Bio-molecules reach their stable configuration in solvent which is primarily water with a small concentration of salt ions. One approximation of the total free energy of a bio-molecule includes the classical molecular mechanical energy EMM (which is understood as the self intra-molecular energy in vacuum) and the solvation energy Gsol which is caused by the change of the environment of the molecule from vacuum to solvent (and hence also known as the molecule-solvent interaction energy). This total free energy is used to model and study the stability of bio-molecules in isolation or in their interactions with drugs. In this paper we present fast O (N log N) multi-level grid based approximation algorithms (where N is the number of atoms) for efficiently estimating the compute-intensive terms of EMM and Gsol. The fast octree-based algorithm for Gsol is additionally dependent on an O (N) size computation of the biomolecular surface and its spatial derivatives (normals). We also provide several examples with timing results, and speed/accuracy tradeoffs, demonstrating the efficiency and scalability of our fast free energy estimation of bio-molecules, potentially with millions of atoms.
{"title":"Multi-level grid algorithms for faster molecular energetics","authors":"R. Chowdhury, C. Bajaj","doi":"10.1145/1839778.1839799","DOIUrl":"https://doi.org/10.1145/1839778.1839799","url":null,"abstract":"Bio-molecules reach their stable configuration in solvent which is primarily water with a small concentration of salt ions. One approximation of the total free energy of a bio-molecule includes the classical molecular mechanical energy <i>E</i><sub><i>MM</i></sub> (which is understood as the self intra-molecular energy in vacuum) and the solvation energy <i>G</i><sub>sol</sub> which is caused by the change of the environment of the molecule from vacuum to solvent (and hence also known as the molecule-solvent interaction energy). This total free energy is used to model and study the stability of bio-molecules in isolation or in their interactions with drugs. In this paper we present fast <i>O</i> (<i>N</i> log <i>N</i>) multi-level grid based approximation algorithms (where <i>N</i> is the number of atoms) for efficiently estimating the compute-intensive terms of <i>E</i><sub><i>MM</i></sub> and <i>G</i><sub>sol</sub>. The fast octree-based algorithm for <i>G</i><sub>sol</sub> is additionally dependent on an <i>O</i> (<i>N</i>) size computation of the biomolecular surface and its spatial derivatives (normals). We also provide several examples with timing results, and speed/accuracy tradeoffs, demonstrating the efficiency and scalability of our fast free energy estimation of bio-molecules, potentially with millions of atoms.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122744889","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 region machining, neighbouring regions may be close together, but disconnected. Boundary curves may also have unwanted geometric artifacts caused by approximation and discretisation. We present a strategy to improve the topology and geometry of such boundary curves, allowing the generation of better tool paths, and in turn, improved tool wear and surface quality of the machined part. We make such improvements in three steps: firstly, disconnected regions are merged where appropriate, using a method based on morphological operations from image processing. Secondly, boundary segments with undesirable geometric properties are identified and replaced by simpler segments, using a vertex deletion operation. Finally, flaws at a smaller geometric scale are removed, using a curve shortening algorithm. Experimental results are given to illustrate our algorithm.
{"title":"Merging and smoothing machining boundaries on cutter location surfaces","authors":"W. Li, Ralph Robert Martin, F. Langbein","doi":"10.1145/1839778.1839803","DOIUrl":"https://doi.org/10.1145/1839778.1839803","url":null,"abstract":"In region machining, neighbouring regions may be close together, but disconnected. Boundary curves may also have unwanted geometric artifacts caused by approximation and discretisation. We present a strategy to improve the topology and geometry of such boundary curves, allowing the generation of better tool paths, and in turn, improved tool wear and surface quality of the machined part. We make such improvements in three steps: firstly, disconnected regions are merged where appropriate, using a method based on morphological operations from image processing. Secondly, boundary segments with undesirable geometric properties are identified and replaced by simpler segments, using a vertex deletion operation. Finally, flaws at a smaller geometric scale are removed, using a curve shortening algorithm. Experimental results are given to illustrate our algorithm.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127371460","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 present algorithms for computing accurate moments of solid models that are represented using multiple trimmed NURBS surfaces. Our algorithms make use of programmable Graphics Processing Units (GPUs) to accelerate the computations. We evaluate the surface coordinates and normals accurately, with theoretical bounds, using our GPU NURBS evaluator. We have developed a framework that makes use of this data to evaluate surface integrals of trimmed NURBS surfaces in real time. With our framework, we can compute volume and moments of solid models with theoretical guarantees. The framework also supports local geometry changes, which is useful for providing interactive feedback to the designer while the solid model is being designed. We can compute the center of mass and check for stability of the solid model interactively. Applications of such real-time moment computation include deformation modeling, animation, and physically based simulations.
{"title":"Accurate moment computation using the GPU","authors":"A. Krishnamurthy, Sara McMains","doi":"10.1145/1839778.1839790","DOIUrl":"https://doi.org/10.1145/1839778.1839790","url":null,"abstract":"We present algorithms for computing accurate moments of solid models that are represented using multiple trimmed NURBS surfaces. Our algorithms make use of programmable Graphics Processing Units (GPUs) to accelerate the computations. We evaluate the surface coordinates and normals accurately, with theoretical bounds, using our GPU NURBS evaluator. We have developed a framework that makes use of this data to evaluate surface integrals of trimmed NURBS surfaces in real time. With our framework, we can compute volume and moments of solid models with theoretical guarantees. The framework also supports local geometry changes, which is useful for providing interactive feedback to the designer while the solid model is being designed. We can compute the center of mass and check for stability of the solid model interactively. Applications of such real-time moment computation include deformation modeling, animation, and physically based simulations.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116767715","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. Jagadeesan, A. Lynn, J. Corney, Xiu-Tian Yan, J. Wenzel, A. Sherlock, W. Regli
The ability to interpret and reason about shapes is a peculiarly human capability that has proven difficult to reproduce algorithmically. So despite the fact that geometric modeling technology has made significant advances in the representation, display and modification of shapes, there have only been incremental advances in geometric reasoning. For example, although today's CAD systems can confidently identify isolated cylindrical holes, they struggle with more ambiguous tasks such as the identification of partial symmetries or similarities in arbitrary geometries. Even well defined problems such as 2D shape nesting or 3D packing generally resist elegant solution and rely instead on brute force explorations of a subset of the many possible solutions. Identifying economic ways to solving such problems would result in significant productivity gains across a wide range of industrial applications. The authors hypothesize that Internet Crowdsourcing might provide a pragmatic way of removing many geometric reasoning bottlenecks. This paper reports the results of experiments conducted with Amazon's mTurk site and designed to determine the feasibility of using Internet Crowdsourcing to carry out geometric reasoning tasks as well as establish some benchmark data for the quality, speed and costs of using this approach. After describing the general architecture and terminology of the mTurk Crowdsourcing system, the paper details the implementation and results of the following three investigations; 1) the identification of "Canonical" viewpoints for individual shapes, 2) the quantification of "similarity" relationships with-in collections of 3D models and 3) the efficient packing of 2D Strips into rectangular areas. The paper concludes with a discussion of the possibilities and limitations of the approach.
{"title":"Geometric reasoning via internet CrowdSourcing","authors":"A. Jagadeesan, A. Lynn, J. Corney, Xiu-Tian Yan, J. Wenzel, A. Sherlock, W. Regli","doi":"10.1145/1629255.1629296","DOIUrl":"https://doi.org/10.1145/1629255.1629296","url":null,"abstract":"The ability to interpret and reason about shapes is a peculiarly human capability that has proven difficult to reproduce algorithmically. So despite the fact that geometric modeling technology has made significant advances in the representation, display and modification of shapes, there have only been incremental advances in geometric reasoning. For example, although today's CAD systems can confidently identify isolated cylindrical holes, they struggle with more ambiguous tasks such as the identification of partial symmetries or similarities in arbitrary geometries. Even well defined problems such as 2D shape nesting or 3D packing generally resist elegant solution and rely instead on brute force explorations of a subset of the many possible solutions.\u0000 Identifying economic ways to solving such problems would result in significant productivity gains across a wide range of industrial applications. The authors hypothesize that Internet Crowdsourcing might provide a pragmatic way of removing many geometric reasoning bottlenecks.\u0000 This paper reports the results of experiments conducted with Amazon's mTurk site and designed to determine the feasibility of using Internet Crowdsourcing to carry out geometric reasoning tasks as well as establish some benchmark data for the quality, speed and costs of using this approach.\u0000 After describing the general architecture and terminology of the mTurk Crowdsourcing system, the paper details the implementation and results of the following three investigations; 1) the identification of \"Canonical\" viewpoints for individual shapes, 2) the quantification of \"similarity\" relationships with-in collections of 3D models and 3) the efficient packing of 2D Strips into rectangular areas. The paper concludes with a discussion of the possibilities and limitations of the approach.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"55 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":"116931198","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}
Fengtao Fan, F. Cheng, Conglin Huang, Yong Li, Jianzhong Wang, S. Lai
An elegant and efficient mesh clustering algorithm is presented. The faces of a polygonal mesh are divided into different clusters for mesh coarsening purpose by approximating the Centroidal Voronoi Tessellation of the mesh. The mesh coarsening process after clustering can be done in an isotropic or anisotropic fashion. The presented algorithm improves previous techniques in local geometric operations and parallel updates. The new algorithm is very simple but is guaranteed to converge, and generates better approximating meshes with the same computation cost. Moreover, the new algorithm is suitable for the variational shape approximation problem with L2, 1 distortion error metric and the convergence is guaranteed. Examples demonstrating efficiency of the new algorithm are also included in the paper.
{"title":"Mesh clustering by approximating centroidal Voronoi tessellation","authors":"Fengtao Fan, F. Cheng, Conglin Huang, Yong Li, Jianzhong Wang, S. Lai","doi":"10.1145/1629255.1629294","DOIUrl":"https://doi.org/10.1145/1629255.1629294","url":null,"abstract":"An elegant and efficient mesh clustering algorithm is presented. The faces of a polygonal mesh are divided into different clusters for mesh coarsening purpose by approximating the Centroidal Voronoi Tessellation of the mesh. The mesh coarsening process after clustering can be done in an isotropic or anisotropic fashion. The presented algorithm improves previous techniques in local geometric operations and parallel updates. The new algorithm is very simple but is guaranteed to converge, and generates better approximating meshes with the same computation cost. Moreover, the new algorithm is suitable for the variational shape approximation problem with L2, 1 distortion error metric and the convergence is guaranteed. Examples demonstrating efficiency of the new algorithm are also included in the paper.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"46 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":"127541945","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. Politis, A. Ginnis, P. Kaklis, K. Belibassakis, C. Feurer
In this paper, the isogeometric concept introduced by Hughes, in the context of Finite Element Method, is applied to Boundary Element Method (BEM), for solving an exterior planar Neumann problem. The developed isogeometric-BEM concept is based on NURBS, for representing the exact body geometry and employs the same basis for representing the potential and/or the density of the single layer. In order to examine the accuracy of the scheme, numerical results for the case of a circle and a free-form body are presented and compared against analytical solutions. This enables performing a numerical error analysis, verifying the superior convergence rate of the isogeometric BEM versus low-order BEM. When starting from the initial NURBS representation of the geometry and then using knot insertion for refinement of the NURBS basis, the achieved rate of convergence is O(DoF-4). This rate may be further improved by using a degree-elevated initial NURBS representation of the geometry (kh-refinement).
{"title":"An isogeometric BEM for exterior potential-flow problems in the plane","authors":"C. Politis, A. Ginnis, P. Kaklis, K. Belibassakis, C. Feurer","doi":"10.1145/1629255.1629302","DOIUrl":"https://doi.org/10.1145/1629255.1629302","url":null,"abstract":"In this paper, the isogeometric concept introduced by Hughes, in the context of Finite Element Method, is applied to Boundary Element Method (BEM), for solving an exterior planar Neumann problem. The developed isogeometric-BEM concept is based on NURBS, for representing the exact body geometry and employs the same basis for representing the potential and/or the density of the single layer. In order to examine the accuracy of the scheme, numerical results for the case of a circle and a free-form body are presented and compared against analytical solutions. This enables performing a numerical error analysis, verifying the superior convergence rate of the isogeometric BEM versus low-order BEM. When starting from the initial NURBS representation of the geometry and then using knot insertion for refinement of the NURBS basis, the achieved rate of convergence is O(DoF-4). This rate may be further improved by using a degree-elevated initial NURBS representation of the geometry (kh-refinement).","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"28 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":"122351761","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}
Surface parameterization refers to the process of mapping the surface to canonical planar domains, which plays crucial roles in texture mapping and shape analysis purposes. Most existing techniques focus on simply connected surfaces. It is a challenging problem for multiply connected genus zero surfaces. This work generalizes conventional Koebe's method for multiply connected planar domains. According to Koebe's uniformization theory, all genus zero multiply connected surfaces can be mapped to a planar disk with multiply circular holes. Furthermore, this kind of mappings are angle preserving and differ by Möbius transformations. We introduce a practical algorithm to explicitly construct such a circular conformal mapping. Our algorithm pipeline is as follows: suppose the input surface has n boundaries, first we choose 2 boundaries, and fill the other n -- 2 boundaries to get a topological annulus; then we apply discrete Yamabe flow method to conformally map the topological annulus to a planar annulus; then we remove the filled patches to get a planar multiply connected domain. We repeat this step for the planar domain iteratively. The two chosen boundaries differ from step to step. The iterative construction leads to the desired conformal mapping, such that all the boundaries are mapped to circles. In theory, this method converges quadratically faster than conventional Koebe's method. We give theoretic proof and estimation for the converging rate. In practice, it is much more robust and efficient than conventional non-linear methods based on curvature flow. Experimental results demonstrate the robustness and efficiency of the method.
{"title":"Generalized Koebe's method for conformal mapping multiply connected domains","authors":"W. Zeng, Xiaotian Yin, Min Zhang, F. Luo, X. Gu","doi":"10.1145/1629255.1629267","DOIUrl":"https://doi.org/10.1145/1629255.1629267","url":null,"abstract":"Surface parameterization refers to the process of mapping the surface to canonical planar domains, which plays crucial roles in texture mapping and shape analysis purposes. Most existing techniques focus on simply connected surfaces. It is a challenging problem for multiply connected genus zero surfaces. This work generalizes conventional Koebe's method for multiply connected planar domains. According to Koebe's uniformization theory, all genus zero multiply connected surfaces can be mapped to a planar disk with multiply circular holes. Furthermore, this kind of mappings are angle preserving and differ by Möbius transformations. We introduce a practical algorithm to explicitly construct such a circular conformal mapping. Our algorithm pipeline is as follows: suppose the input surface has n boundaries, first we choose 2 boundaries, and fill the other n -- 2 boundaries to get a topological annulus; then we apply discrete Yamabe flow method to conformally map the topological annulus to a planar annulus; then we remove the filled patches to get a planar multiply connected domain. We repeat this step for the planar domain iteratively. The two chosen boundaries differ from step to step. The iterative construction leads to the desired conformal mapping, such that all the boundaries are mapped to circles. In theory, this method converges quadratically faster than conventional Koebe's method. We give theoretic proof and estimation for the converging rate. In practice, it is much more robust and efficient than conventional non-linear methods based on curvature flow. Experimental results demonstrate the robustness and efficiency of the method.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"229 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":"123023163","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 present a method for procedurally modeling general complex 3D shapes. Our approach is targeted towards applications in digital entertainment and gaming and can automatically generate complex models of buildings, man-made structures, or urban datasets in a few minutes based on user-defined inputs. The algorithm attempts to generate results that resemble a user-defined input model and that satisfy various dimensional, geometric, and algebraic constraints. These constraints are used to capture the intent of the user and generate shapes that look more natural. We also describe efficient techniques to handle complex shapes and demonstrate their performance on many different types of models.
{"title":"Constraint-based model synthesis","authors":"Paul C. Merrell, Dinesh Manocha","doi":"10.1145/1629255.1629269","DOIUrl":"https://doi.org/10.1145/1629255.1629269","url":null,"abstract":"We present a method for procedurally modeling general complex 3D shapes. Our approach is targeted towards applications in digital entertainment and gaming and can automatically generate complex models of buildings, man-made structures, or urban datasets in a few minutes based on user-defined inputs. The algorithm attempts to generate results that resemble a user-defined input model and that satisfy various dimensional, geometric, and algebraic constraints. These constraints are used to capture the intent of the user and generate shapes that look more natural. We also describe efficient techniques to handle complex shapes and demonstrate their performance on many different types of models.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"42 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":"129920661","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 key problem when interpolating a network of curves occurs at vertices: an algebraic condition called the vertex enclosure constraint must hold wherever an even number of curves meet. This paper recasts the constraint in terms of the local geometry of the curve network. This allows formulating a new geometric constraint, related to Euler's Theorem on local curvature, that implies the vertex enclosure constraint and is equivalent to it where four curve segments meet without forming an X.
{"title":"A geometric criterion for smooth interpolation of curve networks","authors":"T. Hermann, J. Peters, T. Strotman","doi":"10.1145/1629255.1629277","DOIUrl":"https://doi.org/10.1145/1629255.1629277","url":null,"abstract":"A key problem when interpolating a network of curves occurs at vertices: an algebraic condition called the vertex enclosure constraint must hold wherever an even number of curves meet. This paper recasts the constraint in terms of the local geometry of the curve network. This allows formulating a new geometric constraint, related to Euler's Theorem on local curvature, that implies the vertex enclosure constraint and is equivalent to it where four curve segments meet without forming an X.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"35 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":"115393573","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}
Principal curvatures and principal directions are fundamental local geometric properties. They are well defined on smooth surfaces. However, due to the nature as higher order differential quantities, they are known to be sensitive to noise. A recent work by Yang et al. combines principal component analysis with integral invariants and computes robust principal curvatures on multiple scales. Although the freedom of choosing the radius r gives results on different scales, in practice it is not an easy task to choose the most appropriate r for an arbitrary given model. Worse still, if the model contains features of different scales, a single r does not work well at all. In this work, we propose a scheme to automatically assign appropriate radii across the surface based on local surface characteristics. The radius r is not constant and adapts to the scale of local features. An efficient, iterative algorithm is used to approach the optimal assignment and the partition of unity is incorporated to smoothly combine the results with different radii. In this way, we can achieve a better balance between the robustness and the accuracy of feature locations. We demonstrate the effectiveness of our approach with robust principal direction field computation and feature extraction.
{"title":"Robust principal curvatures using feature adapted integral invariants","authors":"Yu-Kun Lai, Shimin Hu, T. Fang","doi":"10.1145/1629255.1629298","DOIUrl":"https://doi.org/10.1145/1629255.1629298","url":null,"abstract":"Principal curvatures and principal directions are fundamental local geometric properties. They are well defined on smooth surfaces. However, due to the nature as higher order differential quantities, they are known to be sensitive to noise. A recent work by Yang et al. combines principal component analysis with integral invariants and computes robust principal curvatures on multiple scales. Although the freedom of choosing the radius r gives results on different scales, in practice it is not an easy task to choose the most appropriate r for an arbitrary given model. Worse still, if the model contains features of different scales, a single r does not work well at all. In this work, we propose a scheme to automatically assign appropriate radii across the surface based on local surface characteristics. The radius r is not constant and adapts to the scale of local features. An efficient, iterative algorithm is used to approach the optimal assignment and the partition of unity is incorporated to smoothly combine the results with different radii. In this way, we can achieve a better balance between the robustness and the accuracy of feature locations. We demonstrate the effectiveness of our approach with robust principal direction field computation and feature extraction.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"9 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":"122447074","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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