Related papers: Escher Tile Deformation via Closed-Form Solution

We present a novel approach for the reconstruction of dynamic geometric shapes using a single hand-held consumer-grade RGB-D sensor at real-time rates. Our method does not require a pre-defined shape template to start with and builds up the…

Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual…

The bending of bilayer plates is a mechanism which allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed herein, consists of a nonlinear fourth order…

We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…

This work presents a construction method for interlocking assemblies based on planar crystallographic symmetries. Planar crystallographic groups, also known as wallpaper groups, correspond to tessellations of the plane with a tile, called a…

We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on…

Tissue deformation recovery based on stereo endoscopic images is crucial for tool-tissue interaction analysis and benefits surgical navigation and autonomous soft tissue manipulation. Previous research suffers from the problems raised from…

Dislocation-mediated plastic deformation in ceramic materials has sparked renewed research interest due to the technological potential of dislocations. Despite the long research history of dislocations as one-dimensional lattice defects in…

We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our…

This study undertakes the mathematical modelling and numerical analysis of dislocations within the framework of differential geometry. The fundamental configurations, i.e. reference, intermediate and current configurations, are expressed as…

The process of self-morphing in curved surfaces found in nature, such as with the growth of flowers and leaves, has generated interest in the study of self-morphing bilayers, which has been used in many soft robots or switchers. However,…

We present a new isogeometric method for the discretization of the Reissner-Mindlin plate bending problem. The proposed scheme follows a recent theoretical framework that makes possible to construct a space of smooth discrete deflections…

Tomographic imaging reveals internal structures of 3D objects and is crucial for medical diagnoses. Visualizing the morphology and appearance of non-planar sparse anatomical structures that extend over multiple 2D slices in tomographic…

In this paper we present a novel approach for representing and evolving deformable active contours. The method combines piecewise regular B{\'e}zier models and curve evolution defined by local Free Form Deformation. The contour deformation…

In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…

We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of…

The algorithmic self-assembly of shapes has been considered in several models of self-assembly. For the problem of \emph{shape construction}, we consider an extended version of the Two-Handed Tile Assembly Model (2HAM), which contains…

This paper studies the mismatch removal problem, which may serve as the subsequent step of feature matching. Non-rigid deformation makes it difficult to remove mismatches because no parametric transformation can be found. To solve this…

Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent…

Spatial tactile feedback can enhance the realism of geometry exploration in virtual reality applications. Current vibrotactile approaches often face challenges with the spatial and temporal resolution needed to render different 3D…