C. Bajaj, S. Chen, Guoliang Xu, Qin Zhang, Wenqi Zhao
Electrostatic interactions play a significant role in determining the binding affinity of molecules and drugs. While significant effort has been devoted to the accurate computation of biomolecular electrostatics based on an all-atomic solution of the Poisson-Boltzmann (PB) equation for smaller proteins and nucleic acids, relatively little has been done to optimize the efficiency of electrostatic energetics and force computations of macromolecules at varying resolutions (also called coarse-graining). We have developed an efficient and comprehensive framework for computing coarse-grained PB electrostatic potentials, polarization energetics and forces for smooth multi-resolution representations of almost all molecular structures, available in the PDB. Important aspects of our framework include the use of variational methods for generating C2-smooth and multi-resolution molecular surfaces (as dielectric interfaces), a parameterization and discretization of the PB equation using an algebraic spline boundary element method, and the rapid estimation of the electrostatic energetics and forces using a kernel independent fast multipole method. We present details of our implementation, as well as several performance results on a number of examples.
{"title":"Hierarchical molecular interfaces and solvation electrostatics","authors":"C. Bajaj, S. Chen, Guoliang Xu, Qin Zhang, Wenqi Zhao","doi":"10.1145/1629255.1629291","DOIUrl":"https://doi.org/10.1145/1629255.1629291","url":null,"abstract":"Electrostatic interactions play a significant role in determining the binding affinity of molecules and drugs. While significant effort has been devoted to the accurate computation of biomolecular electrostatics based on an all-atomic solution of the Poisson-Boltzmann (PB) equation for smaller proteins and nucleic acids, relatively little has been done to optimize the efficiency of electrostatic energetics and force computations of macromolecules at varying resolutions (also called coarse-graining). We have developed an efficient and comprehensive framework for computing coarse-grained PB electrostatic potentials, polarization energetics and forces for smooth multi-resolution representations of almost all molecular structures, available in the PDB. Important aspects of our framework include the use of variational methods for generating C2-smooth and multi-resolution molecular surfaces (as dielectric interfaces), a parameterization and discretization of the PB equation using an algebraic spline boundary element method, and the rapid estimation of the electrostatic energetics and forces using a kernel independent fast multipole method. We present details of our implementation, as well as several performance results on a number of examples.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"115 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":"116591241","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}
Over the last fifty years, there have been numerous efforts to develop comprehensive discrete formulations of geometry and physics from first principles: from Whitney's geometric integration theory [33] to Harrison's theory of chainlets [16], including Regge calculus in general relativity [26, 34], Tonti's work on the mathematical structure of physical theories [30] and their discrete formulation [31], plus multifarious researches into so-called mimetic discretization methods [28], discrete exterior calculus [11, 12], and discrete differential geometry [2, 10]. All these approaches strive to tell apart the different mathematical structures---topological, differentiable, metrical---underpinning a physical theory, in order to make the relationships between them more transparent. While each component is reasonably well understood, computationally effective connections between them are not yet well established, leading to difficulties in combining and progressively refining geometric models and physics-based simulations. This paper proposes such a connection by introducing the concept of metrized chains, meant to establish a discrete metric structure on top of a discrete measure-theoretic structure embodied in the underlying notion of measured (real-valued) chains. These, in turn, are defined on a cell complex, a finite approximation to a manifold which abstracts only its topological properties. The algebraic-topological approach to circuit design and network analysis first proposed by Branin [7] was later extensively applied by Tonti to the study of the mathematical structure of physical theories [30]. (Co-)chains subsequently entered the field of physical modeling [4, 18, 24, 25, 31, 37], and were related to commonly-used discretization methods such as finite elements, finite differences, and finite volumes [1, 8, 21, 22]. Our modus operandi is characterized by the pivotal role we accord to the construction of a physically based inner product between chains. This leads us to criticize the emphasis placed on the choice of an appropriate dual mesh: in our opinion, the "good" dual mesh is but a red herring, in general.
{"title":"Discrete physics using metrized chains","authors":"A. DiCarlo, F. Milicchio, A. Paoluzzi, V. Shapiro","doi":"10.1145/1629255.1629273","DOIUrl":"https://doi.org/10.1145/1629255.1629273","url":null,"abstract":"Over the last fifty years, there have been numerous efforts to develop comprehensive discrete formulations of geometry and physics from first principles: from Whitney's geometric integration theory [33] to Harrison's theory of chainlets [16], including Regge calculus in general relativity [26, 34], Tonti's work on the mathematical structure of physical theories [30] and their discrete formulation [31], plus multifarious researches into so-called mimetic discretization methods [28], discrete exterior calculus [11, 12], and discrete differential geometry [2, 10]. All these approaches strive to tell apart the different mathematical structures---topological, differentiable, metrical---underpinning a physical theory, in order to make the relationships between them more transparent. While each component is reasonably well understood, computationally effective connections between them are not yet well established, leading to difficulties in combining and progressively refining geometric models and physics-based simulations. This paper proposes such a connection by introducing the concept of metrized chains, meant to establish a discrete metric structure on top of a discrete measure-theoretic structure embodied in the underlying notion of measured (real-valued) chains. These, in turn, are defined on a cell complex, a finite approximation to a manifold which abstracts only its topological properties.\u0000 The algebraic-topological approach to circuit design and network analysis first proposed by Branin [7] was later extensively applied by Tonti to the study of the mathematical structure of physical theories [30]. (Co-)chains subsequently entered the field of physical modeling [4, 18, 24, 25, 31, 37], and were related to commonly-used discretization methods such as finite elements, finite differences, and finite volumes [1, 8, 21, 22]. Our modus operandi is characterized by the pivotal role we accord to the construction of a physically based inner product between chains. This leads us to criticize the emphasis placed on the choice of an appropriate dual mesh: in our opinion, the \"good\" dual mesh is but a red herring, in general.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"56 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":"116254308","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}
Digital preservation is the mitigation of the deleterious effects of technology obsolescence, media degradation, and fading human memory. For engineering, design, manufacturing, and physics-based simulation data this requires formats that are semantically accessible for 30-to-50 year lifespans. One of the fundamental challenges is the development of digital geometry-centric engineering representations that are self describing and assured to be interpretable over the long lifespans required by archival applications. This paper introduces the challenge of long-term preservation of digital geometric models. We describe a digital preservation case study for an engineering model which required, for just a single part, over 3.5 GB of data, including 39 file formats and over 750 distinct model and shape files. Based on lessons learned in this case study, we present a framework for enhancing the preservation of geometry-centric engineering knowledge. This framework is currently being used on a number of projects in engineering education.
{"title":"A framework for preservable geometry-centric artifacts","authors":"W. Regli, Michael Grauer, Joseph B. Kopena","doi":"10.1145/1629255.1629265","DOIUrl":"https://doi.org/10.1145/1629255.1629265","url":null,"abstract":"Digital preservation is the mitigation of the deleterious effects of technology obsolescence, media degradation, and fading human memory. For engineering, design, manufacturing, and physics-based simulation data this requires formats that are semantically accessible for 30-to-50 year lifespans. One of the fundamental challenges is the development of digital geometry-centric engineering representations that are self describing and assured to be interpretable over the long lifespans required by archival applications.\u0000 This paper introduces the challenge of long-term preservation of digital geometric models. We describe a digital preservation case study for an engineering model which required, for just a single part, over 3.5 GB of data, including 39 file formats and over 750 distinct model and shape files.\u0000 Based on lessons learned in this case study, we present a framework for enhancing the preservation of geometry-centric engineering knowledge. This framework is currently being used on a number of projects in engineering education.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"6 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":"125324905","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 simple algorithm to generate a topology-preserving, error-bounded approximation of the outer boundary of the volume swept by a polyhedron along a parametric trajectory. Our approach uses a volumetric method that generates an adaptive volumetric grid, computes signed distance on the grid points, and extracts an isosurface from the distance field. In order to guarantee geometric and topological bounds, we present a novel sampling and front propagation algorithm for adaptive grid generation. We highlight the performance of our algorithm on many complex benchmarks that arise in geometric and solid modeling, motion planning and CNC milling applications. To the best of our knowledge, this is the first practical algorithm that can generate swept volume approximations with geometric and topological guarantees on complex polyhedral models swept along any parametric trajectory.
{"title":"Reliable sweeps","authors":"Xinyu Zhang, Young J. Kim, Dinesh Manocha","doi":"10.1145/1629255.1629306","DOIUrl":"https://doi.org/10.1145/1629255.1629306","url":null,"abstract":"We present a simple algorithm to generate a topology-preserving, error-bounded approximation of the outer boundary of the volume swept by a polyhedron along a parametric trajectory. Our approach uses a volumetric method that generates an adaptive volumetric grid, computes signed distance on the grid points, and extracts an isosurface from the distance field. In order to guarantee geometric and topological bounds, we present a novel sampling and front propagation algorithm for adaptive grid generation. We highlight the performance of our algorithm on many complex benchmarks that arise in geometric and solid modeling, motion planning and CNC milling applications. To the best of our knowledge, this is the first practical algorithm that can generate swept volume approximations with geometric and topological guarantees on complex polyhedral models swept along any parametric trajectory.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"112 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":"120947117","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 practical algorithms for accelerating geometric queries on models made of NURBS surfaces using programmable Graphics Processing Units (GPUs). We provide a generalized framework for using GPUs as co-processors in accelerating CAD operations. By attaching the data corresponding to surface-normals to a surface bounding-box structure, we can calculate view-dependent geometric features such as silhouette curves in real time. We make use of additional surface data linked to surface bounding-box hierarchies on the GPU to answer queries such as finding the closest point on a curved NURBS surface given any point in space and evaluating the clearance between two solid models constructed using multiple NURBS surfaces. We simultaneously output the parameter values corresponding to the solution of these queries along with the model space values. Though our algorithms make use of the programmable fragment processor, the accuracy is based on the model space precision, unlike earlier graphics algorithms that were based only on image space precision. In addition, we provide theoretical bounds for both the computed minimum distance values as well as the location of the closest point. Our algorithms are at least an order of magnitude faster than the commercial solid modeling kernel ACIS.
{"title":"Accelerating geometric queries using the GPU","authors":"A. Krishnamurthy, Sara McMains, Kirk Haller","doi":"10.1145/1629255.1629281","DOIUrl":"https://doi.org/10.1145/1629255.1629281","url":null,"abstract":"We present practical algorithms for accelerating geometric queries on models made of NURBS surfaces using programmable Graphics Processing Units (GPUs). We provide a generalized framework for using GPUs as co-processors in accelerating CAD operations. By attaching the data corresponding to surface-normals to a surface bounding-box structure, we can calculate view-dependent geometric features such as silhouette curves in real time. We make use of additional surface data linked to surface bounding-box hierarchies on the GPU to answer queries such as finding the closest point on a curved NURBS surface given any point in space and evaluating the clearance between two solid models constructed using multiple NURBS surfaces. We simultaneously output the parameter values corresponding to the solution of these queries along with the model space values. Though our algorithms make use of the programmable fragment processor, the accuracy is based on the model space precision, unlike earlier graphics algorithms that were based only on image space precision. In addition, we provide theoretical bounds for both the computed minimum distance values as well as the location of the closest point. Our algorithms are at least an order of magnitude faster than the commercial solid modeling kernel ACIS.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"88 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":"127891299","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}
R. Joan-Arinyo, Marta I. Tarrés-Puertas, S. Vila-Marta
The graph-based geometric constraint solving technique works in two steps. First the geometric problem is translated into a graph whose vertices represent the set of geometric elements and whose edges are the constraints. Then the constraint problem is solved by decomposing the graph into a collection of subgraphs each representing a standard problem which is solved by a dedicated equational solver. In this work we report on an algorithm to decompose biconnected tree-decomposable graphs representing either under-or wellconstrained 2D geometric constraint problems. The algorithm recursively first computes a set of fundamental circuits in the graph then splits the graph into a set of subgraphs each sharing exactly three vertices with the fundamental circuit. Practical experiments show that the reported algorithm clearly outperforms the treedecomposition approach based on identifying subgraphs by applying specific decomposition rules.
{"title":"Treedecomposition of geometric constraint graphs based on computing graph circuits","authors":"R. Joan-Arinyo, Marta I. Tarrés-Puertas, S. Vila-Marta","doi":"10.1145/1629255.1629270","DOIUrl":"https://doi.org/10.1145/1629255.1629270","url":null,"abstract":"The graph-based geometric constraint solving technique works in two steps. First the geometric problem is translated into a graph whose vertices represent the set of geometric elements and whose edges are the constraints. Then the constraint problem is solved by decomposing the graph into a collection of subgraphs each representing a standard problem which is solved by a dedicated equational solver.\u0000 In this work we report on an algorithm to decompose biconnected tree-decomposable graphs representing either under-or wellconstrained 2D geometric constraint problems. The algorithm recursively first computes a set of fundamental circuits in the graph then splits the graph into a set of subgraphs each sharing exactly three vertices with the fundamental circuit. Practical experiments show that the reported algorithm clearly outperforms the treedecomposition approach based on identifying subgraphs by applying specific decomposition rules.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"5 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":"124646686","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 six-dimensional space SE(3) is traditionally associated with the space of configurations of a rigid solid (a subset of Euclidean three-dimensional space E3). But a solid can be also considered to be a set of configurations, and therefore a subset of SE(3). This observation removes the artificial distinction between shapes and their configurations, and allows formulation and solution of a large class of problems in mechanical design and manufacturing. In particular, the configuration product of two subsets of configuration space is the set of all configurations obtained when one of the sets is transformed by all configurations of the other. The usual definitions of various sweeps, Minkowski sum, and other motion related operations are then realized as projections of the configuration product into E3. Similarly, the dual operation of configuration quotient subsumes the more common operations of unsweep and Minkowski difference. We identify the formal properties of these operations that are instrumental in formulating and solving both direct and inverse problems in computer aided design and manufacturing. Finally, we show that all required computations may be implemented using a fast parallel sampling method on a GPU.
{"title":"Configuration products in geometric modeling","authors":"S. Nelaturi, V. Shapiro","doi":"10.1145/1629255.1629286","DOIUrl":"https://doi.org/10.1145/1629255.1629286","url":null,"abstract":"The six-dimensional space SE(3) is traditionally associated with the space of configurations of a rigid solid (a subset of Euclidean three-dimensional space E3). But a solid can be also considered to be a set of configurations, and therefore a subset of SE(3). This observation removes the artificial distinction between shapes and their configurations, and allows formulation and solution of a large class of problems in mechanical design and manufacturing. In particular, the configuration product of two subsets of configuration space is the set of all configurations obtained when one of the sets is transformed by all configurations of the other. The usual definitions of various sweeps, Minkowski sum, and other motion related operations are then realized as projections of the configuration product into E3. Similarly, the dual operation of configuration quotient subsumes the more common operations of unsweep and Minkowski difference. We identify the formal properties of these operations that are instrumental in formulating and solving both direct and inverse problems in computer aided design and manufacturing. Finally, we show that all required computations may be implemented using a fast parallel sampling method on a GPU.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"1 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":"130315353","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}
This paper presents a new solver for systems of nonlinear equations. Such systems occur in Geometric Constraint Solving, e.g., when dimensioning parts in CAD-CAM, or when computing the topology of sets defined by nonlinear inequalities. The paper does not consider the problem of decomposing the system and assembling solutions of subsystems. It focuses on the numerical resolution of well-constrained systems. Instead of computing an exponential number of coefficients in the tensorial Bernstein basis, we resort to linear programming for computing range bounds of system equations or domain reductions of system variables. Linear programming is performed on a so called Bernstein polytope: though, it has an exponential number of vertices (each vertex corresponds to a Bernstein polynomial in the tensorial Bernstein basis), its number of hyperplanes is polynomial: O(n2) for a system in n unknowns and equations, and total degree at most two. An advantage of our solver is that it can be extended to non-algebraic equations. In this paper, we present the Bernstein and LP polytope construction, and how to cope with floating point inaccuracy so that a standard LP code can be used. The solver has been implemented with a primal-dual simplex LP code, and some implementation variants have been analyzed. Furthermore, we show geometric-constraint-solving applications, as well as numerical intersection and distance computation examples.
{"title":"Nonlinear systems solver in floating-point arithmetic using LP reduction","authors":"Christoph Fünfzig, D. Michelucci, S. Foufou","doi":"10.1145/1629255.1629271","DOIUrl":"https://doi.org/10.1145/1629255.1629271","url":null,"abstract":"This paper presents a new solver for systems of nonlinear equations. Such systems occur in Geometric Constraint Solving, e.g., when dimensioning parts in CAD-CAM, or when computing the topology of sets defined by nonlinear inequalities. The paper does not consider the problem of decomposing the system and assembling solutions of subsystems. It focuses on the numerical resolution of well-constrained systems. Instead of computing an exponential number of coefficients in the tensorial Bernstein basis, we resort to linear programming for computing range bounds of system equations or domain reductions of system variables. Linear programming is performed on a so called Bernstein polytope: though, it has an exponential number of vertices (each vertex corresponds to a Bernstein polynomial in the tensorial Bernstein basis), its number of hyperplanes is polynomial: O(n2) for a system in n unknowns and equations, and total degree at most two. An advantage of our solver is that it can be extended to non-algebraic equations. In this paper, we present the Bernstein and LP polytope construction, and how to cope with floating point inaccuracy so that a standard LP code can be used. The solver has been implemented with a primal-dual simplex LP code, and some implementation variants have been analyzed. Furthermore, we show geometric-constraint-solving applications, as well as numerical intersection and distance computation examples.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"1 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":"128866580","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}
Given a triangular mesh defining the geometry of a 3D workpiece filled with water, we propose an algorithm to test whether, for an arbitrary given axis, the workpiece will be completely drained under gravity when rotated around the axis. Observing that all water traps contain a concave vertex, we solve our problem by constructing and analyzing a directed "draining graph" whose nodes correspond to concave vertices of the geometry and whose edges are set according to the transition of trapped water when we rotate the workpiece around the given axis. Our algorithm to check whether or not a given rotation axis drains the workpiece outputs a result in about a second for models with more than 100,000 triangles.
{"title":"Testing an axis of rotation for 3D workpiece draining","authors":"Y. Yasui, Sara McMains","doi":"10.1145/1629255.1629283","DOIUrl":"https://doi.org/10.1145/1629255.1629283","url":null,"abstract":"Given a triangular mesh defining the geometry of a 3D workpiece filled with water, we propose an algorithm to test whether, for an arbitrary given axis, the workpiece will be completely drained under gravity when rotated around the axis. Observing that all water traps contain a concave vertex, we solve our problem by constructing and analyzing a directed \"draining graph\" whose nodes correspond to concave vertices of the geometry and whose edges are set according to the transition of trapped water when we rotate the workpiece around the given axis. Our algorithm to check whether or not a given rotation axis drains the workpiece outputs a result in about a second for models with more than 100,000 triangles.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"367 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":"115902268","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}
Suraj Musuvathy, E. Cohen, Joon-Kyung Seong, J. Damon
Ridges are characteristic curves of a surface that mark salient intrinsic features of its shape and are therefore valuable for shape matching, surface quality control, visualization and various other applications. Ridges are loci of points on a surface where either of the principal curvatures attain a critical value in its respective principal direction. These curves have complex behavior near umbilics on a surface, and may also pass through certain turning points causing added complexity for ridge computation. We present a new algorithm for numerically tracing ridges on B-Spline surfaces that also accurately captures ridge behavior at umbilics and ridge turning points. The algorithm traverses ridge segments by detecting ridge points while advancing and sliding in principal directions on a surface in a novel manner, thereby computing connected curves of ridge points. The output of the algorithm is a set of curve segments, some or all of which, may be selected for other applications such as those mentioned above. The results of our technique are validated by comparison with results from previous research and with a brute-force domain sampling technique.
{"title":"Tracing ridges on B-Spline surfaces","authors":"Suraj Musuvathy, E. Cohen, Joon-Kyung Seong, J. Damon","doi":"10.1145/1629255.1629263","DOIUrl":"https://doi.org/10.1145/1629255.1629263","url":null,"abstract":"Ridges are characteristic curves of a surface that mark salient intrinsic features of its shape and are therefore valuable for shape matching, surface quality control, visualization and various other applications. Ridges are loci of points on a surface where either of the principal curvatures attain a critical value in its respective principal direction. These curves have complex behavior near umbilics on a surface, and may also pass through certain turning points causing added complexity for ridge computation. We present a new algorithm for numerically tracing ridges on B-Spline surfaces that also accurately captures ridge behavior at umbilics and ridge turning points. The algorithm traverses ridge segments by detecting ridge points while advancing and sliding in principal directions on a surface in a novel manner, thereby computing connected curves of ridge points. The output of the algorithm is a set of curve segments, some or all of which, may be selected for other applications such as those mentioned above. The results of our technique are validated by comparison with results from previous research and with a brute-force domain sampling technique.","PeriodicalId":216067,"journal":{"name":"Symposium on Solid and Physical Modeling","volume":"144 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":"124300761","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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