Related papers: Efficient Shape Formation by 3D Hybrid Programmabl…
The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly…
Implicit functions represented as deep learning approximations are powerful for reconstructing 3D surfaces. However, they can only produce static surfaces that are not controllable, which provides limited ability to modify the resulting…
This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed structures can be realised in a two-step process. One first…
Deep Implicit Function (DIF) has gained popularity as an efficient 3D shape representation. To capture geometry details, current methods usually learn DIF using local latent codes, which discretize the space into a regular 3D grid (or…
Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…
Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
Materials exhibit geometric structures across mesoscopic to microscopic scales, influencing macroscale properties such as appearance, mechanical strength, and thermal behavior. Capturing and modeling these multiscale structures is…
We present Image Sculpting, a new framework for editing 2D images by incorporating tools from 3D geometry and graphics. This approach differs markedly from existing methods, which are confined to 2D spaces and typically rely on textual…
The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light…
Conventional topological insulators exhibit exotic gapless edge or surface states, as a result of non-trivial bulk topological properties. In periodically-driven systems the bulk-boundary correspondence is fundamentally modified and…
This paper proposes a distributed algorithm for a set of tiny unit disc shaped robot to form a straight line. The robots are homoge- neous, autonomous, anonymous. They observe their surrounding up to a certain distance, compute destinations…
This paper presents a new boundary integral equation (BIE) method for simulating particulate and multiphase flows through periodic channels of arbitrary smooth shape in two dimensions. The authors consider a particular system---multiple…
We introduce a method to analyze and modify a shape to make it manufacturable for a given additive manufacturing (AM) process. Different AM technologies, process parameters or materials introduce geometric constraints on what is…
Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…
Many proposals have already been made for realizing programmable matter, ranging from shape-changing molecules, DNA tiles, and synthetic cells to reconfigurable modular robotics. Envisioning systems of nano-sensors devices, we are…
This paper presents a method for computing interleaved additive and subtractive manufacturing operations to fabricate models of arbitrary shapes. We solve the manufacturing planning problem by searching a sequence of inverse operations that…
The computation of the elastic shape registration of two simple surfaces in 3-dimensional space and therefore of the elastic shape distance between them has been investigated by Kurtek, Jermyn, et al. who have proposed algorithms to carry…
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…
Implicit functions provide a fundamental basis to model 3D objects, no matter they are rigid or deformable, in computer graphics and geometric modeling. This paper introduces a new constructive scheme of implicitly-defined 3D objects based…