Wardetzky, Max

[["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","247"],["dc.bibliographiccitation.issue","5"],["dc.bibliographiccitation.journal","Computer Graphics Forum"],["dc.bibliographiccitation.lastpage","256"],["dc.bibliographiccitation.volume","33"],["dc.contributor.author","Heeren, Behrend"],["dc.contributor.author","Rumpf, Martin"],["dc.contributor.author","Schröder, Peter"],["dc.contributor.author","Wardetzky, Max"],["dc.contributor.author","Wirth, Benedikt"],["dc.date.accessioned","2017-09-07T11:54:07Z"],["dc.date.available","2017-09-07T11:54:07Z"],["dc.date.issued","2014"],["dc.description.abstract","We prove both in the smooth and discrete setting that the Hessian of an elastic deformation energy results in a proper Riemannian metric on the space of shells (modulo rigid body motions). Based on this foundation we develop a time- and space-discrete geodesic calculus. In particular we show how to shoot geodesics with prescribed initial data, and we give a construction for parallel transport in shell space. This enables, for example, natural extrapolation of paths in shell space and transfer of large nonlinear deformations from one shell to another with applications in animation, geometric, and physical modeling. Finally, we examine some aspects of curvature on shell space."],["dc.identifier.doi","10.1111/cgf.12450"],["dc.identifier.gro","3146517"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4299"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Wiley-Blackwell"],["dc.relation.issn","0167-7055"],["dc.title","Exploring the Geometry of the Space of Shells"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","111"],["dc.bibliographiccitation.issue","5"],["dc.bibliographiccitation.journal","Computer Graphics Forum"],["dc.bibliographiccitation.lastpage","120"],["dc.bibliographiccitation.volume","35"],["dc.contributor.author","Heeren, Behrend"],["dc.contributor.author","Rumpf, Martin"],["dc.contributor.author","Schröder, Peter"],["dc.contributor.author","Wardetzky, Max"],["dc.contributor.author","Wirth, Benedikt"],["dc.date.accessioned","2017-09-07T11:54:08Z"],["dc.date.available","2017-09-07T11:54:08Z"],["dc.date.issued","2016"],["dc.description.abstract","Cubic splines in Euclidean space minimize the mean squared acceleration among all curves interpolating a given set of data points. We extend this observation to the Riemannian manifold of discrete shells in which the associated metric measures both bending and membrane distortion. Our generalization replaces the acceleration with the covariant derivative of the velocity. We introduce an effective time-discretization for this novel paradigm for navigating shell space. Further transferring this concept to the space of triangular surface descriptors-edge lengths, dihedral angles, and triangle areas-results in a simplified interpolation method with high computational efficiency."],["dc.identifier.doi","10.1111/cgf.12968"],["dc.identifier.gro","3146513"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4295"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0167-7055"],["dc.title","Splines in the Space of Shells"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","184"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","GAMM-Mitteilungen"],["dc.bibliographiccitation.lastpage","216"],["dc.bibliographiccitation.volume","37"],["dc.contributor.author","Rumpf, Martin"],["dc.contributor.author","Wardetzky, Max"],["dc.date.accessioned","2017-09-07T11:54:08Z"],["dc.date.available","2017-09-07T11:54:08Z"],["dc.date.issued","2014"],["dc.description.abstract","Triggered by the development of new hardware, such as laser range scanners for high resolution acquisition of complex geometric objects, new graphics processors for realtime rendering and animation of extremely detailed geometric structures, and novel rapid prototyping equipment, such as 3D printers, the processing of highly resolved complex geometries has established itself as an important area of both fundamental research and impressive applications. Concepts from image processing have been picked up and carried over to curved surfaces, physically based modeling plays a central role, and aspects of computer aided geometry design have been incorporated. This paper aims at highlighting some of these developments, with a particular focus on methods related to the mechanics of thin elastic surfaces. We provide an overview of different geometric representations ranging from polyhedral surfaces over level sets to subdivision surfaces. Furthermore, with an eye on differential-geometric concepts underlying continuum mechanics, we discuss fundamental computational tasks, such as surface flows and fairing, surface deformation and matching, physical simulations, as well as spectral and modal methods in geometry processing. Finally, beyond focusing on single shapes, we describe how spaces of shapes can be investigated using concepts from Riemannian geometry."],["dc.identifier.doi","10.1002/gamm.201410009"],["dc.identifier.gro","3146515"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4297"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0936-7195"],["dc.title","Geometry processing from an elastic perspective"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1179"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","IEEE Transactions on Visualization and Computer Graphics"],["dc.bibliographiccitation.lastpage","1192"],["dc.bibliographiccitation.volume","23"],["dc.contributor.author","Vantzos, Orestis"],["dc.contributor.author","Azencot, Omri"],["dc.contributor.author","Rumpf, Martin"],["dc.contributor.author","Ben-Chen, Mirela"],["dc.contributor.author","Wardetzky, Max"],["dc.date.accessioned","2020-12-10T18:26:23Z"],["dc.date.available","2020-12-10T18:26:23Z"],["dc.date.issued","2017"],["dc.description.abstract","The motion of a thin viscous film of fluid on a curved surface exhibits many intricate visual phenomena, which are challenging to simulate using existing techniques. A possible alternative is to use a reduced model, involving only the temporal evolution of the mass density of the film on the surface. However, in this model, the motion is governed by a fourth-order nonlinear PDE, which involves geometric quantities such as the curvature of the underlying surface, and is therefore difficult to discretize. Inspired by a recent variational formulation for this problem on smooth surfaces, we present a corresponding model for triangle meshes. We provide a discretization for the curvature and advection operators which leads to an efficient and stable numerical scheme, requires a single sparse linear solve per time step, and exactly preserves the total volume of the fluid. We validate our method by qualitatively comparing to known results from the literature, and demonstrate various intricate effects achievable by our method, such as droplet formation, evaporation, droplets interaction and viscous fingering. Finally, we extend our method to incorporate non-linear van der Waals forcing terms which stabilize the motion of the film and allow additional effects such as pearling."],["dc.identifier.doi","10.1109/TVCG.2016.2605083"],["dc.identifier.gro","3146510"],["dc.identifier.issn","1077-2626"],["dc.identifier.pmid","27608468"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/76067"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.title","Functional Thin Films on Surfaces"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]