Edgebreaker is a simple technique for compressing three-dimensional triangle meshes. We introduce here a new formulation of Edgebreaker, which leads to a very simple implementation. We describe it in terms of a simple data structure, which we call the Corner Table. It represents the connectivity of any manifold mesh as two tables, V and O, such that for a corner c, which is the association of a triangle with a vertex, V[c] is an integer reference to the vertex of c and O[c] is an integer reference to the opposite corner. For meshes that are homeomorphic to a sphere, Edgebreaker encodes these two tables with less than 2 bits per triangle. It compresses vertex locations using Touma and Gottsman's parallelogram predictor. We also present a new decompression, inspired by the Wrap&Zip decompression technique developed in collaboration with Andrzej Szymczak. We call it Zip&Wrap, because it works in the inverse direction from Wrap&Zip and zips cracks in the reconstructed mesh sooner. The detailed source code for the compression and the decompression algorithms fits on a single page. A further improvement of the codebook of Edgebreaker, developed with D. King, guarantees no more than 1.73 bits per triangle for the connectivity. Entropy encoding reduces this cost in practice to less than a bit per triangle when the mesh is large. Through minor modifications, the Edgebreaker algorithm has been adapted to manifold meshes with holes and handles, to non-triangle meshes, and to non-manifold meshes. A Corner-Table implementation of these is described elsewhere.
{"title":"3D compression made simple: Edgebreaker with ZipandWrap on a corner-table","authors":"J. Rossignac","doi":"10.1109/SMA.2001.923399","DOIUrl":"https://doi.org/10.1109/SMA.2001.923399","url":null,"abstract":"Edgebreaker is a simple technique for compressing three-dimensional triangle meshes. We introduce here a new formulation of Edgebreaker, which leads to a very simple implementation. We describe it in terms of a simple data structure, which we call the Corner Table. It represents the connectivity of any manifold mesh as two tables, V and O, such that for a corner c, which is the association of a triangle with a vertex, V[c] is an integer reference to the vertex of c and O[c] is an integer reference to the opposite corner. For meshes that are homeomorphic to a sphere, Edgebreaker encodes these two tables with less than 2 bits per triangle. It compresses vertex locations using Touma and Gottsman's parallelogram predictor. We also present a new decompression, inspired by the Wrap&Zip decompression technique developed in collaboration with Andrzej Szymczak. We call it Zip&Wrap, because it works in the inverse direction from Wrap&Zip and zips cracks in the reconstructed mesh sooner. The detailed source code for the compression and the decompression algorithms fits on a single page. A further improvement of the codebook of Edgebreaker, developed with D. King, guarantees no more than 1.73 bits per triangle for the connectivity. Entropy encoding reduces this cost in practice to less than a bit per triangle when the mesh is large. Through minor modifications, the Edgebreaker algorithm has been adapted to manifold meshes with holes and handles, to non-triangle meshes, and to non-manifold meshes. A Corner-Table implementation of these is described elsewhere.","PeriodicalId":247602,"journal":{"name":"Proceedings International Conference on Shape Modeling and Applications","volume":"29 17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122324885","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}
In this paper, we present hierarchical D-NURBS as a new shape modeling representation which generalizes powerful, physics-based D-NURBS for interactive geometric design. Our hierarchical D-NURBS can be viewed as a collection of standard D-NURBS finite elements, organized hierarchically in a tree structure and subject to continuity constraints across the shared boundaries of adjacent D-NURBS elements at different levels. The layered and composite construction of hierarchical D-NURBS affords users the effective creation of local features and their flexible, global/local control at different level of details. Within the framework of hierarchical D-NURBS, users can interactively sculpt NURBS geometry more intuitively and conveniently through both global and local toolkits. Based on the data structure of hierarchical D-NURBS, we have developed a prototype software equipped with various physics based toolkits in the form of geometric constraints and simulated forces. Our modeling system allows users to undertake the design tasks of point manipulation, normal editing, curvature control, curve fitting, and area sculpting in interactive graphics and CAD/CAM.
{"title":"Hierarchical D-NURBS surfaces and their physics-based sculpting","authors":"Meijing Zhang, Hong Qin","doi":"10.1109/SMA.2001.923397","DOIUrl":"https://doi.org/10.1109/SMA.2001.923397","url":null,"abstract":"In this paper, we present hierarchical D-NURBS as a new shape modeling representation which generalizes powerful, physics-based D-NURBS for interactive geometric design. Our hierarchical D-NURBS can be viewed as a collection of standard D-NURBS finite elements, organized hierarchically in a tree structure and subject to continuity constraints across the shared boundaries of adjacent D-NURBS elements at different levels. The layered and composite construction of hierarchical D-NURBS affords users the effective creation of local features and their flexible, global/local control at different level of details. Within the framework of hierarchical D-NURBS, users can interactively sculpt NURBS geometry more intuitively and conveniently through both global and local toolkits. Based on the data structure of hierarchical D-NURBS, we have developed a prototype software equipped with various physics based toolkits in the form of geometric constraints and simulated forces. Our modeling system allows users to undertake the design tasks of point manipulation, normal editing, curvature control, curve fitting, and area sculpting in interactive graphics and CAD/CAM.","PeriodicalId":247602,"journal":{"name":"Proceedings International Conference on Shape Modeling and Applications","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122499940","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}
The rendering of an implicit surface requires many function evaluations of the underlying implicit function. The time efficiency of the rendering is dominated by the number of function evaluations times the efficiency of these evaluations. If the implicit surface is created by means of a constructive solid geometry (CSG) model, the function evaluations can be made more efficient if the underlying function is a Lipschitz function. In this paper, implicit surfaces defined as a blended CSG model with Lipschitz functions are considered. It is shown how bounding volumes can be integrated in this framework and how they can be exploited to improve the evaluation efficiency.
{"title":"Efficient Lipschitz function evaluation for CSG implicit surfaces","authors":"Phap Nguyen, H. V. D. Wetering","doi":"10.1109/SMA.2001.923380","DOIUrl":"https://doi.org/10.1109/SMA.2001.923380","url":null,"abstract":"The rendering of an implicit surface requires many function evaluations of the underlying implicit function. The time efficiency of the rendering is dominated by the number of function evaluations times the efficiency of these evaluations. If the implicit surface is created by means of a constructive solid geometry (CSG) model, the function evaluations can be made more efficient if the underlying function is a Lipschitz function. In this paper, implicit surfaces defined as a blended CSG model with Lipschitz functions are considered. It is shown how bounding volumes can be integrated in this framework and how they can be exploited to improve the evaluation efficiency.","PeriodicalId":247602,"journal":{"name":"Proceedings International Conference on Shape Modeling and Applications","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132985630","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}
A method for the extraction of the extended Reeb graph (ERG) from a closed 3D triangular mesh is presented. The ERG encodes the relationships among critical points of the height function associated to the mesh, and it can represent isolated as well as degenerate critical points. The extraction process is based on a re-meshing strategy of the original mesh, which is forced to follow contour levels. The occurrence and configuration of flat areas in the re-triangulated model identify critical areas of the shape, and their relationships allow the reconstruction of the global topological structure of the shape.
{"title":"Re-meshing techniques for topological analysis","authors":"M. Attene, S. Biasotti, M. Spagnuolo","doi":"10.1109/SMA.2001.923385","DOIUrl":"https://doi.org/10.1109/SMA.2001.923385","url":null,"abstract":"A method for the extraction of the extended Reeb graph (ERG) from a closed 3D triangular mesh is presented. The ERG encodes the relationships among critical points of the height function associated to the mesh, and it can represent isolated as well as degenerate critical points. The extraction process is based on a re-meshing strategy of the original mesh, which is forced to follow contour levels. The occurrence and configuration of flat areas in the re-triangulated model identify critical areas of the shape, and their relationships allow the reconstruction of the global topological structure of the shape.","PeriodicalId":247602,"journal":{"name":"Proceedings International Conference on Shape Modeling and Applications","volume":"527 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123086764","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}
Modeling three-dimensional faces on the computer has been an interesting yet challenging problem. This paper presents a method for creating cartoon faces by using a subdivision scheme. We use set-operations for conceptual design of subdivision control meshes. To ensure the quality of the control mesh, we have eliminated high valenced extraordinary vertices since smoothness of the surface decreases with valence. In addition, we have limited the number of extraordinary vertices to eliminate ripples. We have also ensured an even structure around extraordinary vertices (The size of each quadrilateral in subdivided meshes are roughly similar). We have also developed a user-friendly interface to sculpt the control mesh. Using this interface we have been able to create a variety of cartoon faces.
{"title":"Modeling subdivision control meshes for creating cartoon faces","authors":"S. Skaria, E. Akleman, F. Parke","doi":"10.1109/SMA.2001.923393","DOIUrl":"https://doi.org/10.1109/SMA.2001.923393","url":null,"abstract":"Modeling three-dimensional faces on the computer has been an interesting yet challenging problem. This paper presents a method for creating cartoon faces by using a subdivision scheme. We use set-operations for conceptual design of subdivision control meshes. To ensure the quality of the control mesh, we have eliminated high valenced extraordinary vertices since smoothness of the surface decreases with valence. In addition, we have limited the number of extraordinary vertices to eliminate ripples. We have also ensured an even structure around extraordinary vertices (The size of each quadrilateral in subdivided meshes are roughly similar). We have also developed a user-friendly interface to sculpt the control mesh. Using this interface we have been able to create a variety of cartoon faces.","PeriodicalId":247602,"journal":{"name":"Proceedings International Conference on Shape Modeling and Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123778328","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}
We develop an efficient algorithm for the construction of common tangents between a set of Bezier curves. Common tangents are important in visibility, lighting, robot motion, and convex hulls. Common tangency is reduced to the intersection of parametric curves in a dual space, rather than the traditional intersection of implicit curves. We show how to represent the tangent space of a plane Bezier curve as a plane rational Bezier curve in the dual space, and compare this representation to the hodograph and the dual Bezier curve. The detection of common tangents that map to infinity is resolved by the use of two cooperating curves in dual space, clipped to avoid redundancy. We establish the equivalence of our solution in dual space to a solution in Plucker space, where all the same issues are encountered in a higher-dimensional context.
{"title":"A parametric solution to common tangents","authors":"J. Johnstone","doi":"10.1109/SMA.2001.923395","DOIUrl":"https://doi.org/10.1109/SMA.2001.923395","url":null,"abstract":"We develop an efficient algorithm for the construction of common tangents between a set of Bezier curves. Common tangents are important in visibility, lighting, robot motion, and convex hulls. Common tangency is reduced to the intersection of parametric curves in a dual space, rather than the traditional intersection of implicit curves. We show how to represent the tangent space of a plane Bezier curve as a plane rational Bezier curve in the dual space, and compare this representation to the hodograph and the dual Bezier curve. The detection of common tangents that map to infinity is resolved by the use of two cooperating curves in dual space, clipped to avoid redundancy. We establish the equivalence of our solution in dual space to a solution in Plucker space, where all the same issues are encountered in a higher-dimensional context.","PeriodicalId":247602,"journal":{"name":"Proceedings International Conference on Shape Modeling and Applications","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133897889","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}
Greg Turk, H. Q. Dinh, J. F. O'Brien, Gary D. Yngve
Implicit surfaces are often created by summing a collection of radial basis functions. Researchers have begun to create implicit surfaces that exactly interpolate a given set of points by solving a simple linear system to assign weights to each basis function. Due to their ability to interpolate, these implicit surfaces are more easily controllable than traditional "blobby" implicits. There are several additional forms of control over these surfaces that make them attractive for a variety of applications. Surface normals may be directly specified at any location over the surface, and this allows the modeller to pivot the normal while still having the surface pass through the constraints. The degree of smoothness of the surface can be controlled by changing the shape of the basis functions, allowing the surface to be pinched or smooth. On a point-by-point basis the modeller may decide whether a constraint point should be exactly interpolated or approximated. Applications of these implicits include shape transformation, creating surfaces from computer vision data, creation of an implicit surface from a polygonal model, and medical surface reconstruction.
{"title":"Implicit surfaces that interpolate","authors":"Greg Turk, H. Q. Dinh, J. F. O'Brien, Gary D. Yngve","doi":"10.1109/SMA.2001.923376","DOIUrl":"https://doi.org/10.1109/SMA.2001.923376","url":null,"abstract":"Implicit surfaces are often created by summing a collection of radial basis functions. Researchers have begun to create implicit surfaces that exactly interpolate a given set of points by solving a simple linear system to assign weights to each basis function. Due to their ability to interpolate, these implicit surfaces are more easily controllable than traditional \"blobby\" implicits. There are several additional forms of control over these surfaces that make them attractive for a variety of applications. Surface normals may be directly specified at any location over the surface, and this allows the modeller to pivot the normal while still having the surface pass through the constraints. The degree of smoothness of the surface can be controlled by changing the shape of the basis functions, allowing the surface to be pinched or smooth. On a point-by-point basis the modeller may decide whether a constraint point should be exactly interpolated or approximated. Applications of these implicits include shape transformation, creating surfaces from computer vision data, creation of an implicit surface from a polygonal model, and medical surface reconstruction.","PeriodicalId":247602,"journal":{"name":"Proceedings International Conference on Shape Modeling and Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117171918","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}
Partial differential equations (PDEs) are powerful tools for the generation of free-form surfaces. In this paper, techniques of surface representation using PDEs of different orders are investigated. In order to investigate the real-time performance and capacity of surface generation based on the PDE method, the forms of three types of partial differential equations are put forward, which are the second, mixed and fourth order PDEs. The closed form solutions of these PDEs are derived. The advantages and disadvantages of each of them are discussed. A number of examples are given to demonstrate the use and effectiveness of the techniques.
{"title":"Surface representation using second, fourth and mixed order partial differential equations","authors":"J. Zhang, L. You","doi":"10.1109/SMA.2001.923396","DOIUrl":"https://doi.org/10.1109/SMA.2001.923396","url":null,"abstract":"Partial differential equations (PDEs) are powerful tools for the generation of free-form surfaces. In this paper, techniques of surface representation using PDEs of different orders are investigated. In order to investigate the real-time performance and capacity of surface generation based on the PDE method, the forms of three types of partial differential equations are put forward, which are the second, mixed and fourth order PDEs. The closed form solutions of these PDEs are derived. The advantages and disadvantages of each of them are discussed. A number of examples are given to demonstrate the use and effectiveness of the techniques.","PeriodicalId":247602,"journal":{"name":"Proceedings International Conference on Shape Modeling and Applications","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115518257","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}
Along with the development of 3D acquisition devices and methods and the increasing number of available 3D objects, new tools are necessary to automatically analyze, search and interpret these models. In this paper, we describe a novel geometric approach to 3D object comparison and analysis. To compare two objects geometrically, we first properly position and align the objects. After solving this pose estimation problem, we generate specific distance histograms that define a measure of the geometric similarity of the inspected objects. The geometric approach is very well-suited for structures with moderate variance, e.g. bones, fruits, etc. The strength of the approach is proven through the results of several tests that we performed on different data sets.
{"title":"A geometric approach to 3D object comparison","authors":"Marcin Novotni, R. Klein","doi":"10.1109/SMA.2001.923387","DOIUrl":"https://doi.org/10.1109/SMA.2001.923387","url":null,"abstract":"Along with the development of 3D acquisition devices and methods and the increasing number of available 3D objects, new tools are necessary to automatically analyze, search and interpret these models. In this paper, we describe a novel geometric approach to 3D object comparison and analysis. To compare two objects geometrically, we first properly position and align the objects. After solving this pose estimation problem, we generate specific distance histograms that define a measure of the geometric similarity of the inspected objects. The geometric approach is very well-suited for structures with moderate variance, e.g. bones, fruits, etc. The strength of the approach is proven through the results of several tests that we performed on different data sets.","PeriodicalId":247602,"journal":{"name":"Proceedings International Conference on Shape Modeling and Applications","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127733319","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}
Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer vision, molecular biology, computer graphics, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, while still discriminating between similar and dissimilar shapes. In this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring the global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence or model fitting. We find that the dissimilarities between sampled distributions of simple shape functions (e.g. the distance between two random points on a surface) provide a robust method for discriminating between classes of objects (e.g. cars versus airplanes) in a moderately sized database, despite the presence of arbitrary translations, rotations, scales, reflections, tessellations, simplifications and model degeneracies. They can be evaluated quickly, and thus the proposed method could be applied as a pre-classifier in an object recognition system or in an interactive content-based retrieval application.
{"title":"Matching 3D models with shape distributions","authors":"R. Osada, T. Funkhouser, B. Chazelle, D. Dobkin","doi":"10.1109/SMA.2001.923386","DOIUrl":"https://doi.org/10.1109/SMA.2001.923386","url":null,"abstract":"Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer vision, molecular biology, computer graphics, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, while still discriminating between similar and dissimilar shapes. In this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring the global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence or model fitting. We find that the dissimilarities between sampled distributions of simple shape functions (e.g. the distance between two random points on a surface) provide a robust method for discriminating between classes of objects (e.g. cars versus airplanes) in a moderately sized database, despite the presence of arbitrary translations, rotations, scales, reflections, tessellations, simplifications and model degeneracies. They can be evaluated quickly, and thus the proposed method could be applied as a pre-classifier in an object recognition system or in an interactive content-based retrieval application.","PeriodicalId":247602,"journal":{"name":"Proceedings International Conference on Shape Modeling and Applications","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117220829","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}
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