Related papers: Variable offsets and processing of implicit forms …
This paper proposes a projection-based implicit modeling method (PIMM) for functionally graded lattice optimization, which does not require any homogenization techniques. In this method, a parametric projection function is proposed to link…
In recent years, new methods have been developed to synthesize complex porous and micro-structured geometry in a variety of ways. In this work, we take these approaches one step further and present these methods as an efficacious design…
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…
Triply periodic minimal surface (TPMS) metamaterials characterized by mathematically-controlled topologies exhibit better mechanical properties compared to uniform structures. The unit cell topology of such metamaterials can be further…
This paper considers the shape formation problem within the 3D hybrid model, where a single agent with a strictly limited viewing range and the computational capacity of a deterministic finite automaton manipulates passive tiles through…
Triply periodic minimal surface (TPMS) structures, a type of lattice structure, have garnered significant attention due to their lightweight nature, controllability, and excellent mechanical properties. Voxel-based modeling is a widely used…
Deep implicit surfaces excel at modeling generic shapes but do not always capture the regularities present in manufactured objects, which is something simple geometric primitives are particularly good at. In this paper, we propose a…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
This paper introduces open-source contributions designed to accelerate research in volumetric multi-material additive manufacturing and metamaterial design. We present a flexible Python-based API facilitating parametric expression of…
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…
Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract…
Porous structures are intricate solid materials with numerous small pores, extensively used in fields like medicine, chemical engineering, and aerospace. However, the design of such structures using computer-aided tools is a time-consuming…
We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization…
Deep implicit functions (DIFs), as a kind of 3D shape representation, are becoming more and more popular in the 3D vision community due to their compactness and strong representation power. However, unlike polygon mesh-based templates, it…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
We discuss how Dokken's methods of approximate implicitization can be applied to triangular B\'ezier surfaces in both the original and weak forms. The matrices $\mathbf{D}$ and $\mathbf{M}$ that are fundamental to the respective forms of…
Architected materials possessing physico-chemical properties adaptable to disparate environmental conditions embody a disruptive new domain of materials science. Fueled by advances in digital design and fabrication, materials shaped into…
Porous structures are materials consisting of minuscule pores, where the microstructure morphology significantly impacts their macroscopic properties. Integrating different porous structures through a blending method is indispensable to…
The goal of this paper is to learn dense 3D shape correspondence for topology-varying objects in an unsupervised manner. Conventional implicit functions estimate the occupancy of a 3D point given a shape latent code. Instead, our novel…
This work presents a computational method for the design of architected truss lattice materials where each strut can be made of one of a set of available materials. We design the lattices to extremize effective properties. As customary in…