{"title":"Multiresolution heterogeneous solid modeling and visualization using trivariate simplex splines","authors":"Jing Hua, Ying He, Hong Qin","doi":"10.2312/SM.20041376","DOIUrl":"https://doi.org/10.2312/SM.20041376","url":null,"abstract":"This paper presents a new and powerful heterogeneous solid modeling paradigm for representing, modeling, and rendering of multi-dimensional, physical attributes across any volumetric objects. The modeled solid can be of complicated geometry and arbitrary topology. It is formulated using a trivariate simplex spline defined over a tetrahedral decomposition of any 3D domain. Heterogeneous material attributes associated with solid geometry can be modeled and edited by manipulating the control vectors and/or associated knots of trivariate simplex splines easily. The multiresolution capability is achieved by interactively subdividing any regions of interest and allocating more knots and control vectors accordingly. We also develop a feature-sensitive fitting algorithm that can reconstruct a more compact, continuous trivariate simplex spline from structured or unstructured volumetric grids. This multiresolution representation results from the adaptive and progressive tetrahedralization of the 3D domain. In addition, based on the simplex spline theory, we derive several theoretical formula and propose a fast direct rendering algorithm for interactive data analysis and visualization of the simplex spline volumes. Our experiments demonstrate that the proposed paradigm augments the current modeling and visualization techniques with the new and unique advantages.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126577493","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":"Shape similarity measurement using ray distances for mass customization","authors":"T. Hwang, Kunwoo Lee, H. Y. Oh, J. Jeong","doi":"10.2312/SM.20041402","DOIUrl":"https://doi.org/10.2312/SM.20041402","url":null,"abstract":"Custom-tailored products are defined as products having various sizes and shapes tailored to meet the customer's different tastes or needs. Thus fabrication of custom-tailored products inherently involves inefficiency. To minimize this inefficiency, a new paradigm is proposed in this work. In this paradigm, different parts are grouped into several groups according to their sizes and shapes. For grouping the different parts, similarity measurement algorithm is used. Similarity comparison starts with the determination of the closest pose between two shapes in consideration. The closest pose is derived by comparing the ray distances while one shape is virtually rotated with respect to the other. Shape similarity value and overall similarity value calculated from ray distances are also used for grouping. A prototype system based on the proposed methodology has been implemented and applied to the grouping and machining of the shoe lasts of various shapes and sizes.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131188851","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":"Handling degeneracies in exact boundary evaluation","authors":"Koji Ouchi, J. Keyser","doi":"10.2312/SM.20041409","DOIUrl":"https://doi.org/10.2312/SM.20041409","url":null,"abstract":"We present a method for dealing with degenerate situations in an exact boundary evaluation system. We describe the possible degeneracies that can arise and how to detect them. We then present a numeric perturbation method that is simpler to implement within a complex system than symbolic perturbation methods.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130752925","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. Hoffmann, Gahyun Park, J. Simard, N. F. Stewart
{"title":"Residual iteration and accurate polynomial evaluation for shape-interrogation applications","authors":"C. Hoffmann, Gahyun Park, J. Simard, N. F. Stewart","doi":"10.2312/SM.20041371","DOIUrl":"https://doi.org/10.2312/SM.20041371","url":null,"abstract":"Surface interrogation and intersection depend crucially on good root-finding algorithms, which in turn depend on accurate polynomial evaluation. Conventional algorithms for evaluation typically encounter difficulties near multiple roots, or roots that are very close, and this may lead to gross errors in the geometric computation, or even catastrophic failure. In this paper we study the cost and accuracy of several approaches to polynomial evaluation, explaining the reasons for non-convergence of certain methods, and supporting our subsequent conclusions with the results of benchmarking experiments.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114142298","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":"Reconstruction with 3D geometric bilateral filter","authors":"Alex Miropolsky, A. Fischer","doi":"10.2312/SM.20041393","DOIUrl":"https://doi.org/10.2312/SM.20041393","url":null,"abstract":"In recent years, reverse engineering (RE) techniques have been developed for surface reconstruction from 3D scanned data. Typical sampling data, however, usually is large scale and contains unorganized points, thus leading to some anomalies in the reconstructed object. To improve performance and reduce processing time, Hierarchical Space Decomposition (HSD) methods can be applied. These methods are based on reducing the sampled data by replacing a set of original points in each voxel by a representative point, which is later connected in a mesh structure. This operation is analogous to smoothing with a simple low- pass filter (LPF). Unfortunately, this principle also smoothes sharp geometrical features, an effect that is not desired. The high performance results of bilateral filtering for removing noise from 2D images while preserving details motivated us to extend this filtering and apply it to 3D scan points. This paper introduces anisotropic 3D scan point filtering, which we have defined as 3D Geometric Bilateral Filtering (GBF). The proposed GBF method smoothes low curvature regions while preserving sharp geometric features, and it is robust, simple and fast.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114269874","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":"Planar parameterization for closed 2-manifold genus-1 meshes","authors":"D. Steiner, A. Fischer","doi":"10.2312/SM.20041379","DOIUrl":"https://doi.org/10.2312/SM.20041379","url":null,"abstract":"Parameterization of 3D meshes is important for many graphics and CAD applications, in particular for texture mapping, re-meshing and morphing. Current parameterization methods for closed manifold genus-n meshes usually involve cutting the mesh according to the object generators, fixing the resulting boundary and then applying the 2D position for each of the mesh vertices on a plane, such that the flattened triangles are not too distorted and do not overlap. Unfortunately, fixing the boundary distorts the resulting parameterization, especially near the boundary. A special case is that of closed manifold genus-1 meshes that have two generators. They can therefore be flattened naturally to a plane without the use of a fixed boundary while still maintaining the continuity of the parameterization. Therefore, in treating genus-1 objects, this attribute must be exploited. This paper introduces a generalized method for planar parameterization of closed manifold genus-1 meshes. As in any planar parameterization with a fixed boundary, weights are assigned over the mesh edges. The type of weights defined depends on the type of mesh characteristics to be preserved. The paper proves that the method satisfies the non-overlapping requirement for any type of positive barycentric weights, including nonsymmetrical weights. Moreover, convergence is guaranteed according to the Gauss-Seidel method. The proposed method is simple to implement, fast and robust. The feasibility of the method will be demonstrated on several complex objects.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121173387","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. Starly, A. Darling, Conny Gomez, J. Nam, Wei Sun, A. Shokoufandeh, W. Regli
{"title":"Image based bio-cad modeling and its applications to biomedical and tissue engineering","authors":"B. Starly, A. Darling, Conny Gomez, J. Nam, Wei Sun, A. Shokoufandeh, W. Regli","doi":"10.2312/SM.20041401","DOIUrl":"https://doi.org/10.2312/SM.20041401","url":null,"abstract":"CAD has been traditionally used to assist in engineering design and modeling for representation, analysis and manufacturing. Advances in Information Technology and in Biomedicine have created new uses for CAD with many novel and important biomedical applications, particularly in tissue engineering in which the CAD based bio-tissue informatics model provides critical information of tissue biological, biophysical, and biochemical properties for modeling, design, and fabrication of complex tissue substitutes. This paper will present some salient advances of bio-CAD modeling and application in computer-aided tissue engineering, including biomimetic design, analysis, simulation and freeform fabrication of tissue engineered substitutes. Overview of computer-aided tissue engineering will be given. Methodology to generate bio-CAD modeling from high resolution non-invasive imaging, the medical imaging process and the 3D reconstruction technique will be described. Enabling state-of-the-art computer program in assisting the 3D reconstruction and in bio-modeling development will be introduced. Utilization of the bio-CAD model for the description and representation of the morphology, heterogeneity, and organizational structure of tissue anatomy will also be presented.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130683173","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":"Stability and homotopy of a subset of the medial axis","authors":"F. Chazal, A. Lieutier","doi":"10.2312/SM.20041396","DOIUrl":"https://doi.org/10.2312/SM.20041396","url":null,"abstract":"Medial Axis is known to be unstable for non smooth objects. For an open set <i>O</i>, we define the Weak Feature Size, wfs, minimum distance between <i>O</i><sup>c</sup> and the critical points of the function distance to <i>O</i><sup>c</sup>. We introduce the \"Lambda-Medial Axis\" of <i>O</i>, Mλ, a subset of the Medial Axis of <i>O</i> which captures the Homotopy type of <i>O</i> when λ < wfs. We show that, at least for some \"regular\" values of λ, M<inf>λ</inf> remains stable under Hausdorff distance perturbations of <i>O</i><sup>c</sup>.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131069088","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":"Efficient and robust computation of an approximated medial axis","authors":"Yuandong Yang, O. Brock, R. Moll","doi":"10.2312/SM.20041372","DOIUrl":"https://doi.org/10.2312/SM.20041372","url":null,"abstract":"The medial axis can be viewed as a compact representation for an arbitrary model; it is an essential geometric structure in many applications. A number of practical algorithms for its computation have been aimed at speeding up its computation and at addressing its instabilities. In this paper we propose a new algorithm to compute the medial axis with arbitrary precision. It exhibits several desirable properties not previously combined in a practical and efficient algorithm. First, it allows for a tradeoff between computation time and accuracy, making it well-suited for applications in which an approximation of the medial axis suffices, but computational efficiency is of particular concern. Second, it is output sensitive: the computation complexity of the algorithm does not depend on the size of the representation of a model, but on the size of the representation of the resulting medial axis. Third, the densities of the approximated medial axis points in different areas are adaptive to local free space volumes, based on the assumption that a coarser approximation in wide open area can still suffice the requirements of the applications. We present theoretical results, bounding the error introduced by the approximation process. The algorithm has been implemented and experimental results are presented that illustrate its computational efficiency and robustness.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131729154","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":"Update operations on 3D simplicial decompositions of non-manifold objects","authors":"L. Floriani, Annie Hui","doi":"10.5555/1217875.1217900","DOIUrl":"https://doi.org/10.5555/1217875.1217900","url":null,"abstract":"We address the problem of updating non-manifold mixed-dimensional objects, described by three-dimensional simplicial complexes embedded in 3D Euclidean space. We consider two local update operations, edge collapse and vertex split, which are the most common operations performed for simplifying a simplicial complex. We examine the effect of such operations on a 3D simplicial complex, and we describe algorithms for edge collapse and vertex split on a compact representation of a 3D simplicial complex, that we call the Non-Manifold Indexed data structure with Adjacencies (NMIA). We also discuss how to encode the information needed for performing a vertex split and an edge collapse on a 3D simplicial complex. The encoding of such information together with the algorithms for updating the NMIA data structure form the basis for defining progressive as well as multi-resolution representations for objects described by 3D simplicial complexes and for extracting variable-resolution object descriptions.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127453458","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}