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Special issue on International Conference on Geometric Modeling and Processing (GMP 2017)
Computer Aided Geometric Design 52–53 (2017) 1–2
Contents lists available at ScienceDirect
Computer Aided Geometric Design www.elsevier.com/locate/cagd
Editorial
Special issue on International Conference on Geometric Modeling and Processing (GMP 2017) Xiamen is a beautiful coastal city at the southeastern part of Fujian province, beside the Taiwan Strait. The International Conference on Geometric Modeling and Processing (GMP 2017) was held between April 17–19, 2017 in Xiamen. The call for papers of GMP 2017 attracted a total of 72 submissions. Among them, 21 were selected for presentation at the conference and for publication in this special issue of Computer Aided Geometric Design. Given the recent rise in popularity of depth sensing and 3D scanning technology, surface reconstruction algorithms are an especially timely area of research. Noise in the positions or estimated normals of the input data can create spurious blobs and sheets during reconstruction. In “Implicit surface reconstruction with total variation regularization,” Liu et al. regularize implicit spline reconstruction by penalizing total variation, mitigating these artifacts. Bracco et al.’s “Adaptive scattered data fitting by extension of local approximations to hierarchical splines” fit scattered data with truncated hierarchical B-splines, using a two-stage approach of local polynomial fitting followed by construction of quasi-interpolants. One limitation of implicit reconstruction of objects with complex geometry is the memory storage cost; in “Phase-field guided surface reconstruction based on implicit hierarchical B-splines,” Pan et al. address this concern by constructing a hierarchical B-spline representing a phase field that is non-constant only in a narrow band around the reconstructed surface. There has been significant interest in the last few years on constructing G1 function spaces over multi-patch domains, and this issue contains two papers that present further progress in this direction. “G 1 -smooth splines on quad meshes with 4-split macro-patch elements” by Blidia et al. describes how to construct C1 spline spaces on quadrilateral meshes by adding introducing knots along shared edges, and describe the dimension and basis of this function space on the vertices, edges, and faces, of the mesh. Kapl et al. study function spaces on two-patch domains, and in their work “Dimension and basis construction for analysis-suitable G1 two-patch parameterizations” they extend the type of parameterization allowed on these domains by constructing a basis for such analysis-suitable parameterizations. Another new development presented here in the realm of isogeometric analysis is Wu et al.’s “Convergence rates for solving elliptic boundary value problems with singular parameterizations in isogeometric analysis,” which analyzes the effect of parameterization singularities on approximation error and convergence rate when solving second-order elliptic PDEs, and show that isogeometric analysis exhibits superior performance than the finite element method when the singularities in the parameterization are well-chosen. Immersogeometric analysis is a relatively new technique for solving computational fluid dynamics problems involving solid–fluid coupling, where the solid object is immersed into the fluid without adapting the fluid discretization to the object boundaries. Previous immersogeometric analysis methods have required geometry represented using NURBS; Wang et al.’s “Rapid B-Rep model preprocessing for immersogeometric analysis using analytic surfaces” push the boundaries of this technique by extending this technique to objects delineated by trimmed analytic surfaces. Much work has been done in the past on extending barycentric coordinates to arbitrary regions. Two papers further explore this area: Anisimov et al. describe a new type of generalized barycentric coordinate on non-convex polygons in “Blended barycentric coordinates,” which are non-negative, smooth, and locally-supported, while still having closed-form expressions. A more traditional formulation of generalized barycentric coordinates is Wachspress coordinates. Wachspress kernels cannot be computed exactly on arbitrary domains, so a common heuristic is to compute them instead on an inscribed polygon discretizing the domain. Hormann and Kosinka’s “Discretizing Wachspress kernels is safe” puts this technique on firm theoretical footing, by proving that the resulting Wachspress coordinates are well-defined over the entire original domain. This issue presents two advances in the area of computational algebraic geometry: Gonzalez-Vega et al.’s “An algebraic framework for computing the topology of offsets to rational curves” locates points of singularity and self-intersection in offsets to rational planar curves using algebraic approaches that, notably, do not require computing the an explicit representation of the offset curves. Shen and Goldman’s “Algorithms for computing strong μ-bases for rational tensor product surfaces” extends the theory of μ-bases in the setting of rational surfaces by introducing a new notion, strong μ-bases, which carry guarantees more suitable to implicitization than arbitrary μ-bases. http://dx.doi.org/10.1016/j.cagd.2017.04.001 0167-8396/© 2017 Published by Elsevier B.V.
2
Editorial / Computer Aided Geometric Design 52–53 (2017) 1–2
Physics is often a source of interesting and challenging geometry processing problems, and likewise advances in our understanding of discrete geometry can lead to breakthroughs in modeling and simulating physical systems. Four papers in this issue lie at this intersection of fields. Given an incompressible fluid, Barton and Kosinka’s paper “Towards optimal advection using stretch-maximizing stream surfaces” seeks out places one can place seed curves so that they expand in arc length as quickly as possible, with applications to oil extraction and efficient crop spraying. The vibration modes of an object are an important summary of its local deformation behavior; unfortunately these vibration modes are global over the entire object geometry and so are expensive to compute and store. As an alternative, Brandt and Hildebrandt introduce compressed vibration modes, which are localized in space as a result of L1 -regularizing the variational formulation of ordinary vibration modes. Their paper “Compressed vibration modes of deformable objects” describes how to compute these localized modes efficiently by solving a sequence of convex problems. Finally Huber et al.’s “Smooth interpolation of key frames in a Riemannian shell space” seeks to smoothly interpolate between deformations of a thin elastic shell by computing, using only local optimizations, a spline on the Riemannian manifold representing the shell’s shape space, where the metric depends on the energy of deformation. As 3D printing advances it becomes increasingly important to be able to design 3D geometries with complex internal structures. Hui et al.’s “By example synthesis of three-dimensional porous materials” extends and enhances 2D texturesynthesis techniques to 3D to enable creation of 3D objects with porous internal structure, given user-provided exemplars. Another area of shape analysis is segmentation of 3D objects into simple parts. Le and Duan present a new take on this problem in “A primitive-based 3D segmentation algorithm for CAD models,” where they make the observation that objects usually have only a few main axes along which geometric features are oriented; the paper proposes first detecting these axes and then projecting along them to turn the 3D segmentation problem into a 2D problem. Finally, GMP 2017 featured advances in an assortment of classical areas of geometry processing and computational geometry, including meshing, decimation, tetrahedralization, geodesic distance computation, and circle-packing. Coarsening a quadrilateral mesh is a nontrivial operation when the mesh contains singularities. Razafindrazaka and Polthier’s “Optimal base complexes for quadrilateral meshes” enhances previous techniques for identifying removal singularities using perfect matching by using a global optimization strategy that guarantees existence of a quadrilateral solution with no T-junctions. Ni et al.’s “Sliver-suppressing tetrahedral mesh optimization with gradient-based shape matching energy” tackles the problem of producing high-quality volume tetrahedralizations that avoid sliver tetrahedra. They do so by defining and optimizing a novel shape-matching energy penalizing deviation of the tetrahedron away from a user-specified template simplex. Hirano et al.’s “Rapid blending of closed curves based on curvature flow” studies the problem of computing homotopies between 2D curves using curvature flow. Remarkably, this method can be applied even to pairs of curves with different turning numbers, and avoids formation of cusps during the interpolation. In “Discrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfaces,” Wang et al. accelerate computation of approximate geodesic distances on polyhedral surfaces by precomputing a coarse geodesic graph, which is then used to perform online queries. The edges of this discrete geodesic graph are chosen so that the computed distance satisfies provable error bounds without sacrificing excessive speed or memory efficiency. Lastly, packing circles inside arbitrary regions is a classic NP-hard computational geometry problem; Machchhar and Elber’s “Dense packing of congruent circles in free-form non-convex containers” proposes a heuristic for finding a dense packing when the region is delineated by arbitrary splines, based on a new algorithm for simulating the shaking of the region. We thank the authors for their contributions, and the numerous program committee members, as well as the CAGD editors in chief, Rida T. Farouki and Konrad Polthier, and the Elsevier publishing and support staff, without whose efforts this special issue would not have been possible.
Contents lists available at ScienceDirect
Computer Aided Geometric Design www.elsevier.com/locate/cagd
Editorial
Special issue on International Conference on Geometric Modeling and Processing (GMP 2017) Xiamen is a beautiful coastal city at the southeastern part of Fujian province, beside the Taiwan Strait. The International Conference on Geometric Modeling and Processing (GMP 2017) was held between April 17–19, 2017 in Xiamen. The call for papers of GMP 2017 attracted a total of 72 submissions. Among them, 21 were selected for presentation at the conference and for publication in this special issue of Computer Aided Geometric Design. Given the recent rise in popularity of depth sensing and 3D scanning technology, surface reconstruction algorithms are an especially timely area of research. Noise in the positions or estimated normals of the input data can create spurious blobs and sheets during reconstruction. In “Implicit surface reconstruction with total variation regularization,” Liu et al. regularize implicit spline reconstruction by penalizing total variation, mitigating these artifacts. Bracco et al.’s “Adaptive scattered data fitting by extension of local approximations to hierarchical splines” fit scattered data with truncated hierarchical B-splines, using a two-stage approach of local polynomial fitting followed by construction of quasi-interpolants. One limitation of implicit reconstruction of objects with complex geometry is the memory storage cost; in “Phase-field guided surface reconstruction based on implicit hierarchical B-splines,” Pan et al. address this concern by constructing a hierarchical B-spline representing a phase field that is non-constant only in a narrow band around the reconstructed surface. There has been significant interest in the last few years on constructing G1 function spaces over multi-patch domains, and this issue contains two papers that present further progress in this direction. “G 1 -smooth splines on quad meshes with 4-split macro-patch elements” by Blidia et al. describes how to construct C1 spline spaces on quadrilateral meshes by adding introducing knots along shared edges, and describe the dimension and basis of this function space on the vertices, edges, and faces, of the mesh. Kapl et al. study function spaces on two-patch domains, and in their work “Dimension and basis construction for analysis-suitable G1 two-patch parameterizations” they extend the type of parameterization allowed on these domains by constructing a basis for such analysis-suitable parameterizations. Another new development presented here in the realm of isogeometric analysis is Wu et al.’s “Convergence rates for solving elliptic boundary value problems with singular parameterizations in isogeometric analysis,” which analyzes the effect of parameterization singularities on approximation error and convergence rate when solving second-order elliptic PDEs, and show that isogeometric analysis exhibits superior performance than the finite element method when the singularities in the parameterization are well-chosen. Immersogeometric analysis is a relatively new technique for solving computational fluid dynamics problems involving solid–fluid coupling, where the solid object is immersed into the fluid without adapting the fluid discretization to the object boundaries. Previous immersogeometric analysis methods have required geometry represented using NURBS; Wang et al.’s “Rapid B-Rep model preprocessing for immersogeometric analysis using analytic surfaces” push the boundaries of this technique by extending this technique to objects delineated by trimmed analytic surfaces. Much work has been done in the past on extending barycentric coordinates to arbitrary regions. Two papers further explore this area: Anisimov et al. describe a new type of generalized barycentric coordinate on non-convex polygons in “Blended barycentric coordinates,” which are non-negative, smooth, and locally-supported, while still having closed-form expressions. A more traditional formulation of generalized barycentric coordinates is Wachspress coordinates. Wachspress kernels cannot be computed exactly on arbitrary domains, so a common heuristic is to compute them instead on an inscribed polygon discretizing the domain. Hormann and Kosinka’s “Discretizing Wachspress kernels is safe” puts this technique on firm theoretical footing, by proving that the resulting Wachspress coordinates are well-defined over the entire original domain. This issue presents two advances in the area of computational algebraic geometry: Gonzalez-Vega et al.’s “An algebraic framework for computing the topology of offsets to rational curves” locates points of singularity and self-intersection in offsets to rational planar curves using algebraic approaches that, notably, do not require computing the an explicit representation of the offset curves. Shen and Goldman’s “Algorithms for computing strong μ-bases for rational tensor product surfaces” extends the theory of μ-bases in the setting of rational surfaces by introducing a new notion, strong μ-bases, which carry guarantees more suitable to implicitization than arbitrary μ-bases. http://dx.doi.org/10.1016/j.cagd.2017.04.001 0167-8396/© 2017 Published by Elsevier B.V.
2
Editorial / Computer Aided Geometric Design 52–53 (2017) 1–2
Physics is often a source of interesting and challenging geometry processing problems, and likewise advances in our understanding of discrete geometry can lead to breakthroughs in modeling and simulating physical systems. Four papers in this issue lie at this intersection of fields. Given an incompressible fluid, Barton and Kosinka’s paper “Towards optimal advection using stretch-maximizing stream surfaces” seeks out places one can place seed curves so that they expand in arc length as quickly as possible, with applications to oil extraction and efficient crop spraying. The vibration modes of an object are an important summary of its local deformation behavior; unfortunately these vibration modes are global over the entire object geometry and so are expensive to compute and store. As an alternative, Brandt and Hildebrandt introduce compressed vibration modes, which are localized in space as a result of L1 -regularizing the variational formulation of ordinary vibration modes. Their paper “Compressed vibration modes of deformable objects” describes how to compute these localized modes efficiently by solving a sequence of convex problems. Finally Huber et al.’s “Smooth interpolation of key frames in a Riemannian shell space” seeks to smoothly interpolate between deformations of a thin elastic shell by computing, using only local optimizations, a spline on the Riemannian manifold representing the shell’s shape space, where the metric depends on the energy of deformation. As 3D printing advances it becomes increasingly important to be able to design 3D geometries with complex internal structures. Hui et al.’s “By example synthesis of three-dimensional porous materials” extends and enhances 2D texturesynthesis techniques to 3D to enable creation of 3D objects with porous internal structure, given user-provided exemplars. Another area of shape analysis is segmentation of 3D objects into simple parts. Le and Duan present a new take on this problem in “A primitive-based 3D segmentation algorithm for CAD models,” where they make the observation that objects usually have only a few main axes along which geometric features are oriented; the paper proposes first detecting these axes and then projecting along them to turn the 3D segmentation problem into a 2D problem. Finally, GMP 2017 featured advances in an assortment of classical areas of geometry processing and computational geometry, including meshing, decimation, tetrahedralization, geodesic distance computation, and circle-packing. Coarsening a quadrilateral mesh is a nontrivial operation when the mesh contains singularities. Razafindrazaka and Polthier’s “Optimal base complexes for quadrilateral meshes” enhances previous techniques for identifying removal singularities using perfect matching by using a global optimization strategy that guarantees existence of a quadrilateral solution with no T-junctions. Ni et al.’s “Sliver-suppressing tetrahedral mesh optimization with gradient-based shape matching energy” tackles the problem of producing high-quality volume tetrahedralizations that avoid sliver tetrahedra. They do so by defining and optimizing a novel shape-matching energy penalizing deviation of the tetrahedron away from a user-specified template simplex. Hirano et al.’s “Rapid blending of closed curves based on curvature flow” studies the problem of computing homotopies between 2D curves using curvature flow. Remarkably, this method can be applied even to pairs of curves with different turning numbers, and avoids formation of cusps during the interpolation. In “Discrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfaces,” Wang et al. accelerate computation of approximate geodesic distances on polyhedral surfaces by precomputing a coarse geodesic graph, which is then used to perform online queries. The edges of this discrete geodesic graph are chosen so that the computed distance satisfies provable error bounds without sacrificing excessive speed or memory efficiency. Lastly, packing circles inside arbitrary regions is a classic NP-hard computational geometry problem; Machchhar and Elber’s “Dense packing of congruent circles in free-form non-convex containers” proposes a heuristic for finding a dense packing when the region is delineated by arbitrary splines, based on a new algorithm for simulating the shaking of the region. We thank the authors for their contributions, and the numerous program committee members, as well as the CAGD editors in chief, Rida T. Farouki and Konrad Polthier, and the Elsevier publishing and support staff, without whose efforts this special issue would not have been possible.