Wardetzky, Max

[["dc.bibliographiccitation.artnumber","1"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","ACM Transactions on Graphics"],["dc.bibliographiccitation.volume","27"],["dc.contributor.author","Bergou, Miklós"],["dc.contributor.author","Wardetzky, Max"],["dc.contributor.author","Robinson, Stephen"],["dc.contributor.author","Audoly, Basile"],["dc.contributor.author","Grinspun, Eitan"],["dc.date.accessioned","2017-09-07T11:54:09Z"],["dc.date.available","2017-09-07T11:54:09Z"],["dc.date.issued","2008"],["dc.description.abstract","We present a discrete treatment of adapted framed curves, parallel transport, and holonomy, thus establishing the language for a discrete geometric model of thin flexible rods with arbitrary cross section and undeformed configuration. Our approach differs from existing simulation techniques in the graphics and mechanics literature both in the kinematic description---we represent the material frame by its angular deviation from the natural Bishop frame---as well as in the dynamical treatment---we treat the centerline as dynamic and the material frame as quasistatic. Additionally, we describe a manifold projection method for coupling rods to rigid-bodies and simultaneously enforcing rod inextensibility. The use of quasistatics and constraints provides an efficient treatment for stiff twisting and stretching modes; at the same time, we retain the dynamic bending of the centerline and accurately reproduce the coupling between bending and twisting modes. We validate the discrete rod model via quantitative buckling, stability, and coupled-mode experiments, and via qualitative knot-tying comparisons."],["dc.identifier.doi","10.1145/1360612.1360662"],["dc.identifier.gro","3146528"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4312"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Association for Computing Machinery (ACM)"],["dc.relation.issn","0730-0301"],["dc.title","Discrete elastic rods"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","50"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","ACM Transactions on Graphics"],["dc.bibliographiccitation.volume","26"],["dc.contributor.author","Bergou, Miklós"],["dc.contributor.author","Mathur, Saurabh"],["dc.contributor.author","Wardetzky, Max"],["dc.contributor.author","Grinspun, Eitan"],["dc.date.accessioned","2017-09-07T11:54:10Z"],["dc.date.available","2017-09-07T11:54:10Z"],["dc.date.issued","2007"],["dc.description.abstract","We combine the often opposing forces of artistic freedom and mathematical determinism to enrich a given animation or simulation of a surface with physically based detail. We present a process called tracking, which takes as input a rough animation or simulation and enhances it with physically simulated detail. Building on the foundation of constrained Lagrangian mechanics, we propose weak-form constraints for tracking the input motion. This method allows the artist to choose where to add details such as characteristic wrinkles and folds of various thin shell materials and dynamical effects of physical forces. We demonstrate multiple applications ranging from enhancing an artist's animated character to guiding a simulated inanimate object."],["dc.identifier.doi","10.1145/1276377.1276439"],["dc.identifier.gro","3146530"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4314"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Association for Computing Machinery (ACM)"],["dc.relation.issn","0730-0301"],["dc.title","TRACKS: toward directable thin shells"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.contributor.author","Bergou, Miklós"],["dc.contributor.author","Wardetzky, Max"],["dc.contributor.author","Harmon, David"],["dc.contributor.author","Zorin, Denis"],["dc.contributor.author","Grinspun, Eitan"],["dc.contributor.editor","Sheffer, Alla"],["dc.contributor.editor","Polthier, Konrad"],["dc.date.accessioned","2017-09-07T11:54:19Z"],["dc.date.available","2017-09-07T11:54:19Z"],["dc.date.issued","2006"],["dc.description.abstract","Relating the intrinsic Laplacian to the mean curvature normal, we arrive at a model for bending of inextensible surfaces. Due to its constant Hessian, our isometric bending model reduces cloth simulation times up to three-fold."],["dc.identifier.doi","10.2312/SGP/SGP06/227-230"],["dc.identifier.gro","3146535"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4319"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","The Eurographics Association"],["dc.relation.isbn","3-905673-24-X"],["dc.relation.ispartof","Symposium on Geometry Processing"],["dc.relation.issn","1727-8384"],["dc.title","A Quadratic Bending Model for Inextensible Surfaces"],["dc.type","conference_paper"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","102"],["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","ACM Transactions on Graphics"],["dc.bibliographiccitation.lastpage","10"],["dc.bibliographiccitation.volume","30"],["dc.contributor.author","Alexa, Marc"],["dc.contributor.author","Wardetzky, Max"],["dc.date.accessioned","2017-09-07T11:54:13Z"],["dc.date.available","2017-09-07T11:54:13Z"],["dc.date.issued","2011"],["dc.description.abstract","While the theory and applications of discrete Laplacians on triangulated surfaces are well developed, far less is known about the general polygonal case. We present here a principled approach for constructing geometric discrete Laplacians on surfaces with arbitrary polygonal faces, encompassing non-planar and non-convex polygons. Our construction is guided by closely mimicking structural properties of the smooth Laplace--Beltrami operator. Among other features, our construction leads to an extension of the widely employed cotan formula from triangles to polygons. Besides carefully laying out theoretical aspects, we demonstrate the versatility of our approach for a variety of geometry processing applications, embarking on situations that would have been more difficult to achieve based on geometric Laplacians for simplicial meshes or purely combinatorial Laplacians for general meshes."],["dc.identifier.doi","10.1145/1964921.1964997"],["dc.identifier.gro","3146524"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4307"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.title","Discrete Laplacians on general polygonal meshes"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","90"],["dc.bibliographiccitation.issue","11"],["dc.bibliographiccitation.journal","Communications of the ACM"],["dc.bibliographiccitation.lastpage","99"],["dc.bibliographiccitation.volume","60"],["dc.contributor.author","Crane, Keenan"],["dc.contributor.author","Weischedel, Clarisse"],["dc.contributor.author","Wardetzky, Max"],["dc.date.accessioned","2020-12-10T18:37:37Z"],["dc.date.available","2020-12-10T18:37:37Z"],["dc.date.issued","2017"],["dc.identifier.doi","10.1145/3131280"],["dc.identifier.eissn","1557-7317"],["dc.identifier.issn","0001-0782"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/77038"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.title","The heat method for distance computation"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1755"],["dc.bibliographiccitation.issue","5"],["dc.bibliographiccitation.journal","Computer Graphics Forum"],["dc.bibliographiccitation.lastpage","1764"],["dc.bibliographiccitation.volume","31"],["dc.contributor.author","Heeren, Behrend"],["dc.contributor.author","Rumpf, Martin"],["dc.contributor.author","Wardetzky, Max"],["dc.contributor.author","Wirth, Benedikt"],["dc.date.accessioned","2017-09-07T11:54:12Z"],["dc.date.available","2017-09-07T11:54:12Z"],["dc.date.issued","2012"],["dc.description.abstract","Building on concepts from continuum mechanics, we offer a computational model for geodesics in the space of thin shells, with a metric that reflects viscous dissipation required to physically deform a thin shell. Different from previous work, we incorporate bending contributions into our deformation energy on top of membrane distortion terms in order to obtain a physically sound notion of distance between shells, which does not require additional smoothing. Our bending energy formulation depends on the so-called relative Weingarten map, for which we provide a discrete analogue based on principles of discrete differential geometry. Our computational results emphasize the strong impact of physical parameters on the evolution of a shell shape along a geodesic path."],["dc.identifier.doi","10.1111/j.1467-8659.2012.03180.x"],["dc.identifier.gro","3146521"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4304"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0167-7055"],["dc.title","Time-Discrete Geodesics in the Space of Shells"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","499"],["dc.bibliographiccitation.issue","8-9"],["dc.bibliographiccitation.journal","Computer Aided Geometric Design"],["dc.bibliographiccitation.lastpage","518"],["dc.bibliographiccitation.volume","24"],["dc.contributor.author","Wardetzky, Max"],["dc.contributor.author","Bergou, Miklós"],["dc.contributor.author","Harmon, David"],["dc.contributor.author","Zorin, Denis"],["dc.contributor.author","Grinspun, Eitan"],["dc.date.accessioned","2017-09-07T11:54:19Z"],["dc.date.available","2017-09-07T11:54:19Z"],["dc.date.issued","2007"],["dc.description.abstract","We present a family of discrete isometric bending models (IBMs) for triangulated surfaces in 3-space. These models are derived from an axiomatic treatment of discrete Laplace operators, using these operators to obtain linear models for discrete mean curvature from which bending energies are assembled. Under the assumption of isometric surface deformations we show that these energies are quadratic in surface positions. The corresponding linear energy gradients and constant energy Hessians constitute an efficient model for computing bending forces and their derivatives, enabling fast time-integration of cloth dynamics with a two- to three-fold net speedup over existing nonlinear methods, and near-interactive rates for Willmore smoothing of large meshes."],["dc.identifier.doi","10.1016/j.cagd.2007.07.006"],["dc.identifier.gro","3146531"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4315"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0167-8396"],["dc.title","Discrete quadratic curvature energies"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.journal","Eurographics (Computer Graphics Forum)"],["dc.contributor.author","Kälberer, Felix"],["dc.contributor.author","Polthier, Konrad"],["dc.contributor.author","Reitebuch, Ulrich"],["dc.contributor.author","Wardetzky, Max"],["dc.date.accessioned","2017-09-07T11:54:19Z"],["dc.date.available","2017-09-07T11:54:19Z"],["dc.date.issued","2005"],["dc.format.extent","469–478"],["dc.identifier.gro","3146537"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4321"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.title","FreeLence - Coding with free Valences"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","ACM Transactions on Graphics"],["dc.bibliographiccitation.lastpage","12"],["dc.bibliographiccitation.volume","33"],["dc.contributor.author","Garg, Akash"],["dc.contributor.author","Sageman-Furnas, Andrew O."],["dc.contributor.author","Deng, Bailin"],["dc.contributor.author","Yue, Yonghao"],["dc.contributor.author","Grinspun, Eitan"],["dc.contributor.author","Pauly, Mark"],["dc.contributor.author","Wardetzky, Max"],["dc.date.accessioned","2017-09-07T11:54:09Z"],["dc.date.available","2017-09-07T11:54:09Z"],["dc.date.issued","2014"],["dc.description.abstract","We present a computational approach for designing wire meshes, i.e., freeform surfaces composed of woven wires arranged in a regular grid. 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. 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. Our algorithm balances globally coupled material constraints with aesthetic and geometric design objectives that can be specified by the user in an interactive design session. In addition to sculptural art, wire meshes represent an innovative medium for industrial applications including composite materials and architectural façades. We demonstrate the effectiveness of our approach using a variety of digital and physical prototypes with a level of shape complexity unobtainable using previous methods."],["dc.identifier.doi","10.1145/2601097.2601106"],["dc.identifier.gro","3146516"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4298"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0730-0301"],["dc.title","Wire mesh design"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","J. Mech. Des"],["dc.bibliographiccitation.volume","139"],["dc.contributor.author","Bös, Friedrich"],["dc.contributor.author","Vouga, Etienne"],["dc.contributor.author","Gottesman, Omer"],["dc.contributor.author","Wardetzky, Max"],["dc.date.accessioned","2017-09-07T11:54:08Z"],["dc.date.available","2017-09-07T11:54:08Z"],["dc.date.issued","2016"],["dc.description.abstract","The art and science of folding intricate three-dimensional structures out of paper has occupied artists, designers, engineers, and mathematicians for decades, culminating in the design of deployable structures and mechanical metamaterials. Here we investigate the axial compressibility of origami cylinders, i.e., cylindrical structures folded from rectangular sheets of paper. We prove, using geometric arguments, that a general fold pattern only allows for a finite number of isometric cylindrical embeddings. Therefore, compressibility of such structures requires either stretching the material or deforming the folds. Our result considerably restricts the space of constructions that must be searched when designing new types of origami-based rigid-foldable deployable structures and metamaterials."],["dc.identifier.arxiv","1507.08472"],["dc.identifier.doi","10.1115/1.4034970"],["dc.identifier.gro","3146511"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4293"],["dc.language.iso","en"],["dc.notes.intern","Not valid abstract: The art and science of folding intricate three-dimensional structures out of paper has occupied artists, designers, engineers, and mathematicians for decades, culminating in the design of deployable structures and mechanical metamaterials. Here we investigate the axial compressibility of origami cylinders, i.e., cylindrical structures folded from rectangular sheets of paper. We prove, using geometric arguments, that a general fold pattern only allows for a finite number of \\\\.emph{isometric} cylindrical embeddings. Therefore, compressibility of such structures requires either stretching the material or deforming the folds. Our result considerably restricts the space of constructions that must be searched when designing new types of origami-based rigid-foldable deployable structures and metamaterials."],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.title","On the incompressibility of cylindrical origami patterns"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]