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Modeling the mechanics of fluid in complex scenes is vital to applications in design, graphics, and robotics. Learning-based methods provide fast and differentiable fluid simulators, however most prior work is unable to accurately model how…
In many covering settings, it is natural to consider the presence both of elements that we seek to include and of elements that we seek to avoid. This paper introduces a novel combinatorial problem formalizing this tradeoff: from a…
Surface metrology is the area of engineering concerned with the study of geometric variation in surfaces. This paper explores the potential for modern techniques from spatial statistics to act as generative models for geometric variation in…
We study low-dimensional problems in topology and geometry via a study of contact and Cauchy-Riemann ($CR$) structures. A contact structure is called spherical if it admits a compatible spherical $CR$ structure. We will talk about spherical…
Finding correspondences between 3D deformable shapes is an important and long-standing problem in geometry processing, computer vision, graphics, and beyond. While various shape matching datasets exist, they are mostly static or limited in…
Topological materials are at the forefront of quantum materials research, offering tremendous potential for next-generation energy and information devices. However, current investigation of these materials remains largely focused on…
Robotic grinding is widely used for shaping workpieces in manufacturing, but it remains difficult to automate this process efficiently. In particular, efficiently grinding workpieces of different shapes and material hardness is challenging…
Engineering wear models are generally empirical and lack connections to the physical processes of debris generation at the nanoscale to microscale. Here, we thus analyze wear particle formation for sliding interfaces in dry contact with…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Defined mathematically as critical points of surface area subject to a volume constraint, constant mean curvatures (CMC) surfaces are idealizations of interfaces occurring between two immiscible fluids. Their behavior elucidates phenomena…
In this paper, we introduce two notions on a surface in a contact manifold. The first one is called degree of transversality (DOT) which measures the transversality between the tangent spaces of a surface and the contact planes. The second…
The sense of touch is fundamental to human dexterity. When mimicked in robotic touch, particularly by use of soft optical tactile sensors, it suffers from distortion due to motion-dependent shear. This complicates tactile tasks like shape…
A topology optimization approach for designing large deformation contact-aided shape morphing compliant mechanisms is presented. Such mechanisms can be used in varying operating conditions. Design domains are described by regular hexagonal…
Let $M$ be a 3-manifold. Every knotted (embedded) surface in $M \times \R$ can be moved via an ambient isotopy in such a way that its projection into $M$ is a generic surface. A surface is generic if every point on it is either a regular,…
The contact between rough surfaces with adhesion is an extremely difficult problem, and the approximation of the DMT theory (to neglect deformations due to attractive forces), originally developed for spherical contact of very small radius,…
Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…
Inspired by recent advances in the chromosome capture techniques, a method is proposed to study the structural organization of systems of polymers rings with topological constraints.To this purpose, the system is divided into compartments…
Augmented Reality (AR) is becoming mobile. Mobile devices have many constraints but also rich new features that traditional desktop computers do not have. There are several survey papers on AR, but none is dedicated to Mobile Augmented…
Attaining animal-like legged locomotion on rough outdoor terrain with sparse foothold affordances -a primary use-case for legs vs other forms of locomotion- is a largely open problem. New advancements in control and perception have enabled…
The rapid development of 3D acquisition technology has made it possible to obtain point clouds of real-world terrains. However, due to limitations in sensor acquisition technology or specific requirements, point clouds often contain defects…