Easy Integral Surfaces: A Fast, Quad-based Stream and Path Surface Algorithm

a fast, quad-based stream and path surface algorith

Putting holes in holey geometry: Topology change for arbitrary surfaces

This paper presents a method for computing topology changes for triangle meshes in an interactive geometric modeling environment. Most triangle meshes in practice do not exhibit desirable geometric properties, so we develop a solution that is independent of standard assumptions and robust to geometric errors. Specifically, we provide the first method for topology change applicable to arbitrary non-solid, non-manifold, non-closed, self-intersecting surfaces. We prove that this new method for topology change produces the expected conventional results when applied to solid (closed, manifold, non-self-intersecting) surfaces---that is, we prove a backwards-compatibility property relative to prior work. Beyond solid surfaces, we present empirical evidence that our method remains tolerant to a variety of surface aberrations through the incorporation of a novel error correction scheme. Finally, we demonstrate how topology change applied to non-solid objects enables wholly new and useful behaviors

Geometric Surface Processing and Virtual Modeling

In this work we focus on two main topics "Geometric Surface Processing" and "Virtual Modeling". The inspiration and coordination for most of the research work contained in the thesis has been driven by the project New Interactive and Innovative Technologies for CAD (NIIT4CAD), funded by the European Eurostars Programme. NIIT4CAD has the ambitious aim of overcoming the limitations of the traditional approach to surface modeling of current 3D CAD systems by introducing new methodologies and technologies based on subdivision surfaces in a new virtual modeling framework. These innovations will allow designers and engineers to transform quickly and intuitively an idea of shape in a high-quality geometrical model suited for engineering and manufacturing purposes. One of the objective of the thesis is indeed the reconstruction and modeling of surfaces, representing arbitrary topology objects, starting from 3D irregular curve networks acquired through an ad-hoc smart-pen device. The thesis is organized in two main parts: "Geometric Surface Processing" and "Virtual Modeling". During the development of the geometric pipeline in our Virtual Modeling system, we faced many challenges that captured our interest and opened new areas of research and experimentation. In the first part, we present these theories and some applications to Geometric Surface Processing. This allowed us to better formalize and give a broader understanding on some of the techniques used in our latest advancements on virtual modeling and surface reconstruction. The research on both topics led to important results that have been published and presented in articles and conferences of international relevance

Constructing streak surfaces for 3D unsteady vector fields

Visualization of 3D, unsteady flow (4D) is very difficult due to both perceptual challenges and the large size of 4D vector field data. One approach to this challenge is to use integral surfaces to visualize the 4D properties of the field. However the construction of streak surfaces has remained elusive due to problems stemming from expensive computation and complex meshing schemes. We present a novel streak surface construction algorithm that generates the surface using a quadrangular mesh. In contrast to previous approaches the algorithm offers a combination of speed for exploration of 3D unsteady flow, high precision, and places less restriction on data or mesh size due to its CPU-based implementation compared to a GPU-based method. The algorithm can be applied to large data sets because it is based on local operations performed on the quad primitives. We demonstrate the technique on a variety of 3D, unsteady simulation data sets to show its speed and robustness. We also present both a detailed implementation and a performance evaluation. We show that a technique based on quad meshes handles large data sets and can achieve interactive frame rates

Workshop on the Integration of Finite Element Modeling with Geometric Modeling

The workshop on the Integration of Finite Element Modeling with Geometric Modeling was held on 12 May 1987. It was held to discuss the geometric modeling requirements of the finite element modeling process and to better understand the technical aspects of the integration of these two areas. The 11 papers are presented except for one for which only the abstract is given

Quantifying Membrane Topology at the Nanoscale

Changes in the shape of cellular membranes are linked with viral replication, Alzheimer\u27s, heart disease and an abundance of other maladies. Some membranous organelles, such as the endoplasmic reticulum and the Golgi, are only 50 nm in diameter. As such, membrane shape changes are conventionally studied with electron microscopy (EM), which preserves cellular ultrastructure and achieves a resolution of 2 nm or better. However, immunolabeling in EM is challenging, and often destroys the cell, making it difficult to study interactions between membranes and other proteins. Additionally, cells must be fixed in EM imaging, making it impossible to study mechanisms of disease. To address these problems, this thesis advances nanoscale imaging and analysis of membrane shape changes and their associated proteins using super-resolution single-molecule localization microscopy. This thesis is divided into three parts. In the first, a novel correlative orientation-independent differential interference contrast (OI-DIC) and single-molecule localization microscopy (SMLM) instrument is designed to address challenges with live-cell imaging of membrane nanostructure. SMLM super-resolution fluorescence techniques image with ~ 20 nm resolution, and are compatible with live-cell imaging. However, due to SMLM\u27s slow imaging speeds, most cell movement is under-sampled. OI-DIC images fast, is gentle enough to be used with living cells and can image cellular structure without labelling, but is diffraction-limited. Combining SMLM with OI-DIC allows for imaging of cellular context that can supplement sparse super-resolution data in real time. The second part of the thesis describes an open-source software package for visualizing and analyzing SMLM data. SMLM imaging yields localization point clouds, which requires non-standard visualization and analysis techniques. Existing techniques are described, and necessary new ones are implemented. These tools are designed to interpret data collected from the OI-DIC/SMLM microscope, as well as from other optical setups. Finally, a tool for extracting membrane structure from SMLM point clouds is described. SMLM data is often noisy, containing multiple localizations per fluorophore and many non-specific localizations. SMLM\u27s resolution reveals labelling discontinuities, which exacerbate sparsity of localizations. It is non-trivial to reconstruct the continuous shape of a membrane from a discrete set of points, and even more difficult in the presence of the noise profile characteristic of most SMLM point clouds. To address this, a surface reconstruction algorithm for extracting continuous surfaces from SMLM data is implemented. This method employs biophysical curvature constraints to improve the accuracy of the surface