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Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…
We propose a method to generate 3D shapes using point clouds. Given a point-cloud representation of a 3D shape, our method builds a kd-tree to spatially partition the points. This orders them consistently across all shapes, resulting in…
Existing auto-regressive mesh generation approaches suffer from ineffective topology preservation, which is crucial for practical applications. This limitation stems from previous mesh tokenization methods treating meshes as simple…
Two-dimensional simulations are used to explore topological transitions that occur during the formation of films grown from grains that are seeded on substrates. This is done for a relatively large range of the initial value $\Phi_s$ of the…
We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then…
Mesh generation is of great value in various applications involving computer graphics and virtual content, yet designing generative models for meshes is challenging due to their irregular data structure and inconsistent topology of meshes…
Point clouds and polygonal meshes are widely used when modeling real-world scenarios. Here, point clouds arise, for instance, from acquisition processes applied in various surroundings, such as reverse engineering, rapid prototyping, or…
In this work, we focus on synthesizing high-quality textures on 3D meshes. We present Point-UV diffusion, a coarse-to-fine pipeline that marries the denoising diffusion model with UV mapping to generate 3D consistent and high-quality…
Although thin films are typically manufactured in planar sheets or rolls, they are often forced into three-dimensional shapes, producing a plethora of structures across multiple length-scales. Existing theoretical approaches have made…
New additive manufacturing methods are needed to realize more complex soft robots. One example is soft fluidic robotics, which exploits fluidic power and stiffness gradients. Porous structures are an interesting type for this approach, as…
Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…
A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a…
We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…
The newly developed "void expansion method" allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions using the discrete element method. Particles are randomly placed under addition…
Explicit surface reconstruction aims to generate a surface mesh that exactly interpolates a given point cloud. This requirement is crucial when the point cloud must lie non-negotiably on the final surface to preserve sharp features and fine…
This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the…
Topology optimization (TO) in two dimensions often presents a trade-off between structural performance and manufacturability, with unpenalized (variable-thickness) methods yielding superior but complex designs, and penalized (SIMP) methods…
Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
Significant progress has been made for assessing the influence of porosity on the performance metrics for cast components through various modeling techniques. However, a computationally efficient framework to account for porosity with…