonnell, Hong Qin","doi":"10.1145/566282.566316","DOIUrl":"https://doi.org/10.1145/566282.566316","url":null,"abstract":"During the past twenty years, much research has been undertaken to study surface representations based on B-splines and box splines. In contrast, volumetric splines have received much less attention as an effective and powerful solid modeling tool. In this paper, we propose a novel solid subdivision scheme based on tri-variate box splines over tetrahedral tessellations in 3D. A new data structure is devised to facilitate the straightforward implementation of our simple, yet powerful solid subdivision scheme. The subdivision hierarchy can be easily constructed by calculating new vertex, edge, and cell points at each level as affine combinations of neighboring control points at the previous level. The masks for our new solid subdivision approach are uniquely obtained from tri-variate box splines, thereby ensuring high-order continuity. Because of rapid convergence rate, we acquire a high fidelity model after only a few levels of subdivision. Through the use of special rules over boundary cells, the B-rep of our subdivision solid reduces to a subdivision surface. To further demonstrate the modeling potential of our subdivision solid, we conduct several solid modeling experiments including free-form deformation. We hope to demonstrate that our box-spline subdivision solid (based on tetrahedral geometry) advances the current state-of-the-art in solid modeling in the following aspects: (1) unifying CSG, B-rep, and cell decomposition within a popular subdivision framework; (2) overcoming the shortfalls of tensor-product spline models; (3) generalizing both subdivision surfaces and free-form spline surfaces to a solid representation of arbitrary topology; and (4) taking advantage of triangle-driven, accelerated graphics hardware.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127841203","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":"Subdivision-based multilevel methods for large scale engineering simulation of thin shells","authors":"Seth Green, G. Turkiyyah, D. Storti","doi":"10.1145/566282.566321","DOIUrl":"https://doi.org/10.1145/566282.566321","url":null,"abstract":"This paper presents a multilevel algorithm to accelerate the numerical solution of thin shell finite element problems de-scribed by subdivision surfaces. Subdivision surfaces have become a widely used geometric representation for general curved three dimensional boundary models and thin shells as they provide a compact and robust framework for mod-eling 3D geometry. More recently, the shape functions used in the subdivision surfaces framework have been proposed as candidates for use as finite element basis functions in the analysis and simulation of the mechanical deformation of thin shell structures. When coupled with standard solvers, however, such simulations do not scale well. Run time costs associated with high-resolution simulations (105 degrees of freedom or more) become prohibitive. The main contribution of the paper is to show that the subdivision framework can be used for accelerating such sim-ulations. Specifically the subdivision matrix is used as the intergrid information transfer operator in a multilevel pre-conditioner. The method described in the paper allows the practical simulation or a broad range of problems. Included examples show that the run time of the algorithm presented scales nearly linearly in time with problem size.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134414766","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":"Smooth surface and triangular mesh: comparison of the area, the normals and the unfolding","authors":"J. Morvan, B. Thibert","doi":"10.1145/566282.566306","DOIUrl":"https://doi.org/10.1145/566282.566306","url":null,"abstract":"Replacing a smooth surface with a triangular mesh (i.e., a polyedron) \"close to it\" leads to some errors. The geometric properties of the triangular mesh can be very different from the geometric properties of the smooth surface, even if both surfaces are very close from one another. In this paper, we give examples of \"developable\" triangular meshes (the discrete Gaussian curvature is equal to 0 at each interior vertex) inscribed in a sphere (whose Gaussian curvature is equal to 1 at every point). However, if we make assumptions on the geometry of the triangular mesh, on the curvature of the smooth surface and on the Hausdorff distance between both surfaces, we get an estimate of several properties of the smooth surface in terms of the properties of the triangular mesh. In particular, we give explicit approximations of the normals and of the area of the smooth surface. Furthermore, if we suppose that the smooth surface is developable (i.e., \"isometric\" to a surface of the plane), we give an explicit approximation of the \"unfolding\" of this surface. Just notice that in some of our approximations, we do not suppose that the vertices of the triangular mesh belong to the smooth surface. Oddly, the upper bounds on the errors are better when triangles are right-angled (even if there are small angles): we do not need every angle of the triangular mesh to be quite large. We just need each triangle of the triangular mesh to contain at least one angle whose sine is large enough. Besides, approximations are better if the triangles of the triangular mesh are quite small where the smooth surface has a large curvature. Some proofs will be omitted.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124928147","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":"Directional offset of a 3D curve","authors":"Hayong Shin, S. K. Cho","doi":"10.1145/566282.566329","DOIUrl":"https://doi.org/10.1145/566282.566329","url":null,"abstract":"Being a fundamental operation in geometric modeling, there have been a number of researches on offsetting of 2D curves and 3D surfaces. However, there is no commonly accepted definition of 3D curve offset. In this paper, we propose a 3D curve offset method, named directional offset, motivated from the observation of the needs in many engineering design practices. Since the normal vector of a 3D curve at a point is not unique, a 3D curve offset definition is about how to select the offset direction vector on the normal plane of the curve. A previous research on this issue specifies the offset direction vector with a constant angle from the principal normal vector. In directional offset, the offset direction vector on the normal plane is chosen to be perpendicular to the user-specified projection direction vector k. Each point on the original curve is then moved along the offset direction by given offset distance. The directional offset has the following characteristics: (a) directional offset is a natural extension of 2D curve offset, in the sense that they produce the same result when applied to 2D planar curve, with k being normal to the plane, and (b) when k is parallel to Z-axis, the directional offset of a 3D curve is similar to 2D curve offset on XY plane projected image, while inheriting the Z-axis ordinate from the original curve. These properties make it useful in many engineering design applications such as the flange of a sheet metal part, the overflow area design of a forging die, and the cutting blade design of a trimming die for a stamped part. An overall procedure to compute a directional offset for a position-continuous NURBS curve is described with an emphasis on avoiding self-intersection loop.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128949322","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":"Sketch- and constraint-based design of B-spline surfaces","authors":"P. Michalik, Dae-Hyun Kim, B. Brüderlin","doi":"10.1145/566282.566325","DOIUrl":"https://doi.org/10.1145/566282.566325","url":null,"abstract":"This paper describes a sketch- and constraint-based approach to editing of free-form curves and surfaces. We present a simple touch-and-replace technique to edit 2D and 3D curves. We introduce auxiliary surfaces that allow for a reliable interpretation of users' pen-strokes in 3D and we present a new method for sketch-and constraint-based surface sculpting.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115026631","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":"A local coordinate system on a surface","authors":"J. Boissonnat, Julia Flötotto","doi":"10.1145/566282.566302","DOIUrl":"https://doi.org/10.1145/566282.566302","url":null,"abstract":"Coordinate systems associated to a finite set of sample points have been extensively studied, especially in the context of interpolation of multivariate scattered data. Notably, Sibson proposed the so-called natural neighbor coordinates that are defined from the Voronoi diagram of the sample points. A drawback of those coordinate systems is that their definition domain is restricted to the convex hull of the sample points. This make them difficult to use when the sample points belong to a surface. To overcome this difficulty, we propose a new system of coordinates. Given a closed surface, i.e. a manifold of, the coordinate system is defined everywhere on the surface, is continuous, and is local even if the sampling density is finite. Moreover, it is inherently 1-dimensional while the previous systems are dimensional. No assumption is made about the ordering, the connectivity or topology of the sample points nor of the surface. We illustrate our results with an application to interpolation over a surface.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128122620","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}
C. Y. Ip, Daniel Lapadat, Leonard Sieger, W. Regli
{"title":"Using shape distributions to compare solid models","authors":"C. Y. Ip, Daniel Lapadat, Leonard Sieger, W. Regli","doi":"10.1145/566282.566322","DOIUrl":"https://doi.org/10.1145/566282.566322","url":null,"abstract":"Our recent work has described how to use feature and topology in-formation to compare 3-D solid models. In this work we describe a new method to compare solid models based on shape distributions. Shape distribution functions are common in the computer graphics and computer vision communities. The typical use of shape dis-tributions is to compare 2-D objects, such as those obtained from imaging devices (cameras and other computer vision equipment). Recent work has applied shape distribution metrics for compari-son of approximate models found in the graphics community, such as polygonal meshes, faceted representation, and Virtual Reality Modeling Language (VRML) models. This paper examines how to adapt these techniques to comparison of 3-D solid models, such as those produced by commercial CAD systems. We provide a brief review of shape matching with distribution functions and present an approach to matching solid models. First, we show how to ex-tend basic distribution-based techniques to handle CAD data that has been exported to VRML format. These extensions address specific geometries that occur in mechanical CAD data. Second, we describe how to use shape distributions to directly interrogate solid models. Lastly, we show how these techniques can be put together to provide a \"query by example\" interface to a large, het-erogeneous, CAD database: The National Design Repository. One significant contribution of our work is the systematic technique for performing consistent, engineering content-based comparisons of CAD models produced by different CAD systems.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131311770","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":"Interactive sculpting with implicit surfaces","authors":"Marie-Paule Cani","doi":"10.1145/566282.566284","DOIUrl":"https://doi.org/10.1145/566282.566284","url":null,"abstract":"Providing the user with an intuitive sculpting system similar to real clay is one of the most challenging long term goals in interactive modeling. The user should ideally be able to deform, add and remove material, with no restriction on the geometry and topological genius of the solid being edited. Implicit surfaces, defined as iso-surfaces of scalar fields, are a very attractive model in such situations. This talk reviews two alternative implicit representations, the constructive approach versus sampled fields, and discusses their convenience for modeling virtual clay. An implicit sculpting system which incorporates force feedback and relies on multiresolution to accelerate editing is presented.","PeriodicalId":286112,"journal":{"name":"International Conference on Smart Media and Applications","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131638019","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}