Related papers: Local and Global Analysis of Parametric Solid Swee…
This paper proposes a robust algorithmic and computational framework to address the problem of modeling the volume obtained by sweeping a solid along a trajectory of rigid motions. The boundary representation (simply brep) of the input…
This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family $h$ of rigid motions. Our extension…
Sweeping is a powerful and versatile method of designing objects. Boundary of volumes (henceforth envelope) obtained by sweeping solids have been extensively investigated in the past, though, obtaining an accurate parametrization of the…
Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…
Shape abstraction is an important task for simplifying complex geometric structures while retaining essential features. Sweep surfaces, commonly found in human-made objects, aid in this process by effectively capturing and representing…
Borrowing elementary ideas from solid mechanics and differential geometry, this presentation shows that the volume swept by a regular solid undergoing a wide class of volume-preserving deformations induces a rather natural metric structure…
Many natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of…
This work presents a robust and efficient sharp interface immersed boundary (IBM) framework, which is applicable for all-speed flow regimes and is capable of handling arbitrarily complex bodies (stationary or moving). The work deploys an…
The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
A method for quantitative analysis of local pattern strength and defects in surface self-assembly imaging is presented and applied to images of stripe and hexagonal ordered domains. The presented method uses "shapelet" functions which were…
Perception research provides strong evidence in favor of part based representation of shapes in human visual system. Despite considerable differences among different theories in terms of how part boundaries are found, there is substantial…
We contribute a dense SLAM system that takes a live stream of depth images as input and reconstructs non-rigid deforming scenes in real time, without templates or prior models. In contrast to existing approaches, we do not maintain any…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
Sampling theory has traditionally drawn tools from functional and complex analysis. Past successes, such as the Shannon-Nyquist theorem and recent advances in frame theory, have relied heavily on the application of geometry and analysis.…
We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…
In this work a novel method for the analysis with trimmed CAD surfaces is presented. The method involves an additional mapping step and the attraction stems from its sim- plicity and ease of implementation into existing Finite Element (FEM)…
The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree…
In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…