Abstract: As a new advancement of traditional finite element method, isogeometric analysis (IGA) adopts the same set of basis functions to represent both the geometry and the solution space, integrating design with analysis seamlessly. In this talk, I will present a practical unstructured spline modeling platform that allows IGA to be incorporated into existing commercial software such as Abaqus and LS-DYNA, heading one step further to bridge the gap between design and analysis. The platform includes all the necessary modules of the design-through-analysis pipeline: pre-processing, surface and volumetric spline construction, analysis and post-processing. Taking IGES files from commercial computer aided design packages, Rhino specific files or mesh data, the platform provides several control mesh generation techniques, such as converting any unstructured quadrilateral/hexahedral meshes to T-meshes, frame field based quadrilateral meshing, and polycube method. Truncated T-splines, hierarchical B-splines and subdivision basis functions are developed, supporting efficient local refinement and sharp feature preservation. To ensure analysis suitability, partition of unity, linear independence and optimal convergence rate of these basis functions are studied in our research. In the end, several practical application problems are presented to demonstrate the capability of our software platform.
Abstract: The question whether one can recover the shape of a geometric object from its Laplacian eigenvalues ('hear the shape of the drum') is a classical problem in spectral geometry with a broad range of implications and applications. While theoretically the answer to this question is negative (there exist examples of iso-spectral but non-isometric manifolds), little is known about the practical possibility of using the spectrum for shape reconstruction and optimization. In this talk, I will introduce a numerical procedure called isospectralization, consisting of deforming one shape to make its Laplacian spectrum match that of another. I will show the application of this procedure to some of the classical and notoriously hard problems in geometry processing, computer vision, and graphics such as shape reconstruction, pose and style transfer, and dense deformable correspondence. In the second part of the talk, I will use perturbation analysis to show how removal of shape parts changes the Laplacian eigenfunctions, and exploit it for the construction of partial functional maps capable of addressing challenging real-world settings of deformable correspondence in the presence of clutter or occlusions.
Abstract: Inspired by the introduction of Volumetric Modeling via volumetric representations (V-reps) by Massarwi and Elber in 2016, we present a novel approach for the construction of numerical methods for PDEs on such geometric models that does not require any re-parametrisation, i.e., without any meshing involved. The stability of PDEs discretisations on such models is analysed and minimal stabilisation techniques are proposed. Our approach is very flexible, and applies to a large class of PDEs. We will show several convincing examples. Coauthors: P. Antolin, R. Puppi, R. Vazquez
Abstract: "Surface parameterization is the computation of a foldover-free, low-distortion map from surface patches to 2D domain. Atlases are constructed by packing 2D parameterized charts into rectangular texture image domains. Both are fundamental problems in computer graphics and geometric processing and have been widely used in many applications, such as texture mapping, remeshing, intersurface mapping, and shape analysis. In this task, I will review on state-of-the-art works on both surface parameterization and texture atlas generation and introduce our recent works on these topics."
Abstract: From the standpoint of the core technology, AR/VR has made massive advances in recent years, from consumer headsets to low-cost and precise head tracking. Arguably however, AR/VR is still a technology in need of the killer app. In this talk, I’ll argue for why the killer app is immersive telepresence, aka virtual teleportation. The concept of virtual teleportation is not new, we’ve all been dreaming about it since the holograms of Star Wars. However, with the advent of consumer AR/VR headsets, it is now tantalisingly close to becoming fact rather than just science fiction. At its core, however, there’s a fundamental machine perception problem still to solve – the digitization of humans in 3D and in real-time. In this talk I'll cover the work that we have done at Microsoft, perceptiveIO and now Google on this topic. I’ll outline the challenges ahead of us and demonstrate some of the core algorithms and technologies that can get us closer to making virtual teleportation a reality in the future.
Abstract: Recent research in textures for rendering has led to some interesting problems that cross the boundaries between shape modeling, rendering and animation. I will discuss a few projects in this area. Inverse modeling of small cale geometric textures is part of a project in appearance modeling. Understanding how people expect to interact with shapes is part of a project on how to model texture and reflectance consistent with shape. Modeling 3D textures has led to a project in exploring new shapes for effective materials in storage batteries. Finally, designing and printing textures on shapes is related to a project in creating objects that carry encoded animations.
Abstract: The needs of modern (additive) manufacturing (AM) technologies can no longer be satisfied by boundary representations (B-reps). AM requires the representation and manipulation of interior fields and materials as well. Further, while the need for a tight coupling between design and analysis has been recognized as crucial almost since geometric modeling (GM) has been conceived, contemporary GM systems only offer a loose link between the two, if at all.
For about half a century, the (trimmed) Non Uniform Rational B-spline (NURBs) representation has been the B-rep of choice for virtually all the GM industry. Fundamentally, B-rep GM has evolved little during this period. In this talk, we seek to examine an extended volumetric representation (V-rep) that successfully confronts the existing and anticipated design, analysis, and manufacturing foreseen challenges. We extend all fundamental B-rep GM operations, such as primitive and surface constructors and Boolean operations, to trimmed trivariate V-reps. This enables the much needed tight link between the designed geometry and (Isogeometric) analysis on one hand and the full support of (heterogeneous and anisotropic) additive manufacturing on the other.
Examples and other applications of V-rep GM, including AM and lattice-and micro-structure synthesis and heterogeneous materials, will also be demonstrated.
* This work is in collaboration with many others, including Ben Ezair, Fady Massarwi, Boris van Sosin, Jinesh Machchhar, Annalisa Buffa, Giancarlo Sangalli, Pablo Antolin, Massimiliano Martinelli, Bob Haimes and Stefanie Elgeti.
Abstract: Advancements in rapid prototyping technology are closing the gap between what we can simulate with computers and what we can build, as it is now possible to create shapes of astounding complexity with relative ease. Despite innovations in hardware, however, barriers still exist for novices to engage in the design phase. 3D modeling software has remained largely unaware of the fundamental laws that govern how materials and structures behave in the real world. As such, creating customized products that perform a specific function depends on extensive expert knowledge. In this talk I will present recent work that aims to enable intuitive control of mechanical and dynamic properties thanks to novel techniques in constrained optimization, numerical methods, and geometry processing.
Abstract: Point cloud, a given set of discrete points in a coordinate system, can naturally capture and express any object in the real world with various scales and rich attributes. We could thus calculate and restore the entire real world from point clouds, so one may say 'everything is a point cloud or point clouds are everywhere:-)' In this talk, I will first review a serial of our research work done on point clouds over the past decade, highlighting in-depth some representation and reconstruction methods for unorganized point clouds, and then provide a perspective on future point cloud learning.
Abstract: This talk describes the motivation and geometry of parameterization in Computer Graphics. In particular, we focus on the difficulty of computing low distortion bijective maps between triangulated surfaces and the two dimensional plane. To do so, we describe an isometric distortion metric and describe how to specialize nonlinear optimization procedures by directly computing all singularities of the function explicitly. We guarantee bijectivity through the use of a barrier function and show how to obtain fast optimization times through the use of a spatial hash. The result is an efficient method for computing a bijective map that obtains low distortion without constraining the boundary.
Abstract: Geometric data abounds, but our algorithms for geometry processing are failing. Whether from medical imagery, free-form architecture, self-driving cars, or 3D-printed parts, geometric data is often messy, riddled with 'defects' that cause algorithms to crash or behave unpredictably. The traditional philosophy assumes geometry is given with 100% certainty and that algorithms can use whatever discretization is most convenient. As a result, geometric pipelines are leaky patchworks requiring esoteric training and involving many different people. Instead, we adapt fundamental mathematics to work directly on messy geometric data. As an archetypical example, I will discuss how to generalize the classic formula for determining the inside from the outside of a curve to messy representations of a 3D surface. This work helps keep the geometry processing pipeline flowing, as validated on our large-scale geometry benchmarks. Our long term vision is to replace the current leaky geometry processing pipeline with a robust workflow where processing operates directly on real geometric data found 'in the wild'. To do this, we need to rethink how algorithms should gracefully degrade when confronted with imprecision and uncertainty. Our most recent work on differentiable rendering and geometry-based adversarial attacks on image classification demonstrates the potential power of this philosophy.
Abstract: Commercial CAD tools have matured at an impressive rate over the last 30 years. Today they provide the de facto industry solution for the creation of sophisticated, highly realistic, parametric geometry, capturing ever increasing levels of detail and complexity. However, for engineers and analysts performing advanced simulation, CAD geometry is frequently quoted as the single biggest bottleneck in their workflow, accounting for hours and days of time lost performing manual clean-up and simplification. The result of this work, a CAE geometry model, drives the most sensitive stage of many simulations, mesh generation. ITI, through their CADfix product, have been tackling the issues of re-using CAD geometry for simulation for over 40 years, starting in the days before CAD, when hand-made mesh was the 'geometry'. In this talk I will attempt to give an overview of some of the most pressing geometry issues affecting the simulation industry, explaining their source and illustrating the nature of their negative impact on producing an acceptable CAE geometry. I will also share some highlights of the progress ITI is making in deploying novel techniques, such as the 3D medial axis transform, to unlock some of the key CAE geometry challenges.