Omri Azencot and Rongjie Lai. SGP 2021 / Computer Graphics Forum. Abstract We propose a method to simultaneously compute scalar basis functions with an associated functional map for a given pair of triangle meshes. Unlike previous techniques that put emphasis on smoothness with respect to the Laplace–Beltrami operator and thus favor low-frequency eigenfunctions, we aim for a basis that allows for better feature matching. This change of perspective introduces many degrees of freedom into the problem allowing to better exploit non-smooth descriptors. To effectively search in this high-dimensional space of solutions, we incorporate into our minimization state-of-the-art regularizers. We solve…

Omri Azencot, Anastasia Dubrovina and Leonidas Guibas. SGP 2019 / Computer Graphics Forum. Abstract We propose a new method for computing accurate point-to-point mappings between a pair of triangle meshes given imperfect initial correspondences. Unlike the majority of existing techniques, we optimize for a map while leveraging information from the inverse map, yielding results which are highly consistent with respect to composition of mappings. Remarkably, our method considers only a linear number of candidate points on the target shape, allowing us to work directly with high resolution meshes, and to avoid a delicate and possibly error-prone up-sampling procedure. Key to…

Omri Azencot, Orestis Vantzos and Mirela Ben-Chen. SGP 2018 / Computer Graphics Forum. Abstract We present a new structure-preserving numerical scheme for solving the Euler–Poincaré Differential (EPDiff) equation on arbitrary triangle meshes. Unlike existing techniques, our method solves the difficult non-linear EPDiff equation by constructing energy preserving, yet fully explicit, update rules. Our approach uses standard differential operators on triangle meshes, allowing for a simple and efficient implementation. Key to the structure-preserving features that our method exhibits is a novel numerical splitting scheme. Namely, we break the integration into three steps which rely on linear solves with a fixed sparse…

Omri Azencot, Orestis Vantzos and Mirela Ben-Chen. SGP 2016 / Computer Graphics Forum. Abstract A tangent vector field on a surface is the generator of a smooth family of maps from the surface to itself, known as the flow. Given a scalar function on the surface, it can be transported, or advected, by composing it with a vector field’s flow. Such transport is exhibited by many physical phenomena, e.g., in fluid dynamics. In this paper, we are interested in the inverse problem: given source and target functions, compute a vector field whose flow advects the source to the target. We…

Omri Azencot*, Steffen Weißmann*, Maks Ovsjanikov, Max Wardetzky and Mirela Ben-Chen. SGP 2014 / Computer Graphics Forum. Abstract Fluid simulation plays a key role in various domains of science including computer graphics. While most existing work addresses fluids on bounded Euclidean domains, we consider the problem of simulating the behavior of an incompressible fluid on a curved surface represented as an unstructured triangle mesh. Unlike the commonly used Eulerian description of the fluid using its time-varying velocity field, we propose to model fluids using their vorticity, i.e., by a (time varying) scalar function on the surface. During each time step,…

Omri Azencot, Mirela Ben-Chen, Frédéric Chazal and Maks Ovsjanikov. SGP 2013 / Computer Graphics Forum. Abstract In this paper, we introduce a novel coordinate-free method for manipulating and analyzing vector fields on discrete surfaces. Unlike the commonly used representations of a vector field as an assignment of vectors to the faces of the mesh, or as real values on edges, we argue that vector fields can also be naturally viewed as operators whose domain and range are functions defined on the mesh. Although this point of view is common in differential geometry it has so far not been adopted in geometry processing applications. We…