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28 results on '"Stefanie Hahmann"'

1. Shape from sensors: Curve networks on surfaces from 3D orientations

Author

Nathalie Saguin-Sprynski, Tibor Stanko, Georges-Pierre Bonneau, Stefanie Hahmann, Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information (CEA-LETI), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Models and Algorithms for Visualization and Rendering (MAVERICK ), and European Project: 291184,EC:FP7:ERC,ERC-2011-ADG_20110209,EXPRESSIVE(2012)

Subjects
Cell complex, Topology (electrical circuits), 010103 numerical & computational mathematics, 02 engineering and technology, shape acquisition, 01 natural sciences, curve networks, Set (abstract data type), surface reconstruction, Inertial measurement unit, 0202 electrical engineering, electronic engineering, information engineering, Computer vision, 0101 mathematics, Mathematics, Orientation (computer vision), business.industry, General Engineering, 020207 software engineering, inertial sensors, Computer Graphics and Computer-Aided Design, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Human-Computer Interaction, Artificial intelligence, Noise (video), 3D sketching, business, Shape reconstruction, Surface reconstruction
Abstract

International audience; We present a novel framework for acquisition and reconstruction of 3D curves using orientations provided by inertial sensors. While the idea of sensor shape reconstruction is not new, we present the first method for creating well-connected networks with cell complex topology using only orientation and distance measurements and a set of user- defined constraints. By working directly with orientations, our method robustly resolves problems arising from data inconsistency and sensor noise. Although originally designed for reconstruction of physical shapes, the framework can be used for “sketching” new shapes directly in 3D space. We test the performance of the method using two types of acquisition devices: a standard smartphone, and a custom-made device.

Published
2017

2. Computing Contour Trees for 2D Piecewise Polynomial Functions

Author

Girijanandan Nucha, Georges-Pierre Bonneau, Vijay Natarajan, Stefanie Hahmann, Indian Institute of Science [Bangalore] (IISc Bangalore), Models and Algorithms for Visualization and Rendering (MAVERICK ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE ), and IFCAM and INRIA

Subjects
Parallelizable manifold, higher-order, Scalar (mathematics), ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, 020207 software engineering, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Computer Graphics and Computer-Aided Design, contour-tree, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Reeb graph, Monotone polygon, 010201 computation theory & mathematics, Isosurface, Path tracing, 0202 electrical engineering, electronic engineering, information engineering, Piecewise, Scalar field, Algorithm, visualization, Computer Science & Automation, Mathematics, ComputingMethodologies_COMPUTERGRAPHICS
Abstract

International audience; Contour trees are extensively used in scalar field analysis. The contour tree is a data structure that tracks the evolution of levelset topology in a scalar field. Scalar fields are typically available as samples at vertices of a mesh and are linearly interpolatedwithin each cell of the mesh. A more suitable way of representing scalar fields, especially when a smoother function needsto be modeled, is via higher order interpolants. We propose an algorithm to compute the contour tree for such functions. Thealgorithm computes a local structure by connecting critical points using a numerically stable monotone path tracing procedure.Such structures are computed for each cell and are stitched together to obtain the contour tree of the function. The algorithmis scalable to higher degree interpolants whereas previous methods were restricted to quadratic or linear interpolants. Thealgorithm is intrinsically parallelizable and has potential applications to isosurface extraction.

Published
2017

3. Flexible G1 interpolation of quad meshes

Author

Stefanie Hahmann, Georges-Pierre Bonneau, Models and Algorithms for Visualization and Rendering (MAVERICK), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE), European Project: 291184,EC:FP7:ERC,ERC-2011-ADG_20110209,EXPRESSIVE(2012), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Surface (mathematics), Degrees of freedom, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Trilinear interpolation, 020207 software engineering, Bézier curve, 010103 numerical & computational mathematics, 02 engineering and technology, Topology, 01 natural sciences, Computer Graphics and Computer-Aided Design, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Computer Science::Graphics, Nearest-neighbor interpolation, Modeling and Simulation, Face (geometry), 0202 electrical engineering, electronic engineering, information engineering, Polygon mesh, Geometry and Topology, 0101 mathematics, Software, ComputingMethodologies_COMPUTERGRAPHICS, Mathematics, Interpolation
Abstract

International audience; Transforming an arbitrary mesh into a smooth G1 surface has been the subject of intensive research works. To get a visual pleasing shape without any imperfection even in the presence of extraordinary mesh vertices is still a challenging problem in particular when interpolation of the mesh vertices is required. We present a new local method, which produces visually smooth shapes while solving the interpolation problem. It consists of combining low degree biquartic Bézier patches with minimum number of pieces per mesh face, assembled together with G1-continuity. All surface control points are given explicitly. The construction is local and free of zero-twists. We further show that within this economical class of surfaces it is however possible to derive a sufficient number of meaningful degrees of freedom so that standard optimization techniques result in high quality surfaces.

Published
2014

4. A 2D Shape Structure for Decomposition and Part Similarity

Author

Axel Carlier, Stefanie Hahmann, Kathryn Leonard, Géraldine Morin, California State University Channel Islands, Real Expression Artificial Life (IRIT-REVA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut National Polytechnique (Toulouse) (Toulouse INP), Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), European Project: 291184,EC:FP7:ERC,ERC-2011-ADG_20110209,EXPRESSIVE(2012), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique - CNRS (FRANCE), California State University Channel Islands - CSU-CI (USA), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Université Grenoble Alpes - UGA (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Institut de Recherche en Informatique de Toulouse - IRIT (Toulouse, France), Institut National Polytechnique de Toulouse - INPT (FRANCE), and Université Toulouse III - Paul Sabatier - UPS (FRANCE)

Subjects
ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, shape decomposition, 02 engineering and technology, Geometric shape, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], Computational geometry, Traitement des images, Heat kernel signature, Salience (neuroscience), Medial axis, Active shape model, 0202 electrical engineering, electronic engineering, information engineering, Traitement du signal et de l'image, Partition (number theory), Computer vision, part similarity, Synthèse d'image et réalité virtuelle, medal axis, Mathematics, ComputingMethodologies_COMPUTERGRAPHICS, WEDF, business.industry, 2D shape, 020207 software engineering, Pattern recognition, Vision par ordinateur et reconnaissance de formes, Intelligence artificielle, shape structure, 020201 artificial intelligence & image processing, Topological skeleton, Shape recognition, Artificial intelligence, business, Shape analysis (digital geometry)
Abstract

International audience; This paper presents a multilevel analysis of 2D shapes and uses it to find similarities between the different parts of a shape. Such an analysis is important for many applications such as shape comparison, editing, and compression. Our robust and stable method decomposes a shape into parts, determines a parts hierarchy, and measures similarity between parts based on a salience measure on the medial axis, the Weighted Extended Distance Function, providing a multi-resolution partition of the shape that is stable across scale and articulation. Comparison with an extensive user study on the MPEG-7 database demonstrates that our geometric results are consistent with user perception.

Published
2016

5. Surfacing Curve Networks with Normal Control

Author

Nathalie Saguin-Sprynski, Stefanie Hahmann, Tibor Stanko, Georges-Pierre Bonneau, Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE ), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information (CEA-LETI), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Models and Algorithms for Visualization and Rendering (MAVERICK ), and European Project: 291184,EC:FP7:ERC,ERC-2011-ADG_20110209,EXPRESSIVE(2012)

Subjects
Mean curvature, Curve network, General Engineering, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, curve network, normal input, 020207 software engineering, 02 engineering and technology, Curvature, Topology, Computer Graphics and Computer-Aided Design, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Human-Computer Interaction, smooth surface, Triangle mesh, 0202 electrical engineering, electronic engineering, information engineering, Piecewise, 020201 artificial intelligence & image processing, shape reconstruction, Normal, Laplace operator, Algorithm, Normal control, Mathematics, ComputingMethodologies_COMPUTERGRAPHICS
Abstract

Recent surface acquisition technologies based on microsensors produce three-space tangential curve data which can be transformed into a network of space curves with surface normals. This paper addresses the problem of surfacing an arbitrary closed 3D curve network with given surface normals. Thanks to the normal vector input, the patch finding problem can be solved unambiguously and an initial piecewise smooth triangle mesh is computed. The input normals are propagated throughout the mesh. Together with the initial mesh, the propagated normals are used to compute mean curvature vectors. We then compute the final mesh as the solution of a new variational optimization method based on the mean curvature vectors. The intuition behind this original approach is to guide the standard Laplacian-based variational methods by the curvature information extracted from the input normals. The normal input increases shape fidelity and allows to achieve globally smooth and visually pleasing shapes. Graphical abstractDisplay Omitted HighlightsA method for surfacing curve networks with prescribed normals is presented.The method does not require an extra parameter to control the magnitude of normals.The key insight is the decoupling of normals from positions before the extrapolation.The resulting shapes are globally smooth and visually pleasing.The method is fully automatic, and, at the same time, simple to implement.

Published
2016

6. Sharp feature preserving MLS surface reconstruction based on local feature line approximations

Author

Georges-Pierre Bonneau, Hans Hagen, Stefanie Hahmann, Christopher Weber, Department of Computer Science [Kaiserslautern], Technische Universität Kaiserslautern (TU Kaiserslautern), Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Models and Algorithms for Visualization and Rendering (MAVERICK), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, 02 engineering and technology, Sharp feature, Clustering, MLS, 0202 electrical engineering, electronic engineering, information engineering, Point set surfaces, ACM: I.: Computing Methodologies/I.3: COMPUTER GRAPHICS/I.3.5: Computational Geometry and Object Modeling/I.3.5.2: Curve, surface, solid, and object representations, Point (geometry), Cluster analysis, Projection (set theory), Mathematics, Feature detection (computer vision), business.industry, 020207 software engineering, Pattern recognition, Computer Graphics and Computer-Aided Design, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Feature (computer vision), Gauss map, Modeling and Simulation, Line (geometry), Piecewise, 020201 artificial intelligence & image processing, Geometry and Topology, Artificial intelligence, Moving least squares, Surface reconstruction, business, Software
Abstract

Graphical abstractDisplay Omitted Highlights? Use of local feature line approximation for MLS with sharp feature reconstruction. ? Feature reconstruction by segmentation and up-sampling of local neighborhoods along feature curves. ? Capable to handle sharp line-type features and corner features. ? Full automatic sharp feature detection as preprocess speeds up iterative reconstructions. Sharp features in manufactured and designed objects require particular attention when reconstructing surfaces from unorganized scan point sets using moving least squares (MLS) fitting. It is an inherent property of MLS fitting that sharp features are smoothed out. Instead of searching for appropriate new fitting functions our approach computes a modified local point neighborhood so that a standard MLS fitting can be applied enhanced by sharp features reconstruction.We present a two-stage algorithm. In a pre-processing step sharp feature points are marked first. This algorithm is robust to noise since it is based on Gauss map clustering. In the main phase, the selected feature points are used to locally approximate the feature curve and to segment and enhance the local point neighborhood. The MLS projection thus leads to a piecewise smooth surface preserving all sharp features. The method is simple to implement and able to preserve line-type features as well as corner-type features during reconstruction.

Published
2012

7. Detail preserving deformation of B-spline surfaces with volume constraint

Author

Georges-Pierre Bonneau, Basile Sauvage, Gershon Elber, Stefanie Hahmann, Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection (LSIIT), Centre National de la Recherche Scientifique (CNRS), Modélisation Géométrique & Multirésolution pour l'Image (MGMI), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Virtual environments for animation and image synthesis of natural objects (EVASION), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Center for Graphics and Geometric Computing (CGGC), Technion - Israel Institute of Technology [Haifa], NoE AIM@SHAPE, and Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)

Subjects
Computation, Multiresolution analysis, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Aerospace Engineering, Geometry, 02 engineering and technology, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], computer.software_genre, multiresolution, 0202 electrical engineering, electronic engineering, information engineering, Computer Aided Design, ComputingMethodologies_COMPUTERGRAPHICS, Mathematics, Sparse matrix, B-spline, deformation, tensor product, 020207 software engineering, Data structure, Computer Graphics and Computer-Aided Design, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Geometric Modeling, Modeling and Simulation, Automotive Engineering, 020201 artificial intelligence & image processing, B-spline surfaces, Minification, volume constraint, Geometric modeling, Algorithm, computer
Abstract

Computer Graphics and Applications -- Selected papers from the 15th Pacific Conference on Computer Graphics and Applications (Pacific Graphics 2007); International audience; Geometric constraints have proved to be helpful for shape modeling. Moreover, they are efficient aids in controlling deformations and enhancing animation realism. The present paper adresses the deformation of B-spline surfaces while constraining the volume enclosed by the surface. Both uniform and non-uniform frameworks are considered. The use of level-of-detail (LoD) editing allows the preservation of tne details during coarse deformations of the shape. The key contribution of this paper is the computation of the volume with respect to the appropriate basis for LoD editing: the volume is expressed through all levels of resolution as a trilinear form and recursive formulas are developped to make the computation e±cient. The volume constrained is maintained through a minimization process for which we develop closed solutions. Real-time deformations are reached thanks to sparse data structures and e±cient algorithms.

Published
2008

8. Idealized Models for FEA Derived from Generative Modeling Processes Based on Extrusion Primitives

Author

Lionel Fine, Stefanie Hahmann, Flavien Boussuge, Jean-Claude Léon, Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), EADS Innovation Works [Suresnes] (EADS IW), EADS - European Aeronautic Defense and Space, European Project: 291184,EC:FP7:ERC,ERC-2011-ADG_20110209,EXPRESSIVE(2012), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
02 engineering and technology, [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], Additive process, computer.software_genre, Robustness (computer science), Component (UML), 0202 electrical engineering, electronic engineering, information engineering, Computer Aided Design, FEA, Mathematics, Generative shape process, General Engineering, ACM: I.: Computing Methodologies/I.3: COMPUTER GRAPHICS/I.3.5: Computational Geometry and Object Modeling, 020207 software engineering, [PHYS.MECA.MSMECA]Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph], [INFO.INFO-IA]Computer Science [cs]/Computer Aided Engineering, Computer Science Applications, Tree (data structure), Tree structure, B-Rep model, Modeling and Simulation, Idealization, Graph (abstract data type), 020201 artificial intelligence & image processing, computer, Algorithm, Software, Initial and terminal objects
Abstract

International audience; Shape idealization transformations are very common operations when adapting a CAD component to FEA requirements. Here, an idealization approach is proposed that is based on generative shape processes used to decompose an initial B-Rep solid, i.e., extru-sion processes with material addition are used to seg-ment a solid. The corresponding extrusion primitives form the basis of candidate sub domains for idealiza-tion and their connections conveyed through the gen-erative processes they belong to, bring robustness to set up the appropriate connections between idealized sub domains. This is made possible because the con-nections between extrusion primitives have an explicit geometric representation and can be used to bound the connections between idealized sub domains. Taking ad-vantage of an existing construction tree as available in a CAD software does not help much because it may be complicated to use it for idealization processes because this tree structure is not unique. Using generative pro-cesses attached to an object that are no longer reduced to a single construction tree but to a graph containing all non trivial construction trees, is more useful for the engineer to evaluate variants of idealization. From this automated decomposition, each primitive is subjected to a morphological analysis to define whether it can idealized or not. Subsequently, geometric interfaces be-tween primitives form also a graph that can be used to process the connections between the idealized sub do-mains generated from the primitives. These interfaces are taken into account to determine more precisely the idealizable sub domains and their contours when primi-tives are incrementally merged to come back to produce the global morphological analysis of the initial object. A user defined threshold is used to tune the morpho-logical analysis with respect to further user parameters. Finally, the idealizable sub domains and their connec-tions are processed to locate the mid-surfaces and con-nect them using generic criteria that the user can tune locally using complementary criteria.

Published
2015

9. Deformations Preserving Gauß Curvature

Author

Anne Berres, Stefanie Hahmann, Hans Hagen, Department of Computer Science [Kaiserslautern], Technische Universität Kaiserslautern (TU Kaiserslautern), Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Bennett, Janine, Vivodtzev, Fabien, Pascucci, Valerio, European Project: 291184,EC:FP7:ERC,ERC-2011-ADG_20110209,EXPRESSIVE(2012), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
Surface (mathematics), Mean curvature flow, Mean curvature, Minimal surface, 010102 general mathematics, deformation, 020207 software engineering, Geometry, 02 engineering and technology, Curvature, 01 natural sciences, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], symbols.namesake, total curvature, 0202 electrical engineering, electronic engineering, information engineering, Gaussian curvature, symbols, Constant-mean-curvature surface, Total curvature, gauss curvature, 0101 mathematics, Mathematics, topologie
Abstract

(Proceedings of LHMTS 2013); International audience; In industrial surface generation, it is important to consider surfaces with minimal areas for two main reasons: these surfaces require less material than non-minimal surfaces, and they are cheaper to manufacture. Based on a prototype, a so-called masterpiece, the final product is created using small deformations to adapt a surface to the desired shape. We present a linear deformation technique preserving the total curvature of the masterpiece. In particular, we derive sufficient conditions for these linear deformations to be total curvature preserving when applied to the masterpiece. It is useful to preserve total curvature of a surface in order to minimise the amount of material needed, and to minimise bending energy.

Published
2014

10. Extraction of generative processes from B-Rep shapes and application to idealization transformations

Author

Flavien Boussuge, Jean-Claude Léon, Stefanie Hahmann, Lionel Fine, Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), EADS Innovation Works [Suresnes] (EADS IW), EADS - European Aeronautic Defense and Space, European Project: 291184,EC:FP7:ERC,ERC-2011-ADG_20110209,EXPRESSIVE(2012), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
Engineering drawing, Theoretical computer science, CAD, 02 engineering and technology, [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], 01 natural sciences, Industrial and Manufacturing Engineering, ACM: J.: Computer Applications/J.6: COMPUTER-AIDED ENGINEERING/J.6.0: Computer-aided design (CAD), Realizability, 0202 electrical engineering, electronic engineering, information engineering, Generative Design, Mathematics, Generative Modelling Language, Generative shape process, ACM: I.: Computing Methodologies/I.3: COMPUTER GRAPHICS/I.3.5: Computational Geometry and Object Modeling, B-Rep model Construction graph, 020207 software engineering, [INFO.INFO-IA]Computer Science [cs]/Computer Aided Engineering, [PHYS.MECA.MSMECA]Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph], Computer Graphics and Computer-Aided Design, 0104 chemical sciences, Computer Science Applications, 010404 medicinal & biomolecular chemistry, Idealization, Design process, Graph (abstract data type), Generative grammar
Abstract

International audience; A construction tree is a set of shape generation processes commonly produced with CAD modelers during a design process of B-Rep objects. However, a construction tree does not bring all the desired properties in many configurations: dimension modifications, idealization processes, etc. Generating a non trivial set of generative processes, possibly forming a construction graph, can significantly improve the adequacy of some of these generative processes to meet user's application needs. This paper proposes to extract generative processes from a given B-rep shape as a high-level shape description. To evaluate the usefulness of this description, finite element analyses (FEA) and particularly idealizations are the applications selected to evaluate the adequacy of additive generative processes. Non trivial construction trees containing generic extrusion and revolution primitives behave like well established CSG trees. Advantageously, the proposed approach is primitive-based, which ensures that any generative process of the construction graph does preserve the realizability of the corresponding volume. In the context of FEA, connections between idealized primitives of a construction graph can be efficiently performed using their interfaces. Consequently, generative processes of a construction graph become a high-level object structure that can be tailored to idealizations of primitives and robust connections between them.

Published
2014

11. Piecewise polynomial monotonic interpolation of 2D gridded data

Author

Léo Allemand-Giorgis, Georges-Pierre Bonneau, Stefanie Hahmann, Fabien Vivodtzev, Models and Algorithms for Visualization and Rendering (MAVERICK), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE), Centre d'études scientifiques et techniques d'Aquitaine (CESTA), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Bennett, Janine, Vivodtzev, Fabien, Pascucci, Valerio, Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Mathematical analysis, Monotone cubic interpolation, Monotonic function, 010103 numerical & computational mathematics, 01 natural sciences, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Interpolation, 010101 applied mathematics, Maxima and minima, Monotone Surfaces, Monotone polygon, Saddle point, Piecewise, Partial derivative, 0101 mathematics, Mathematics, Visualization
Abstract

International audience; A method for interpolating monotone increasing 2D scalar data with a monotone piecewise cubic C$^1$-continuous surface is presented. Monotonicity is a sufficient condition for a function to be free of critical points inside its domain. The standard axial monotonicity for tensor-product surfaces is however too restrictive. We therefore introduce a more relaxed monotonicity constraint. We derive sufficient conditions on the partial derivatives of the interpolating function to ensure its monotonicity. We then develop two algorithms to effectively construct a monotone C$^1$ surface composed of cubic triangular Bézier surfaces interpolating a monotone gridded data set. Our method enables to interpolate given topological data such as minima, maxima and saddle points at the corners of a rectangular domain without adding spurious extrema inside the function domain. Numerical examples are given to illustrate the performance of the algorithm.

Published
2014

12. Knot-removal surface fairing using search strategies

Author

Stefanie Hahmann and Stefan Konz

Subjects
Mathematical optimization, B-spline, Best-first search, Computer Graphics and Computer-Aided Design, Industrial and Manufacturing Engineering, Search tree, Computer Science Applications, Search algorithm, Simulated annealing, Metric (mathematics), Smoothing, ComputingMethodologies_COMPUTERGRAPHICS, Knot (mathematics), Mathematics
Abstract

This paper presents two automatic fairing algorithms for para- metric C 2 -continuous bi-cubic B-spline surfaces. The fairing method consists of a knot removal and knot reinsertion step which locally smooths the surface. Search strategies like best-flrst-search and simulated-annealing are searching for the global minimum of the fairing measure. The best-flrst-search algorithm constructs only partially a search tree and reduces signiflcantly the complex- ity of a systematic search. Simulated annealing is a heuristic algorithm which needs a probability function and some further parameters as input. Both methods can satisfy end constraints and tolerances. Their performance is discussed for two numerical experiments.

Published
1998

13. Visualization and computation of curvature behaviour of freeform curves and surfaces

Author

Hans Hagen, Stefanie Hahmann, and Thomas Schreiber

Subjects
Surface (mathematics), Computation, Geometry, Bézier curve, Computational geometry, computer.software_genre, Curvature, Computer Graphics and Computer-Aided Design, Industrial and Manufacturing Engineering, Computer Science Applications, Visualization, Computer Science::Graphics, Computer Aided Design, Representation (mathematics), computer, Mathematics
Abstract

The paper consists of two parts. In the first, an interrogation method for a visualization of curvature behaviour is introduced. The method consists of a generalized focal analysis. The second part concerns the accurate computation of surface behaviour. Arithmetic operations on Bezier surfaces are used to achieve an exact representation of surface properties. With these property surfaces in Bezier form, qualitative and quantitative statements relating to the investigated surface are possible.

Published
1995

14. Substructure Topology Preserving Simplification of Tetrahedral Meshes

Author

Fabien Vivodtzev, Georges-Pierre Bonneau, Stefanie Hahmann, Hans Hagen, Centre d'études scientifiques et techniques d'Aquitaine (CESTA), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Virtual environments for animation and image synthesis of natural objects (EVASION), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Department of Computer Science [Kaiserslautern], Technische Universität Kaiserslautern (TU Kaiserslautern), and Valerio Pascucci and Xavier Tricoche and Hans Hagen and Julien Tierny

Subjects
Collapse (topology), Shape, 020207 software engineering, 02 engineering and technology, Volume mesh, Combinatorial topology, Topology, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Domain (software engineering), Simplicial complex, 0202 electrical engineering, electronic engineering, information engineering, Substructure, 020201 artificial intelligence & image processing, Topology (chemistry), Geometry and topology, Mathematics, ComputingMethodologies_COMPUTERGRAPHICS
Abstract

International audience; Interdisciplinary efforts in modeling and simulating phenomena have led to complex multi-physics models involving different physical properties and materials in the same system. Within a 3d domain, substructures of lower dimensions appear at the interface between different materials. Correspondingly, an unstructured tetrahedral mesh used for such a simulation includes 2d and 1d substructures embedded in the vertices, edges and faces of the mesh. The simplification of such tetrahedral meshes must preserve (1) the geometry and the topology of the 3d domain, (2) the simulated data and (3) the geometry and topology of the embedded substructures. Although intensive research has been conducted on the first two goals, the third objective has received little attention. This paper focuses on the preservation of the topology of 1d and 2d substructures embedded in an unstructured tetrahedral mesh, during edge collapse simplification. We define these substructures as simplicial sub-complexes of the mesh, which is modeled as an extended simplicial complex. We derive a robust algorithm, based on combinatorial topology results, in order to determine if an edge can be collapsed without changing the topology of both the mesh and all embedded substructures. Based on this algorithm we have developed a system for simplifying scientific datasets defined on irregular tetrahedral meshes with substructures. The implementation of our system is discussed in detail. We demonstrate the power of our system with real world scientific datasets from electromagnetism simulations.

Published
2011

15. Sharp Feature Detection in Point Clouds

Author

Stefanie Hahmann, Christopher Weber, Hans Hagen, Department of Computer Science [Kaiserslautern], Technische Universität Kaiserslautern (TU Kaiserslautern), Modélisation Géométrique & Multirésolution pour l'Image (MGMI), Laboratoire Jean Kuntzmann (LJK), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
business.industry, Iterative method, Computation, Feature extraction, Point cloud, feature detection, Gauss map clustering, 020207 software engineering, Pattern recognition, 02 engineering and technology, Computational geometry, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], sharp features, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Feature (computer vision), point sets, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Artificial intelligence, Cluster analysis, business, Feature detection (computer vision), Mathematics
Abstract

International audience; This paper presents a new technique for detecting sharp features on point-sampled geometry. Sharp features of different nature and possessing angles varying from obtuse to acute can be identified without any user interaction. The algorithm works directly on the point cloud, no surface reconstruction is needed. Given an unstructured point cloud, our method first computes a Gauss map clustering on local neighborhoods in order to discard all points which are unlikely to belong to a sharp feature. As usual, a global sensitivity parameter is used in this stage. In a second stage, the remaining feature candidates undergo a more precise iterative selection process. Central to our method is the automatic computation of an adaptive sensitivity parameter, increasing significantly the reliability and making the identification more robust in the presence of obtuse and acute angles. The algorithm is fast and does not depend on the sampling resolution, since it is based on a local neighbor graph computation.

Published
2010

16. Design with free-form splines over irregular meshes

Author

Me´lanie Cornillac, Se´bastien Barbier, Georges-Pierre Bonneau, Stefanie Hahmann, Modélisation Géométrique & Multirésolution pour l'Image (MGMI), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Virtual environments for animation and image synthesis of natural objects (EVASION), Inria Grenoble - Rhône-Alpes, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK)

Subjects
Polynomial, quad meshes, Quadrilateral, MathematicsofComputing_NUMERICALANALYSIS, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, I.3.5 Computational Geometry and Object Modeling, Topology, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], interpolation, arbitrary topology, Spline (mathematics), ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Tangent space, Polygon mesh, Geometric modeling, Normal, Interpolation, Mathematics, ComputingMethodologies_COMPUTERGRAPHICS
Abstract

Generating smooth surfaces of arbitrary topology is still a challenge. This paper considers the problem of creating a smooth parametric polynomial surface interpolating the vertices of an irregular triangular or quadrilateral mesh of arbitrary topological type. The surface is overall tangent plane continuous without any singular points and without any singular parameterizations. We particularly focus on design issues related to this spline model which offers several degrees of freedom. In particular, an exhaustive description of all available degrees of freedom is given and their geometric interpretation for shape design is specified. An extension of the model allows for additional normal vector interpolation and increases thus the number of design parameters. Finally several design issues are discussed and illustrated.Copyright © 2008 by ASME

Published
2008

17. Multiresolution morphing for planar curves

Author

Mélanie Cornillac, Baptiste Caramiaux, Georges-Pierre Bonneau, Stefanie Hahmann, Modélisation Géométrique & Multirésolution pour l'Image (MGMI), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Virtual environments for animation and image synthesis of natural objects (EVASION), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)

Subjects
curves, 68U07, 68U05, 65D05, 65D08, 65D17, Computation, Multiresolution analysis, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Geometry, 02 engineering and technology, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, Theoretical Computer Science, multiresolution analysis, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Mathematics, ComputingMethodologies_COMPUTERGRAPHICS, interpolation vertex correspondence, Numerical Analysis, Numerical analysis, 020207 software engineering, morphing, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Computer Science Applications, 010101 applied mathematics, Computational Mathematics, Morphing, Computer Science::Graphics, Computational Theory and Mathematics, Polygon, Piecewise, Geometric modeling, Decomposition method (constraint satisfaction), Algorithm, Software
Abstract

International audience; We present a multiresolution morphing algorithm using "as-rigid-as-possible" shape interpolation combined with an angle-length based multiresolution decomposition of simple 2D piecewise curves. This novel multiresolution representation is defined intrinsically and has the advantage that the details' orientation follows any deformation naturally. The multiresolution morphing algorithm consists of transforming separately the coarse and detail coefficients of the multiresolution decomposition. Thus all LoD (level of detail) applications like LoD display, compression, LoD editing etc.\ can be applied directly to all morphs without any extra computation. Furthermore, the algorithm can robustly morph between very large size polygons with many local details as illustrated in numerous figures. The intermediate morphs behave natural and least-distorting due to the particular intrinsic multiresolution representation.

Published
2007

18. Length Constrained Multiresolution Deformation for Surface Wrinkling

Author

Stefanie Hahmann, Georges-Pierre Bonneau, Basile Sauvage, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Virtual environments for animation and image synthesis of natural objects (EVASION), Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble (GRAVIR - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Hahmann, Stefanie, and Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes

Subjects
[INFO.INFO-GR] Computer Science [cs]/Graphics [cs.GR], ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Solid modelling, 020207 software engineering, Geometry, 02 engineering and technology, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 16. Peace & justice, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Piecewise linear function, [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG], Mesh generation, 0202 electrical engineering, electronic engineering, information engineering, Curve fitting, 020201 artificial intelligence & image processing, Minification, Surface wrinkling, Algorithm, ComputingMethodologies_COMPUTERGRAPHICS, Mathematics
Abstract

International audience; We present a method for deforming piescewise linear 3D curves on surfaces with constant length constraint. We show how this constraint can be integrated into a multiresolution editing tool allowing an intuitive control of the deformation's extent and aspect. The constraint is enforced following two steps. A first step consists in approximating the initial length by modifying the multiresolution decomposition at some specified scale. In a second step the constraint is axactly enforced by constrained minimization of a smoothness criterion. This process then provides the core of an integrated wrinkling tool for soft tissues modelling. A curve on the mesh is deformed, providing a deformation profile which is propagated in a user-defined neighbourhood.

Published
2006

19. Hierarchical Triangular Splines

Author

Alex Yvart, Georges-Pierre Bonneau, Stefanie Hahmann, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Virtual environments for animation and image synthesis of natural objects (EVASION), Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble (GRAVIR - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Inria Grenoble - Rhône-Alpes

Subjects
Surface (mathematics), Bézier patches, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, G1-continuity, 010103 numerical & computational mathematics, 02 engineering and technology, hierarchical splines, Topology, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, Hierarchical database model, local frames, multiresolution, Parametric surface, 0202 electrical engineering, electronic engineering, information engineering, Tangent space, Polygon mesh, 0101 mathematics, Mathematics, ComputingMethodologies_COMPUTERGRAPHICS, I.3.5 [Computer Graphics]: Computational Geometry and, 020207 software engineering, Base (topology), Computer Graphics and Computer-Aided Design, interpolation, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], arbitrary topology, triangular meshes, Piecewise, Geometric modeling, Interpolation
Abstract

Smooth parametric surfaces interpolating triangular meshes are very useful for modeling surfaces of arbitrary topology. Several interpolants based on these kind of surfaces have been developed over the last fifteen years. However, with current 3D acquisition equipments, models are becoming more and more complex. Since previous interpolation methods lack a local refinement property, there is no way to locally adapt the level of detail. In this article, we introduce a hierarchical triangular surface model. The surface is overall tangent plane continuous and is defined parametrically as a piecewise quintic polynomial. It can be adaptively refined while preserving the overall tangent plane continuity. This model enables designers to create a complex smooth surface of arbitrary topology composed of a small number of patches to which details can be added by locally refining the patches until an arbitrary small size is reached. It is implemented as a hierarchical data structure where the top layer describes a coarse, smooth base surface and the lower levels encode the details in local frame coordinates.

Published
2005

20. Area preserving deformation of multiresolution curves

Author

Georges-Pierre Bonneau, Basile Sauvage, Stefanie Hahmann, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Virtual environments for animation and image synthesis of natural objects (EVASION), Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble (GRAVIR - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes

Subjects
Multiresolution analysis, Computation, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Aerospace Engineering, Area preservation, Geometry, 02 engineering and technology, Deformation (meteorology), Bilinear form, Wavelets, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], Matrix (mathematics), Wavelet, 0202 electrical engineering, electronic engineering, information engineering, ComputingMethodologies_COMPUTERGRAPHICS, Mathematics, Curves, Mathematical analysis, Constrained deformation, 020207 software engineering, Computer Graphics and Computer-Aided Design, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Constraint (information theory), Geometric Modeling, Modeling and Simulation, Automotive Engineering, 020201 artificial intelligence & image processing, Multiresolution editing, Constant (mathematics)
Abstract

We describe a method for multiresolution deformation of closed planar curves that keeps the enclosed area constant. We use a wavelet based multiresolution representation of the curves that are represented by a finite number of control points at each level of resolution. A deformation can then be applied to the curve by modifying one or more control points at any level of resolution. This process is generally known as multiresolution editing to which we add the constraint of constant area. The key contribution of this paper is the efficient computation of the area in the wavelet decomposition form: the area is expressed through all levels of resolution as a bilinear form of the coarse and detail coefficients, and recursive formulas are developed to compute the matrix of this bilinear form. A similar result is also given for the bending energy of the curve. The area constraint is maintained through an optimization process. These contributions allow a real time multiresolution deformation with area constraint of complex curves.

Published
2005

21. Length preserving multiresolution editing of curves

Author

Basile Sauvage, Georges-Pierre Bonneau, Stefanie Hahmann, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Virtual environments for animation and image synthesis of natural objects (EVASION), Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble (GRAVIR - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes

Subjects
Multiresolution analysis, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Geometry, linearization, 02 engineering and technology, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], Theoretical Computer Science, Piecewise linear function, Wavelet, 0202 electrical engineering, electronic engineering, information engineering, length constraint, Mathematics, ComputingMethodologies_COMPUTERGRAPHICS, Numerical Analysis, Numerical analysis, deformation, 020207 software engineering, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Computer Science Applications, Computational Mathematics, Computational Theory and Mathematics, Geometric Modeling, Curve fitting, curve length, wrinkle generation, 020201 artificial intelligence & image processing, Decomposition method (constraint satisfaction), Arc length, Algorithm, 68U07, 68U05, 65D17, 65D18, Software, Smoothing
Abstract

International audience; In this paper a method for multiresolution deformation of planar piecewise linear curves that preserves the curve length is presented. In a wavelet based multiresolution editing framework, the curve can be deformed at any level of resolution through its control points. Enforcing the length constraint is carried out in two steps. In a first step the multiresolution decomposition of the curve is used in order to approximate the initial curve length. In a second step the length constraint is satisfied exactly by iteratively smoothing the deformed curve. Wrinkle generation is an application the paper particularly focuses on. It is shown how the multiresolution definition of the curve allows to explicitly and intuitively control the scale of the generated wrinkles.

Published
2004

22. Polynomial surfaces interpolating arbitrary triangulations

Author

Stefanie Hahmann, Georges-Pierre Bonneau, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Models, Algorithms and Geometry for Computer Generated Image Graphics (iMAGIS), Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble (GRAVIR - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Inria Grenoble - Rhône-Alpes

Subjects
Surface (mathematics), reconstruction, Geometry, 02 engineering and technology, surfaces, arbitrary tangent vectors, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, Triangulation, triangular patches, Triangle mesh, 0202 electrical engineering, electronic engineering, information engineering, Tangent space, Subdivision surface, Polygon mesh, irregular 3D meshes, Mathematics, piecewise polynomial patches, Mathematical analysis, Tangent, 020207 software engineering, modeling, Computer Graphics and Computer-Aided Design, interpolation, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], 0104 chemical sciences, arbitrary topology, 010404 medicinal & biomolecular chemistry, Computer Science::Graphics, Mesh generation, Signal Processing, Computer Vision and Pattern Recognition, Software, Interpolation
Abstract

International audience; Triangular Bezier patches are an important tool for defining smooth surfaces over arbitrary triangular meshes. The previously introduced 4-split method interpolates the vertices of a 2-manifold triangle mesh by a set of tangent plane continuous triangular Bezier patches of degree five. The resulting surface has an explicit closed form representation and is defined locally. In this paper, we introduce a new method for visually smooth interpolation of arbitrary triangle meshes based on a regular 4-split of the domain triangles. Ensuring tangent plane continuity of the surface is not enough for producing an overall fair shape. Interpolation of irregular control-polygons, be that in 1D or in 2D, often yields unwanted undulations. Note that this undulation problem is not particular to parametric interpolation, but also occur with interpolatory subdivision surfaces. Our new method avoids unwanted undulations by relaxing the constraint of the first derivatives at the input mesh vertices: the tangent directions of the boundary curves at the mesh vertices are now completely free. Irregular triangulations can be handled much better in the sense that unwanted undulations due to flat triangles in the mesh are now avoided.

Published
2003

23. Subdivision Invariant Polynomial Interpolation

Author

Georges-Pierre Bonneau, Stefanie Hahmann, Alex Yvart, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Models, Algorithms and Geometry for Computer Generated Image Graphics (iMAGIS), Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble (GRAVIR - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria), Hege, Hans-Christian and Polthier, Konrad, Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Grenoble (INPG)-Inria Grenoble - Rhône-Alpes, Artis, Team, and Hege, Hans-Christian and Polthier, Konrad

Subjects
Surface (mathematics), Invariant polynomial, business.industry, [INFO.INFO-GR] Computer Science [cs]/Graphics [cs.GR], ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Triangulation (social science), 020207 software engineering, 02 engineering and technology, Topology, 01 natural sciences, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], 0104 chemical sciences, Vertex (geometry), Polynomial interpolation, 010404 medicinal & biomolecular chemistry, 0202 electrical engineering, electronic engineering, information engineering, Polygon mesh, business, Subdivision, Interpolation, Mathematics, ComputingMethodologies_COMPUTERGRAPHICS
Abstract

International audience; In previous works a polynomial interpolation method for triangular meshes has been introduced. This interpolant can be used to design smooth surfaces of arbitrary topological type. In a design process, it is very useful to be able to locate the deformation made on a geometric model. The previously introduced interpolant has the so-called strict locality property: when a mesh vertex is changed, only the surface patches containing this vertex are changed. This enables to locate the deformation at the size of the input triangles. Unfortunately this is not sufficient if the designer wants to add some detail at a smaller size than that of the input triangles. In this paper, we propose a modification of our interpolant, that enables to arbitrary refine the input triangulation, without changing the resulting surface. We call this property the subdivision invariance. After refinement of the input triangulation, the modification of one of the vertices will change the shape of the interpolant at the scale of the refined triangulation. In this way, it is possible to add details at an arbitrary fine scale.

Published
2002

24. Localizing the 4-Split Method for G1 Free-Form Surface Fitting

Author

Georges-Pierre Bonneau, Stefanie Hahmann, and Riadk Taleb

Subjects
Computer Science::Graphics, Triangle mesh, Piecewise, Tangent, Subdivision surface, Laplacian smoothing, Topology, ComputingMethodologies_COMPUTERGRAPHICS, Mathematics, Interpolation, Vertex (geometry), Parametric statistics
Abstract

One common technique for modeling closed surfaces of arbitrary topological type is to define them by piecewise parametric triangular patches on an irregular mesh. This surface mesh serves as a control mesh which is either interpolated or approximated. A new method for smooth triangular mesh interpolation has been developed. It is based on a regular 4-split of the domain triangles in order to solve the vertex consistency problem. In this paper a generalization of the 4-split domain method is presented in that the method becomes completely local. It will further be shown how normal directions, i.e. tangent planes, can be prescribed at the patch vertices.

Published
2001

25. Triangular G1 interpolation by 4-splitting domain triangles

Author

Georges-Pierre Bonneau, Stefanie Hahmann, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Virtual environments for animation and image synthesis of natural objects (EVASION), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
Bézier surface, Triangle 4-split, B-spline, Mathematical analysis, Aerospace Engineering, 020207 software engineering, Bézier curve, 02 engineering and technology, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], Computer Graphics and Computer-Aided Design, Vertex (geometry), Interpolation, Spline (mathematics), Twist compatibility, Triangular Bézier surfaces, Modeling and Simulation, Automotive Engineering, 0202 electrical engineering, electronic engineering, information engineering, Piecewise, G1 continuity, 020201 artificial intelligence & image processing, Affine transformation, Mathematics
Abstract

International audience; A piecewise quintic G1 spline surface interpolating the vertices of a triangular surface mesh of arbitrary topological type is presented. The surface has an explicit triangular Bezier representation, is affine invariant and has local support. The twist compatibility problem which arises when joining an even number of polynomial patches G1 continuously around a common vertex is solved by constructing C2-consistent boundary curves. Piecewise C1 boundary curves and a regular 4-split of the domain triangle make shape parameters available for controlling locally the boundary curves. A small number of free inner control points can be chosen for some additional local shape effects.

Published
2000

26. Shape Improvement of Surfaces

Author

Stefanie Hahmann

Subjects
Spline (mathematics), Computer Science::Graphics, Bicubic interpolation, Topology, Knot (mathematics), Mathematics
Abstract

An automatic and local fairing algorithm for bicubic B-spline surfaces is proposed. A local fairness criterion selects the knot, where the spline surface has to be faired. A fairing step is then applied, which locally modifies the control net by a constrained least-squares approximation. It consists of increasing locally the smoothness of the surface from C 2 to C 3. Some extensions of this method are also presented, which show how to build further methods by the same basic fairing principle.

Published
1998

27. Stability Concept for Surfaces

Author

Stefanie Hahmann and Hans Hagen

Subjects
Parametric surface, Infinitesimal, Stability (learning theory), CAD, Topology, Geometric modeling, Engineering design process, Object (computer science), ComputingMethodologies_COMPUTERGRAPHICS, Mathematics, Domain (software engineering)
Abstract

In CAD/CAM technologies the design of free form surfaces is the beginning of a chain of operation that ends with the numerically controlled (NC-) production of the designed object. Apart from the design process of parametric surfaces another important domain in geometric modeling exists: shape control. In this paper we present a stability concept for surfaces based on infinitesimal bendings.

Published
1995

28. Repeated Knots in Least Squares Multiquadric Functions

Author

Richard Franke, Stefanie Hahmann, and Hans Hagen

Subjects
Knot (unit), Computational stability, Computation, Basis function, Radial basis function, Minification, Least squares, Algorithm, Mathematics
Abstract

A previous paper by the authors [2] noted that there was a strong tendency to obtain near-repeated knots in their algorithm for least squares approximation of scattered data by multiquadric functions. In this paper we observe that this leads naturally to the inclusion of derivatives of the multiquadric basis function in the approximation, and give an algorithm for accomplishing this. A comparison of the results obtained with this algorithm and the previous one is made. While the multiple knot algorithm usually has the advantage in terms of accuracy and computational stability, there are datasets for which this is reversed.

Published
1995

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