{"title":"Robust mesh reconstruction from unoriented noisy points","authors":"Hoi Sheung, Charlie C. L. Wang","doi":"10.1145/1629255.1629258","DOIUrl":"https://doi.org/10.1145/1629255.1629258","url":null,"abstract":"We present a robust method to generate mesh surfaces from unoriented noisy points in this paper. The whole procedure consists of three steps. Firstly, the normal vectors at points are evaluated by a highly robust estimator which can fit surface corresponding to less than half of the data points and fit data with multi-structures. This benefits us with the ability to well reconstruct the normal vectors around sharp edges and corners. Meanwhile, clean point cloud equipped with piecewise normal is obtained by projecting points according to the robust fitting. Secondly, an error-minimized subsampling is applied to generate a well-sampled point cloud. Thirdly, a combinatorial approach is employed to reconstruct a triangular mesh connecting the down-sampled points, and a polygonal mesh which preserves sharp features is constructed by the dual-graph of triangular mesh. Parallelization method of the algorithm on a consumer PC using the architecture of GPU is also given.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124975547","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":"Log-aesthetic space curve segments","authors":"N. Yoshida, Ryo Fukuda, Takafumi Saito","doi":"10.1145/1629255.1629261","DOIUrl":"https://doi.org/10.1145/1629255.1629261","url":null,"abstract":"For designing aesthetic surfaces, such as the car bodies, it is very important to use aesthetic curves as characteristic lines. In such curves, the curvature should be monotonically varying, since it dominates the distortion of reflected images on curved surfaces. In this paper, we present an interactive control method of log-aesthetic space curves. We define log-aesthetic space curves to be curves whose logarithmic curvature and torsion graphs are both linear. The linearity of these graphs constrains that the curvature and torsion are monotonically varying. We clarify the characteristics of log-aesthetic space curves and identify their family. Moreover, we present a novel method for drawing a log-aesthetic space curve segment by specifying two endpoints, their tangents, the slopes, α and β, of straight lines of the logarithmic curvature and torsion graphs, and the torsion parameter Ω. Our implementation shows that log-aesthetic curve segments can be controlled fully interactively.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114825554","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":"b-morphs between b-compatible curves in the plane","authors":"B. Whited, J. Rossignac","doi":"10.1145/1629255.1629279","DOIUrl":"https://doi.org/10.1145/1629255.1629279","url":null,"abstract":"We define b-compatibility for planar curves and propose three ball morphing techniques (b-morphs) between pairs of b-compatible curves. B-morphs use the automatic ball-map correspondence, proposed by Chazal et al. [12], from which they derive vertex trajectories (Linear, Circular, Parabolic). All are symmetric, meeting both curves with the same angle, which is a right angle for the Circular and Parabolic. We provide simple constructions for these b-morphs using the maximal disks in the finite region bounded by the two curves. We compare the b-morphs to each other and to other simple morphs (Linear Interpolation (LI), Closest Projection (CP), Curvature Interpolation (CI), Laplace Blending (LB), Heat Propagation (HP)) using seven measures of quality deficiency (travel distance, distortion, stretch, local acceleration, surface area, average curvature, maximal curvature). We conclude that the ratios of these measures depends heavily on the test case, especially for LI, CI, and LB, which compute correspondence from a uniform geodesic parameterization. Nevertheless, we found that the Linear b-morph has consistently the shortest travel distance and that the Circular b-morph has the least amount of distortion.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126788678","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 symbolic-numerical envelope algorithm using quadratic MOS patches","authors":"Bohumír Bastl, J. Kosinka, Miroslav Lávička","doi":"10.1145/1629255.1629278","DOIUrl":"https://doi.org/10.1145/1629255.1629278","url":null,"abstract":"In this paper, we describe an algorithm for generating an exact rational envelope of a two-parameter family of spheres given by a quadratic patch in R3, 1, which is considered as a medial surface transform (MST) of a spatial domain. Recently, it has been proved that quadratic triangular Bézier patches in R3, 1 belong to the class of MOS surfaces (i.e., surfaces providing rational envelopes of the associated two-parameter family of spheres). We give a detailed description of the symbolic and numerical steps of the envelope algorithm and study the error involved in the numerical part. The presented method is then demonstrated on several examples. Moreover, since quadratic MOS patches are capable of producing C1 approximations of MSTs, this algorithm offers a good basis for consequent methods, e.g. computing rational approximations of envelopes associated to general (free-form) MSTs and inner offsets trimming.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127125731","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":"Particle-based forecast mechanism for continuous collision detection in deformable environments","authors":"Thomas Jund, David Cazier, Jean-François Dufourd","doi":"10.1145/1629255.1629274","DOIUrl":"https://doi.org/10.1145/1629255.1629274","url":null,"abstract":"Collision detection in geometrically complex scenes is crucial in physical simulations and real time applications. Works based on spatial hierarchical structures have been proposed for years. If correct performances are obtained for static scenes, these approaches show some limitations when the complexity of the scene increases and particularly in case of deformable meshes. The main drawback is the time needed to update the spatial structures - often trees - when global deformations or topological changes occur in the scene. We propose a method to detect collisions in complex and deformable environments with constant time amortized complexity for small displacements.\u0000 Our method is based on a convex decomposition of the environment coupled with a forecast mechanism exploiting temporal coherence. We use the topological adjacencies and incidence relationships to reduce the number of geometrical tests. Deformations of the scenes are handled with no cost as far as no topological changes occur. Topological transformations, like cuts and sewings, are handled locally, exploiting the spatial coherence and do not imply global updates. We illustrate our method in two experimental frameworks: a particles flow simulation and a meshless animation system both lying in a deformable mesh. We compare our work with classical optimization based on bounding volumes hierarchies to validate its efficiency on large scenes.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"118 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127957636","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 computation of a near-optimal primary parting line","authors":"Rahul Khardekar, Sara McMains","doi":"10.1145/1629255.1629297","DOIUrl":"https://doi.org/10.1145/1629255.1629297","url":null,"abstract":"In injection molding, a flat parting surface that is normal to the mold parting direction achieves the best mold alignment with the least cost. However, for complex parts, parting surfaces that consist of a number of planes are necessary. In this paper, we provide an algorithm to find a near-optimal parting surface as a series of planes that intersect the boundary of the part.\u0000 We form a continuous band of triangles on the part boundary that are parallel to the parting direction within a tolerance and perform vertical trapezoidation of the band. We can then find a set of planes that intersect vertical lines in the trapezoidation. We use a linear program to keep the planes normal to the parting direction.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114568814","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":"Computer aided design and evaluation of new anatomic fixation system on entire pelvic model","authors":"Shenghui Liao, Ruofeng Tong, Min Tang","doi":"10.1145/1629255.1629299","DOIUrl":"https://doi.org/10.1145/1629255.1629299","url":null,"abstract":"This paper presented a special computer aided procedure to design a new sacroliliac anatomic bar-plate internal fixation system, and evaluated its biomechanical properties on an accurate patient-specific finite element model of entire pelvis, compared with two conventional internal fixation methods. Based on virtual anatomical measure of 30 digital pelvic models reconstructed from CT, an anatomic plate was designed according to the complicated structure of the outer table of the posterior ilium, and was integrated into the complete fixation system. Then, an ad hoc semi-automatic mesh generator was employed to construct a patient-specific finite element model of whole pelvis, including elaborate sacroiliac joints, important pelvic ligaments, and interpubic disc, as well as position-dependent cortical thickness and trabecular bone elastic modulus. Following, one side of sacroiliac joint related ligaments were deleted to simulate a complete unilateral sacroiliac joint disruption. Then the new anatomic fixation system was integrated to fix the fracture, and two comparing models including iliosacral screw fixation and front reconstruction plate fixation were also generated. Finally, all models were simulated under same loading conditions. The results demonstrated that the mechanical stability of the new anatomic fixation system was superior, with obviously improved stress distribution and little displacement, which implied an effective internal fixation method for potential clinical application.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"248 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114860280","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":"SOT: compact representation for tetrahedral meshes","authors":"Topraj Gurung, J. Rossignac","doi":"10.1145/1629255.1629266","DOIUrl":"https://doi.org/10.1145/1629255.1629266","url":null,"abstract":"The Corner Table (CT) promoted by Rossignac et al. provides a simple and efficient representation of triangle meshes, storing 6 integer references per triangle (3 vertex references in the V table and 3 references to opposite corners in the O table that accelerate access to adjacent triangles). The Compact Half Face (CHF) proposed by Lage et al. extends CT to tetrahedral meshes, storing 8 references per tetrahedron (4 in the V table and 4 in the O table). We call it the Vertex Opposite Table (VOT) and propose a sorted variation, SVOT, which does not require any additional storage and yet provides, for each vertex, a reference to an incident corner from which an incident tetrahedron may be recovered and the star of the vertex may be traversed at a constant cost per visited element. We use a set of powerful wedge-based operators for querying and traversing the mesh. Finally, inspired by tetrahedral mesh encoding techniques used by Weiler et al. and by Szymczak and Rossignac, we propose our Sorted O Table (SOT) variation, which eliminates the V table completely and hence reduces storage requirements by 50% to only 4 references and 9 bits per tetrahedron, while preserving the vertex-to-incident-corner references and supporting our wedge operators with a linear average cost.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114184580","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":"Repairing and meshing imperfect shapes with Delaunay refinement","authors":"Oleksiy Busaryev, T. Dey, J. Levine","doi":"10.1145/1629255.1629259","DOIUrl":"https://doi.org/10.1145/1629255.1629259","url":null,"abstract":"As a direct consequence of software quirks, designer errors, and representation flaws, often three-dimensional shapes are stored in formats that introduce inconsistencies such as small gaps and overlaps between surface patches. We present a new algorithm that simultaneously repairs imperfect geometry and topology while generating Delaunay meshes of these shapes. At the core of this approach is a meshing algorithm for input shapes that are piecewise smooth complexes (PSCs), a collection of smooth surface patches meeting at curves non-smoothly or in non-manifold configurations. Guided by a user tolerance parameter, we automatically merge nearby components while building a Delaunay mesh that has many of these errors fixed. Experimental evidence is provided to show the results of our algorithm on common computer-aided design (CAD) formats. Our algorithm may also be used to simplify shapes by removing small features which would require an excessive number of elements to preserve them in the output mesh.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131663174","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":"Stable mesh decimation","authors":"C. Bajaj, A. Gillette, Qin Zhang","doi":"10.1145/1629255.1629290","DOIUrl":"https://doi.org/10.1145/1629255.1629290","url":null,"abstract":"Current mesh reduction techniques, while numerous, all primarily reduce mesh size by successive element deletion (e.g. edge collapses) with the goal of geometric and topological feature preservation. The choice of geometric error used to guide the reduction process is chosen independent of the function the end user aims to calculate, analyze, or adaptively refine. In this paper, we argue that such a decoupling of structure from function modeling is often unwise as small changes in geometry may cause large changes in the associated function. A stable approach to mesh decimation, therefore, ought to be guided primarily by an analysis of functional sensitivity, a property dependent on both the particular application and the equations used for computation (e.g. integrals, derivatives, or integral/partial differential equations). We present a methodology to elucidate the geometric sensitivity of functionals via two major functional discretization techniques: Galerkin finite element and discrete exterior calculus. A number of examples are given to illustrate the methodology and provide numerical examples to further substantiate our choices.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126643202","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}