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Discrete Geodesic Nets for Modeling Developable Surfaces [article]

Michael Rabinovich, Tim Hoffmann, Olga Sorkine-Hornung
2017 arXiv   pre-print
We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints.  ...  The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be parameterized through orthogonal geodesics.  ...  ACKNOWLEDGMENTS The authors would like to thank Noam Aigerman, Mario Botsch, Oliver Glauser, Roi Poranne, Katja Wolff, Christian Schüller, Jan Wezel and Hantao Zhao for illuminating discussions and help  ... 
arXiv:1707.08360v1 fatcat:xzq3xvkc6jho3od452am57v63e

Voss Surfaces: A Design Space for Geodesic Gridshells

Nicolas Montagne, Cyril Douthe, Xavier Tellier, Corentin Fivet, Olivier Baverel
2020 Journal of the International Association for Shell and Spatial Structures  
In this paper, the design of a special family of structures, called geodesic shells, is addressed using Voss nets, a family of discrete surfaces.  ...  These advantageous constructive properties arise from the existence of a conjugate network of geodesic curves on the underlying smooth surface.  ...  Hauswirth for the enlightening advices in differential geometry.  ... 
doi:10.20898/j.iass.2020.008 fatcat:tfis27bqfvdyndm2aqf7fm4m7e

Paper strips driven design: Application on doubly curved surfaces

Aleksandar Cucakovic, Biljana Jovic, Milos Tripkovic
2017 FME Transaction  
Results are addressing possibilities of achieving an overall smooth surface and developing a model for the generation of curvature continuous surfaces composed of paper strip surfaces, as well as generating  ...  A developable surface has zero Gaussian curvature at all points, while a non-developable surface has non-zero Gaussian curvature at least in some region.  ...  ACKNOWLEDGMENT Authors are supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, Project No. TP 36008.  ... 
doi:10.5937/fmet1702251c fatcat:i4ageemiinhpzegcso36oib5we

Shape approximation by developable wrapping

Alexandra Ion, Michael Rabinovich, Philipp Herholz, Olga Sorkine-Hornung
2020 ACM Transactions on Graphics  
ACKNOWLEDGMENTS We would like to thank David Lindlbauer for feedback, support and help with paper model fabrication and video production.  ...  We use the model of discrete orthogonal geodesic nets (DOGs) [Rabinovich et al. 2018a ], as they allow for modeling of developable surfaces without rulings.  ...  At the center of our work is an algorithm that wraps a given 3D input surface with multiple developable patches, each modeled as a discrete orthogonal geodesic net.  ... 
doi:10.1145/3414685.3417835 fatcat:rspupdl6xrcy3lsvplfb3gteei

Quad-mesh based isometric mappings and developable surfaces

Caigui Jiang, Cheng Wang, Florian Rist, Johannes Wallner, Helmut Pottmann
2020 ACM Transactions on Graphics  
Design with developables in freeform architecture. We propose a simple approach to isometric mappings between quad meshes, which immediately leads to a way to model developable surfaces.  ...  consisting of developable spline surfaces.  ...  Quad-mesh based isometric mappings and developable surfaces • 1:13 Fig. 26 . Isometric deformation.  ... 
doi:10.1145/3386569.3392430 fatcat:qnszp4566janjme5lyj5pe64te

Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces [article]

Floor Verhoeven, Amir Vaxman, Tim Hoffmann, Olga Sorkine-Hornung
2021 arXiv   pre-print
Other representations of developable surfaces, such as arbitrary triangle or quad meshes, are more suitable for interactive freeform modeling, but generally have non-planar faces or are not aligned to  ...  Our method leverages the modeling flexibility of non-ruling based representations of developable surfaces, while still obtaining developable, curvature aligned PQ-strip meshes.  ...  ACKNOWLEDGMENTS The authors would like to thank Michael Rabinovich and Helmut Pottmann for illuminating discussions.  ... 
arXiv:2103.00239v2 fatcat:7l45gs5k5bezhoxpoupenfrcfa

An effective third-order local fitting patch and its application

Zhong Li, Brian Barsky, Xiaogang Jin
2009 2009 IEEE International Conference on Shape Modeling and Applications  
Furthermore, we define the principal geodesic torsion of each vertex on the mesh model and estimate it through this local fitting patch.  ...  In the end of this paper, we apply the third-order fitting patch for the mesh smoothing and hole-filling which can get the satisfactory results.  ...  ACKNOWLEDGEMENTS The authors gratefully appreciate the anonymous referees for the useful comments and suggestions which improved this paper considerably.  ... 
doi:10.1109/smi.2009.5170157 dblp:conf/smi/LiBJ09 fatcat:gzz332vvxvb57jwj3y45tt6d24

Caging complex objects with geodesic balls

Dmitry Zarubin, Florian T. Pokorny, Marc Toussaint, Danica Kragic
2013 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems  
The first uses winding angles measuring how much a geodesic ball on the surface winds around a dominant axis, while the second explores using the total discrete Gaussian curvature of a geodesic ball to  ...  We introduce the idea of using geodesic balls on the object's surface in order to approximate the maximal contact surface between a robotic hand and an object.  ...  We model the maximal contact surface between the robot's hand and a given closed surface S as a geodesic ball B r (p) of radius r and centred at a point p ∈ S.  ... 
doi:10.1109/iros.2013.6696781 dblp:conf/iros/ZarubinPTK13 fatcat:j7az5vzvyffdlagtvytn2tfxfa

Freeform surfaces from single curved panels

Helmut Pottmann, Alexander Schiftner, Pengbo Bo, Heinz Schmiedhofer, Wenping Wang, Niccolo Baldassini, Johannes Wallner
2008 ACM SIGGRAPH 2008 papers on - SIGGRAPH '08  
Together with geodesic models and cylindrical models they offer a rich source of solutions for surface panelization problems.  ...  The basic entity we are working with is the developable strip model. It is the semi-discrete equivalent of a quad mesh with planar faces, or a conjugate parametrization of a smooth surface.  ...  We want to thank Benjamin Schneider for his help in preparing illustrations.  ... 
doi:10.1145/1399504.1360675 fatcat:ye2fpwiowzctrhbywfcczoc2pe

Freeform surfaces from single curved panels

Helmut Pottmann, Alexander Schiftner, Pengbo Bo, Heinz Schmiedhofer, Wenping Wang, Niccolo Baldassini, Johannes Wallner
2008 ACM Transactions on Graphics  
Together with geodesic models and cylindrical models they offer a rich source of solutions for surface panelization problems.  ...  The basic entity we are working with is the developable strip model. It is the semi-discrete equivalent of a quad mesh with planar faces, or a conjugate parametrization of a smooth surface.  ...  We want to thank Benjamin Schneider for his help in preparing illustrations.  ... 
doi:10.1145/1360612.1360675 fatcat:ghe4q7loffbgrjbw7rpr3qmz6e

A Computational Model of Multidimensional Shape

Xiuwen Liu, Yonggang Shi, Ivo Dinov, Washington Mio
2010 International Journal of Computer Vision  
We develop algorithms to calculate geodesics and geodesic distances, as well as tools to quantify local shape similarities and contrasts, thus obtaining a formulation that accounts for regional differences  ...  We develop a computational model of shape that extends existing Riemannian models of curves to multidimensional objects of general topological type.  ...  For example, it integrates discrete models developed over different meshes as approximations to a common model and it might help to interpret our shape metrics as a step towards a new approach to registration  ... 
doi:10.1007/s11263-010-0323-0 pmid:21057668 pmcid:PMC2971560 fatcat:f63wog2h6zdbfoi7arotwmywem

GeoNet: Deep Geodesic Networks for Point Cloud Analysis [article]

Tong He, Haibin Huang, Li Yi, Yuqian Zhou, Chihao Wu, Jue Wang, Stefano Soatto
2019 arXiv   pre-print
Surface-based geodesic topology provides strong cues for object semantic analysis and geometric modeling. However, such connectivity information is lost in point clouds.  ...  Thus we introduce GeoNet, the first deep learning architecture trained to model the intrinsic structure of surfaces represented as point clouds.  ...  The proposed geodesic fusion methods, called PU-Net fusion (PUF) and PointNet++ fusion (POF), integrate GeoNet with the baseline or backbone models to conduct geodesic-aware point set analysis.  ... 
arXiv:1901.00680v1 fatcat:klcyeywb4vhdhjuvmxsfpacsk4

Wire mesh design

Akash Garg, Andrew O. Sageman-Furnas, Bailin Deng, Yonghao Yue, Eitan Grinspun, Mark Pauly, Max Wardetzky
2014 ACM Transactions on Graphics  
While the theory of Chebyshev nets suggests a highly constrained design space, we show that allowing controlled deviations from the underlying surface provides a rich shape space for design exploration  ...  To facilitate shape exploration, we map material properties of wire meshes to the geometric model of Chebyshev nets. This abstraction is exploited to build an efficient optimization scheme.  ...  Acknowledgements We thank Cosmo Wenman for providing the digital models of the torsos from their physical counterparts in The Louvre; Zohreh Sasanian for helping with the fabrication process; Keenan Crane  ... 
doi:10.1145/2601097.2601106 fatcat:bwfm3mqp6jdbfkssgzuqe74644

Algorithmic design of self-folding polyhedra

S. Pandey, M. Ewing, A. Kunas, N. Nguyen, D. H. Gracias, G. Menon
2011 Proceedings of the National Academy of Sciences of the United States of America  
We also find that shortest paths between 2D nets and the 3D polyhedron in a discrete model of the configuration space of foldings are a useful idealization of experimentally observed folding pathways.  ...  In order to realize these ambitions, it is necessary to develop model experimental systems and theoretical analyses that make precise the analogies between natural and synthetic self-assembly.  ...  Shortest paths between 2D nets and the 3D polyhedron are called geodesics. The discrete configuration space and geodesics for the cube are illustrated in Fig. 7 .  ... 
doi:10.1073/pnas.1110857108 pmid:22139373 pmcid:PMC3250184 fatcat:ouxpzcmakrgvjgr53aszyx4gka

Front Matter

2021 Computer graphics forum (Print)  
Bradley studied architecture at Pratt Institute in Brooklyn, New York, and has been developing computational design tools for advanced manufacturing for the last 10-plus years.  ...  This talk describes the new design problems that engineers today face and the software we have developed for solving them.  ...  belief nets.  ... 
doi:10.1111/cgf.14376 fatcat:chf2craanrfhzdhgfnc4nh5ohi
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