{"title":"Mitered offset of a mesh using QEM and vertex split","authors":"I. Yi, Yuan-Shin Lee, Hayong Shin","doi":"10.1145/1364901.1364945","DOIUrl":"https://doi.org/10.1145/1364901.1364945","url":null,"abstract":"In this paper, we present a mitered offsetting method of a triangular mesh. Though our main target application is machining tool path generation, it can also be applied to shelling/hollowing of solid objects, collision avoidance in robot path planning, and so on. Previous literature on mesh offsetting mostly suggest inserting a portion of a cylinder (or a ball) in order to fill the gap between offset faces adjacent to a sharp edge (or a sharp vertex, respectively). The gap filling elements (cylinders or balls) are approximated by a number of small triangles depending on the offset error tolerance. Those small gap filling triangles not only increase tool path computation time, but also cause harmful effect in the accuracy of the machined result around the sharp edges. In this research, we try to reduce the number of gap filling triangles while meeting the given tolerance by introducing the concept of mitered offset, which is popularly used in 2D profile machining practice. We borrowed and modified the notion of quadric error metric (QEM) from the mesh simplification area. A modified version of QEM is used for robust computation of the offset vertex position which minimizes the sum of squared distance error from the faces around the original mesh vertex. If the error is within tolerance, the offset vertex is accepted. Otherwise, the offset vertex is split repeatedly until the error is acceptable. Vertex split occurs at the sharp features. A rigorous foundation is given to the mitered offset of 3D mesh with sharp features as well as smooth regions. The experimental results indicate that only a small number of triangles are added in offset mesh.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134457311","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":"Geometry of architectural freeform structures","authors":"H. Pottmann","doi":"10.1145/1364901.1364903","DOIUrl":"https://doi.org/10.1145/1364901.1364903","url":null,"abstract":"Complex freeform structures are one of the most striking trends in contemporary architecture. This direction has been pioneered by architects such as F. Gehry, who exploit digital technology originally developed for the automotive and airplane industry for architectural design and construction. This is not a simple task at all, since the architectural application differs from the original target industries in many ways, including aesthetics, statics, scale and manufacturing technologies.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124556476","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 constraint-based dynamic geometry system","authors":"Marc Freixas, R. Joan-Arinyo, Antoni Soto-Riera","doi":"10.1145/1364901.1364909","DOIUrl":"https://doi.org/10.1145/1364901.1364909","url":null,"abstract":"Dynamic geometry systems are tools for geometric visualization. They allow the user to define geometric elements, establish relationships between them and explore the dynamic behavior of the remaining geometric elements when one of them is moved. The main problem in dynamic geometry systems is the ambiguity that arises from operations which lead to more than one possible solution. Most dynamic geometry systems deal with this problem in such a way that the solution selection method leads to a fixed dynamic behavior of the system. This is specially annoying when the behavior observed is not the one the user intended.\u0000 In this work we propose a modular architecture for dynamic geometry systems built upon a set of functional units which will allow to apply some well known results from the Geometric Constraint Solving field. A functional unit called filter will provide the user with tools to unambiguously capture the expected dynamic behavior of a given geometric problem.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128766506","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":"An enlarged-surface based solid model for robust blending","authors":"N. Matsuki, Yoshiyuki Furukawa, F. Kimura","doi":"10.1145/1364901.1364957","DOIUrl":"https://doi.org/10.1145/1364901.1364957","url":null,"abstract":"In this paper, we present an algorithm of modeling a solid object by defining enlarged-surfaces sequentially in Boundary representation (B-rep) solid models. We describe how our approach can solve current problems of blending in solid models such as terminating-edge-blends, overlap-blends and global-blends. Our approach is based on a simple and robust surface modeling method and its application to B-rep solid models. We also present a novel rule for B-rep solid models in order to include surface modeling methods. We illustrate how our approach overcomes problems of blending cases.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124647853","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":"Voronoi diagram computations for planar NURBS curves","authors":"Joon-Kyung Seong, E. Cohen, G. Elber","doi":"10.1145/1364901.1364913","DOIUrl":"https://doi.org/10.1145/1364901.1364913","url":null,"abstract":"We present robust and efficient algorithms for computing Voronoi diagrams of planar freeform curves. Boundaries of the Voronoi diagram consist of portions of the bisector curves between pairs of planar curves. Our scheme is based on computing critical structures of the Voronoi diagrams, such as self-intersections and junction points of bisector curves. Since the geometric objects we consider in this paper are represented as freeform NURBS curves, we were able to reformulate the solution to the problem of computing those critical structures into the zero-set solutions of a system of nonlinear piecewise rational equations in parameter space. We present a new algorithm for computing error-bounded bisector curves using a distance surface constructed from error-bounded offset approximations of planar curves. This error-bounded algorithm is fast and produces bisector curves that are correct both in topology and geometry. Once bisectors are computed, both local and global self-intersections of the bisector curves are located and trimmed away by solving a system of three piecewise rational equations in three variables. Further, our method computes junction points at which three or more trimmed bisector curves intersect by transforming them into the solutions to a system of piecewise rational equations in the merged parameter space of the planar curves. The bisectors are trimmed at those self-intersection and global junction points. The Voronoi diagram is then computed from the trimmed bisectors using a pruning algorithm. We demonstrate the effectiveness of our approach with several experimental results.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"47 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113931495","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":"Geometrically adaptive numerical integration","authors":"B. Luft, V. Shapiro, I. Tsukanov","doi":"10.1145/1364901.1364923","DOIUrl":"https://doi.org/10.1145/1364901.1364923","url":null,"abstract":"Numerical integration over solid domains often requires geometric adaptation to the solid's boundary. Traditional approaches employ hierarchical adaptive space decomposition, where the integration cells intersecting the boundary are either included or discarded based on their position with respect to the boundary and/or statistical measures. These techniques are inadequate when accurate integration near the boundary is particularly important. In boundary value problems, for instance, a small error in the boundary cells can lead to a large error in the computed field distribution.\u0000 We propose a novel technique for exploiting the exact local geometry in boundary cells. A classification system similar to marching cubes is combined with a suitable parameterization of the boundary cell's geometry. We can then allocate integration points in boundary cells using the exact geometry instead of relying on statistical techniques. We show that the proposed geometrically adaptive integration technique yields greater accuracy with fewer integration points than previous techniques.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116157404","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":"Poisson surface reconstruction and its applications","authors":"Hugues Hoppe","doi":"10.1145/1364901.1364904","DOIUrl":"https://doi.org/10.1145/1364901.1364904","url":null,"abstract":"Surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function schemes, the Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. To reconstruct detailed models in limited memory, we solve this Poisson formulation efficiently using a streaming framework. Specifically, we introduce a multilevel streaming representation, which enables efficient traversal of a sparse octree by concurrently advancing through multiple streams, one per octree level. Remarkably, for our reconstruction application, a sufficiently accurate solution to the global linear system is obtained using a single iteration of cascadic multigrid, which can be evaluated within a single multi-stream pass. Finally, we explore the application of Poisson reconstruction to the setting of multi-view stereo, to reconstruct detailed 3D models of outdoor scenes from collections of Internet images.\u0000 This is joint work with Michael Kazhdan, Matthew Bolitho, and Randal Burns (Johns Hopkins University), and Michael Goesele, Noah Snavely, Brian Curless, and Steve Seitz (University of Washington).","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121568960","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":"Sweeping solids on manifolds","authors":"S. Azernikov","doi":"10.1145/1364901.1364936","DOIUrl":"https://doi.org/10.1145/1364901.1364936","url":null,"abstract":"This work describes a new method for modeling of sweep solids on manifolds, considering various geometric and functional constrains. The proposed method is applied in semi-automatic computer aided design of ventilation tubes for hearing aid devices. The sweeping procedure begins with definition of a trajectory. Besides smoothness and minimal length, other requirements may be considered. Therefore, it is convenient to formulate the optimal trajectory problem as a geodesic computing over Riemannian manifold. The trajectory defined on the manifold is ofsetted, in order to make the sweep solid tangent to the manifold. The offset curve shape is iteratively smoothed while preserving minimal distance from the manifold. Then, a frame field is defined over the offset curve and the cross section contour is transformed according to this field. The major problem is how to construct the frame field such that the resulting sweep solid will be smooth and free of self-intersections. It is well known, that Frenet frame imposes restrictions on the trajectory and may create undesirable twist. In order to overcome these obstacles, an efficient procedure is proposed to compute the discrete minimal rotation frame. Finally, a new approach to the self-intersection problem of sweep solids is proposed. The key idea is to weaken the orthogonality requirement between the cross section plane and the trajectory curve, in order to avoid self-intersections.\u0000 The described method was implemented and tested in real production environment, where it was proved robust and efficient. The proposed techniques can be utilized in many related applications where sweep surface modeling and manipulation is involved.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131794770","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":"Filament tracking and encoding for complex biological networks","authors":"D. Mayerich, J. Keyser","doi":"10.1145/1364901.1364952","DOIUrl":"https://doi.org/10.1145/1364901.1364952","url":null,"abstract":"We present a framework for segmenting and storing filament networks from scalar volume data. Filament structures are commonly found in data generated using high-throughput microscopy. These data sets can be several gigabytes in size because they are either spatially large or have a high number of scalar channels. Filaments in microscopy data sets are difficult to segment because their diameter is often near the sampling resolution of the microscope, yet single filaments can span large data sets. We describe a novel method to trace filaments through scalar volume data sets that is robust to both noisy and under-sampled data. We use a GPU-based scheme to accelerate the tracing algorithm, making it more useful for large data sets. After the initial structure is traced, we can use this information to create a bounding volume around the network and encode the volumetric data associated with it. Taken together, this framework provides a convenient method for accessing network structure and connectivity while providing compressed access to the original volumetric data associated with the network.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133158026","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":"Laser brush: a flexible device for 3D reconstruction of indoor scenes","authors":"Martin Habbecke, L. Kobbelt","doi":"10.1145/1364901.1364933","DOIUrl":"https://doi.org/10.1145/1364901.1364933","url":null,"abstract":"While many techniques for the 3D reconstruction of small to medium sized objects have been proposed in recent years, the reconstruction of entire scenes is still a challenging task. This is especially true for indoor environments where existing active reconstruction techniques are usually quite expensive and passive, image-based techniques tend to fail due to high scene complexities, difficult lighting situations, or shiny surface materials. To fill this gap we present a novel low-cost method for the reconstruction of depth maps using a video camera and an array of laser pointers mounted on a hand-held rig. Similar to existing laser-based active reconstruction techniques, our method is based on a fixed camera, moving laser rays and depth computation by triangulation. However, unlike traditional methods, the position and orientation of the laser rig does not need to be calibrated a-priori and no precise control is necessary during image capture. The user rather moves the laser rig freely through the scene in a brush-like manner, letting the laser points sweep over the scene's surface. We do not impose any constraints on the distribution of the laser rays, the motion of the laser rig, or the scene geometry except that in each frame at least six laser points have to be visible. Our main contributions are twofold. The first is the depth map reconstruction technique based on irregularly oriented laser rays that, by exploiting robust sampling techniques, is able to cope with missing and even wrongly detected laser points. The second is a smoothing operator for the reconstructed geometry specifically tailored to our setting that removes most of the inevitable noise introduced by calibration and detection errors without damaging important surface features like sharp edges.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131663694","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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