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A flat sheet programmed with a planar pattern of spontaneous shape change will morph into a curved surface. Such metric mechanics is seen in growing biological sheets, and may be engineered in actuating soft matter sheets such as…
Recently, the mapping approach to surface hopping (MASH) was proposed as a method to simulate the non-adiabatic dynamics of two-level systems. It was shown that the method possesses many desirable qualities, both theoretically and through…
We consider an open, bounded, simply connected (Lipschitz) domain in $\mathbb{R}^d$, which contains a closed polyhedral surface or polygonal contour, referred to as the interface. From this interface, forces are exerted in the normal…
Accurate 3D reconstruction using multi-camera RGB-D systems critically depends on precise extrinsic calibration to achieve proper alignment between captured views. In this paper, we introduce an iterative extrinsic calibration method that…
Recent developments for mathematical modeling and numerical simulation of biomolecular systems raise new demands for qualified, stable, and efficient surface meshing, especially in implicit-solvent modeling. In our former work, we have…
In this paper, we propose a parallel and scalable approach for geodesic distance computation on triangle meshes. Our key observation is that the recovery of geodesic distance with the heat method from [Crane et al. 2013] can be reformulated…
Precise 3D measurements of rigid surfaces are desired in many fields of application like quality control or surgery. Often, views from all around the object have to be acquired for a full 3D description of the object surface. We present a…
The integration of Transparent Displays (TD) in various applications, such as Heads-Up Displays (HUDs) in vehicles, is a burgeoning field, poised to revolutionize user experiences. However, this innovation brings forth significant…
We propose a new two-dimensional meshing algorithm called PINW able to generate meshes that accurately approximate the distance between any two domain points by paths composed only of cell edges. This technique is based on an extension of…
Eye tracking is a key technology for human-computer interaction, particularly crucial in augmented reality (AR) and virtual reality (VR) systems. We propose a novel eye-tracking approach based on incorporating passive eye-tracking modules…
Following the tracking-by-attention paradigm, this paper introduces an object-centric, transformer-based framework for tracking in 3D. Traditional model-based tracking approaches incorporate the geometric effect of object- and ego motion…
This paper proposes improvements to the physically-based surface triangulation method, bubble meshing. The method simulates physical bubbles to automatically generate mesh vertices, resulting in high-quality Delaunay triangles. Despite its…
This paper presents a real-time 3D mapping framework based on global matching cost minimization and LiDAR-IMU tight coupling. The proposed framework comprises a preprocessing module and three estimation modules: odometry estimation, local…
This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry,…
Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh…
This research presents a novel method of determining relative bearing and elevation measurements, to a remote signal, that is suitable for implementation on small embedded systems - potentially in a GPS denied environment. This is an…
For mobile robots to operate autonomously in general environments, perception is required in the form of a dense metric map. For this purpose, we present the stochastic triangular mesh (STM) mapping technique: a 2.5-D representation of the…
In many applications, maintaining a consistent dense map of the environment is key to enabling robotic platforms to perform higher level decision making. Several works have addressed the challenge of creating precise dense 3D maps from…
In this paper we present an immersed weak Galerkin method for solving second-order elliptic interface problems on polygonal meshes, where the meshes do not need to be aligned with the interface. The discrete space consists of constants on…
Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup…