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Algebraic Representations in Computer-Aided Design for complEx Shapes

Deliverables

Software and Industrial Workshops

Software and Industrial Workshop I (Month 21). Software and Industrial Workshop II (Month 36).

ARDACDES Certificate and Doctoral degrees

Awarding of ARCADES Certificate, recognized by all participants, listing all aspects of training undertaken by the ESR within ARCADES. Awarding of doctoral degrees of those ESRs who have completed their PhD Theses according to local rules.

Learning Weeks

Learning Week I (Month 15), Learning Week II (month 26) and Learning Week III (Month 42) for Network-wide Complementary skills training.

Kickoff Workshop & Recruitment Event

Network Kickoff workshop, and Recruitment event.

Advertisement of ESR openings

Advertisement of ESR positions and the recruitment event using the project's and the Euraxess webportals, emailing lists and social networks, and printed material such as posters, leaflets, etc.

Doctoral Schools and ESR workshop

Doctoral School I (Month 9), Doctoral School II (Month 31), and Workshop (Month 31) organised by the ESRs. The latter two events are consecutive and co-located. All events are Network-wide.

Final Open Conference, and Career Fair

Open international Conference (WP6, Evolute) with emphasis on dissemination, and Career Fair (WP5, INRIA).

Midterm Review Meeting

Midterm review meeting.

1st scientific advances report on WP1

1st scientific advances report: state of the art, research organisation and first results. Task 1.1 Adaptive algebraic representations (ESR1): New, adaptive and efficient implicit representation of parametric, and point-cloud models. Task 1.2 Locally refined approximate implicitisation (ESR9): Bivariate approximate implicitisation using LR B-splines. Task 1.3 Constraint formulation and computing with constraint varieties at interactive rates (ESR12): Interactive modelling with developable NURBS surfaces. Task 1.4 Constrained geometry for fabrication (ESR13): Computational design of pattern-like arrangements and support structures in equilibrium.

1st scientific advances report on WP2

1st scientific advances report: state of the art, research organisation and first results. Task 2.1 Refinement strategies for LR-splines (ESR8): First results on refinement strategies and linear independence. Task 2.2 Parametric modelling of complex shapes (ESR5): Analysis and construction of Gk splines on domains with arbitrary topology. Task 2.3 Integrating novel shape representations with Isogeometric Analysis (ESR11): CADfix-aligned T/LR-spline based IGA-BEM solver with applications in ship-system hydrodynamics. Task 2.4 Integration and evaluation of novel parametric modellers tools for design optimisation (ESR10): T-spline based parametric modellers that can handle smoothness, interpolation and shape-preservation constraints.

Draft 1st Periodic report

Report on advances in research, training, dissemination, and management. The basis for the midterm review.

Research data

This deliverable describes how the Project generates and/or collects research data and its policy towards providing open access to these data.

Scientific Publications

Publication of Final Conference proceedings (ARCADES Book). Benchmarks on representations of complex data: Chapters in ARCADES Book and Webportal. Journal publications, conference presentations, technical reports, prototype software.

1st scientific advances report on WP3

1st scientific advances report: state of the art, research organisation, and first results. Task 3.1 Control structures for motion design (ESR7): State of the art and performance comparisons of known approaches, possibly new approaches, if sufficiently developed, in motion design. Task 3.2 Skeleton-based design of surfaces (ESR6): Formulation and experimentation of topologically accurate convolution surfaces for skeletons made of arcs of circles and line segments. Task 3.3 Singularities and syzygies of parameterisations (ESR3): Familiarity with methods already known to compute invariants of parameterisations by exploiting syzygies and singularities, and implementations to use these ideas in an efficient and fast way. Task 3.4 Distance to NURBS curves and surfaces (ESR4): New method based on matrix representations for determining all the closest points to a single Bezier patch. Task 3.5 Path planning and workspace modelling (ESR2): Design of adaptive algebraic algorithms to model the workspace of mechanisms.

Final project report

Report on achievements and advances in all aspects of the project, namely research, training, dissemination, and management.

2nd scientific advances report on WP2

2nd scientific advances report: results and transfer. Task 2.1 Refinement strategies for LR-splines (ESR8): Refinement strategies for big data approximation. Task 2.2 Parametric modelling of complex shapes (ESR5): Extensions and applications of Gk-splines for modeling and simulation. Task 2.3 Integrating novel shape representations with Isogeometric Analysis (ESR11): 3D volumetric meshing of complex computational domains arising in ship hydrodynamic applications. Task 2.4 Integration and evaluation of novel parametric modellers tools for design optimisation (ESR10): T-spline based parametric modellers and their use for ship-system optimisation.

2nd scientific advances report on WP3

2nd scientific advances report: results and transfer. Task 3.1 Control structures for motion design (ESR7): New approaches in motion design and related aspects. Task 3.2 Skeleton-based design of surfaces (ESR6): Approximate parameterisation of topologically accurate convolution surfaces. Task 3.3 Singularities and syzygies of parameterisations (ESR3): Development of new algebro-geometrical connections between invariants of curves and surfaces and singularities of their parameterisations, and also implementation of them. Task 3.4 Distance to NURBS curves and surfaces (ESR4): New method for solving the closest point problem for a complete NURBS model and its application to surface fitting. Task 3.5 Path planning and workspace modelling (ESR2): Development of tools for path planning using sparse and motion polynomials.

1st progress report

Detailing the project progress so far including all aspects (hiring situation, training, and management).

2nd scientific advances report on WP1

2nd scientific advances report: results and transfer. Task 1.1 Adaptive algebraic representations (ESR1): Exact and approximate implicitisation from different representations, using rational and numerical methods. Task 1.2 Locally refined approximate implicitisation (ESR9): 3-variate approximate implicitization using LR B-splines. Task 1.3 Constraint formulation and computing with constraint varieties at interactive rates (ESR12): Understanding fast projection onto constraint varieties using a simplified algebraic structure. Task 1.4 Constrained geometry for fabrication (ESR13): Computing constrained curves on surfaces related to manufacturing.

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Publications

Graphs with Flexible Labelings

Author(s): Georg Grasegger, Jan Legerský, Josef Schicho
Published in: Discrete & Computational Geometry, 2018, ISSN 0179-5376
DOI: 10.1007/s00454-018-0026-9

Scaffolding skeletons using spherical Voronoi diagrams: Feasibility, regularity and symmetry

Author(s): A.J. Fuentes Suárez, E. Hubert
Published in: Computer-Aided Design, Issue 102, 2018, Page(s) 83-93, ISSN 0010-4485
DOI: 10.1016/j.cad.2018.04.016

Regularity of bicyclic graphs and their powers

Author(s): Yairon Cid-Ruiz, Sepehr Jafari, Navid Nemati, Beatrice Picone
Published in: Journal of Algebra and Its Applications, 2019, Page(s) 2050057, ISSN 0219-4988
DOI: 10.1142/s0219498820500577

Optimizing B-spline surfaces for developability and paneling architectural freeform surfaces

Author(s): Konstantinos Gavriil, Alexander Schiftner, Helmut Pottmann
Published in: Computer-Aided Design, Issue 111, 2019, Page(s) 29-43, ISSN 0010-4485
DOI: 10.1016/j.cad.2019.01.006

Multiplicity of the saturated special fiber ring of height two perfect ideals

Author(s): Yairon Cid-Ruiz
Published in: Proceedings of the American Mathematical Society, Issue 148/1, 2020, Page(s) 59-70, ISSN 0002-9939
DOI: 10.1090/proc/14693

Bounding the degrees of a minimal μ-basis for a rational surface parametrization

Author(s): Yairon Cid-Ruiz
Published in: Journal of Symbolic Computation, Issue 95, 2019, Page(s) 134-150, ISSN 0747-7171
DOI: 10.1016/j.jsc.2019.02.003

Curved optimal delaunay triangulation

Author(s): Leman Feng, Pierre Alliez, Laurent Busé, Hervé Delingette, Mathieu Desbrun
Published in: ACM Transactions on Graphics, Issue 37/4, 2018, Page(s) 1-16, ISSN 0730-0301
DOI: 10.1145/3197517.3201358

Anisotropic convolution surfaces

Author(s): Alvaro Javier Fuentes Suarez, Evelyne Hubert, Cedric Zanni
Published in: Computers & Graphics, Issue 82, 2019, Page(s) 106-116, ISSN 0097-8493
DOI: 10.1016/j.cag.2019.05.018

Implicit representations of high-codimension varieties

Author(s): Ioannis Z. Emiris, Christos Konaxis, Clément Laroche
Published in: Computer Aided Geometric Design, Issue 74, 2019, Page(s) 101764, ISSN 0167-8396
DOI: 10.1016/j.cagd.2019.07.003

On the maximal number of real embeddings of minimally rigid graphs in R 2 , R

Author(s): Evangelos Bartzos, Ioannis Z. Emiris, Jan Legerský, Elias Tsigaridas
Published in: Journal of Symbolic Computation, 2019, ISSN 0747-7171
DOI: 10.1016/j.jsc.2019.10.015

Graphs with flexible labelings allowing injective realizations

Author(s): Georg Grasegger, Jan Legerský, Josef Schicho
Published in: Discrete Mathematics, 2019, Page(s) 111713, ISSN 0012-365X
DOI: 10.1016/j.disc.2019.111713

Implicitizing rational curves by the method of moving quadrics

Author(s): Laurent Busé, Clément Laroche, Fatmanur Yıldırım
Published in: Computer-Aided Design, Issue 114, 2019, Page(s) 101-111, ISSN 0010-4485
DOI: 10.1016/j.cad.2019.05.019

The Rees algebra of parametric curves via liftings

Author(s): Teresa Cortadellas Benítez, David A. Cox, Carlos D'Andrea
Published in: Journal of Pure and Applied Algebra, Issue 224/2, 2020, Page(s) 869-893, ISSN 0022-4049
DOI: 10.1016/j.jpaa.2019.06.015

Transfinite mean value interpolation over polygons

Author(s): Michael S. Floater, Francesco Patrizi
Published in: Numerical Algorithms, 2018, ISSN 1017-1398
DOI: 10.1007/s11075-019-00849-w

Void Filling of Digital Elevation Models With Deep Generative Models

Author(s): Konstantinos Gavriil, Georg Muntingh, Oliver J. D. Barrowclough
Published in: IEEE Geoscience and Remote Sensing Letters, Issue 16/10, 2019, Page(s) 1645-1649, ISSN 1545-598X
DOI: 10.1109/LGRS.2019.2902222

Linear dependence of bivariate Minimal Support and Locally Refined B-splines over LR-meshes

Author(s): Francesco Patrizi, Tor Dokken
Published in: Computer Aided Geometric Design, Issue 77, 2020, Page(s) 101803, ISSN 0167-8396
DOI: 10.1016/j.cagd.2019.101803

G 1 -smooth splines on quad meshes with 4-split macro-patch elements

Author(s): Ahmed Blidia, Bernard Mourrain, Nelly Villamizar
Published in: Computer Aided Geometric Design, Issue 52-53, 2017, Page(s) 106-125, ISSN 0167-8396
DOI: 10.1016/j.cagd.2017.03.003

A T-splines-based parametric modeller for computer-aided ship design

Author(s): T. Katsoulis, X. Wang, P.D. Kaklis
Published in: Ocean Engineering, Issue 191, 2019, Page(s) 106433, ISSN 0029-8018
DOI: 10.1016/j.oceaneng.2019.106433

Geometrically smooth spline bases for data fitting and simulation

Author(s): Ahmed Blidia, Bernard Mourrain, Gang Xu
Published in: Computer Aided Geometric Design, Issue 78, 2020, Page(s) 101814, ISSN 0167-8396
DOI: 10.1016/j.cagd.2020.101814

Discretizations of Surfaces with Constant Ratio of Principal Curvatures

Author(s): Michael R. Jimenez, Christian Müller, Helmut Pottmann
Published in: Discrete & Computational Geometry, 2019, ISSN 0179-5376
DOI: 10.1007/s00454-019-00098-7

Scaffolding skeletons using spherical Voronoi diagrams

Author(s): A.J. Fuentes Suárez, E. Hubert
Published in: Electronic Notes in Discrete Mathematics, Issue 62, 2017, Page(s) 45-50, ISSN 1571-0653
DOI: 10.1016/j.endm.2017.10.009

A D-module approach on the equations of the Rees algebra

Author(s): Yairon Cid Ruiz
Published in: J. Commut. Algebra, 2019

Regularity and Gröbner bases of the Rees algebra of edge ideals of bipartite graphs

Author(s): Yairon Cid-Ruiz
Published in: LE MATEMATICHE, Issue Vol. LXXIII (2018) – Fasc. II, 2018, Page(s) pp. 279–296
DOI: 10.4418/2018.73.2.4

Degree and birationality of multi-graded rational maps

Author(s): Busé , Laurent; Cid-Ruiz , Yairon; D 'andrea , Carlos
Published in: Proc. Lond. Math. Soc. To appear, 2018

Minimal solutions of the rational interpolation problem

Author(s): Benitez, Teresa Cortadellas; D'Andrea, Carlos; Montoro, Eulalia
Published in: Revista de la Unión Matemática Argentina, 2018

Classification of motions of the 3-connected Harary graph on 7 vertices

Author(s): Grasegger, Georg; Legerský, Jan; Schicho, Josef
Published in: Issue 11, 2019
DOI: 10.5281/zenodo.3561921

Degree of rational maps via specialization

Author(s): Cid-Ruiz, Yairon; Simis, Aron
Published in: 2019

Fibers of multi-graded rational maps and orthogonal projection onto rational surfaces

Author(s): Botbol, Nicolás; Busé, Laurent; Chardin, Marc; Yildirim, Fatmanur
Published in: https://hal.inria.fr/hal-02112357, 2019

Reverse engineering of CAD models via clustering and approximate implicitization

Author(s): Raffo, Andrea; Barrowclough, Oliver J. D.; Muntingh, Georg
Published in: 2018

Weighted Quasi Interpolant Spline Approximation of 3D point clouds via local refinement

Author(s): Raffo, Andrea; Biasotti, Silvia
Published in: 2019

Weighted Quasi Interpolant Spline Approximations: Properties and Applications

Author(s): A. Raffo, S. Biasotti
Published in: 2019

Adaptive refinement with locally linearly independent LR B-splines: Theory and Applications

Author(s): F. Patrizi, C. Manni, F. Pelosi, H. Speleers
Published in: 2019

On the existence of paradoxical motions of generically rigid graphs on the sphere

Author(s): M. Gallet, G. Grasegger, J. Legerský, J. Schicho.
Published in: 2019

Interpolation of syzygies for implicit matrix representations

Author(s): Emiris, Ioannis; Gavriil, Konstantinos; Konaxis, Christos
Published in: https://hal.inria.fr/hal-01421866, Issue 1, 2017

Wave-Resistance Computation via CFD and IGA-BEM Solvers: A Comparative Study

Author(s): X. Wang, S. Chouliaras, P. Kaklis, A-A. Ginnis, C. Politis, K. Kostas
Published in: Proceedings of the 27th International Ocean & Polar Engineering Conference, Issue 4, 2017
DOI: 10.5281/zenodo.1169033

Convolution Surfaces with Varying Radius: Formulae for Skeletons Made of Arcs of Circles and Line Segments

Author(s): Alvaro Javier Fuentes Suárez, Evelyne Hubert
Published in: Research in Shape Analysis: WiSH2, Sirince, Turkey, June 2016, 2018, Page(s) 37-60
DOI: 10.1007/978-3-319-77066-6_3

On the Maximal Number of Real Embeddings of Spatial Minimally Rigid Graphs

Author(s): Evangelos Bartzos, Ioannis Z. Emiris, Jan Legerský, Elias Tsigaridas
Published in: Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '18, 2018, Page(s) 55-62
DOI: 10.1145/3208976.3208994

Animated Motions of Exceptional Flexible Instances of Generically Rigid Graphs

Author(s): Grasegger, Georg; Legerský, Jan; Schicho, Josef
Published in: BridgesLinz 2019 Conference Proceedings, Issue 11, 2019
DOI: 10.5281/zenodo.3518805

Matrix Representations by Means of Interpolation

Author(s): Ioannis Z. Emiris, Christos Konaxis, Ilias S. Kotsireas, Clément Laroche
Published in: Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17, 2017, Page(s) 149-156
DOI: 10.1145/3087604.3087629

Modeling shapes with skeletons: scaffolds & anisotropic convolution

Author(s): Fuentes Suárez, Alvaro Javier
Published in: Mathematics [math]. Université Côte D'Azur, 2019. English, 2019