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Durham, NC, United States

Sallas J.J.,Geomagic
Geophysical Prospecting | Year: 2010

In order to have realistic expectations of what output is achievable from a seismic vibrator, an understanding of the machine's limitations is essential. This tutorial is intended to provide some basics on how hydraulic vibrators function and the constraints that arise from their design. With these constraints in mind, informed choices can be made to match machine specifications to a particular application or sweeps can be designed to compensate for performance limits. © 2009 European Association of Geoscientists & Engineers. Source


Cohen-Steiner D.,French Institute for Research in Computer Science and Automation | Edelsbrunner H.,Duke University | Edelsbrunner H.,Geomagic | Harer J.,Duke University | Mileyko Y.,Duke University
Foundations of Computational Mathematics | Year: 2010

We prove two stability results for Lipschitz functions on triangulable, compact metric spaces and consider applications of both to problems in systems biology. Given two functions, the first result is formulated in terms of the Wasserstein distance between their persistence diagrams and the second in terms of their total persistence. © 2010 SFoCM. Source


Grant
Agency: Department of Health and Human Services | Branch: | Program: SBIR | Phase: Phase I | Award Amount: 100.00K | Year: 2007

DESCRIPTION (provided by applicant): The goal of this project is to develop a complete digital shape reconstruction and manufacturing software system for dental restoration. More specifically, this research will deliver innovative algorithms to automatically generate patient-specific tooth shapes and occlusal surfaces. It will also provide computer guidance for high quality restoration through feedback on fit and undercuts. The result is expected to be superior to partial and manual systems in use or known today. It will make a fundamental impact in replacing the century-old craftsmanship by digital manufacturing processes for, inlays, onlays, crowns, bridges, veneers and implants. The benefits of the proposed project are measurable: (i) dentists will receive better quality products and reduce seat time; (ii) dental labs will reduce labor cost and control variability due to human skill; and (iii) patients will be happier with better fit and longer lasting restorations. We will evaluate our solution against state-of-the-art commercial systems and leading academic results. The success of this project will impact research in material science, laser sintering, optical scanning, and NC machining. Aim 1: Optimal preparation line creation. We will develop an algorithm to automatically segment the prepared tooth of a patient, which is represented by 3D scanned data. As a result, a smooth, optimally located, non-branching separation curve defining the preparation line will be obtained. Aim 2: Faithful tooth restoration using full 3D models. Overcoming the deficiencies of former 2.5D approaches, we develop a new, automatic 3D method that uses extended Iterative Closest Point algorithms and warping techniques. It is combined with special morphological steps such as detecting tooth cusps, matching dental features, and prescribing antagonist and proximal contact areas. The novelty of the approach is constrained correspondence between the reference and residual tooth that makes it possible to restore smoothly connected, natural occlusal surfaces. Aim 3: Constrained modification for personalized tooth restoration. We will provide a set of constraint based sculpting and warping tools to satisfy aesthetic or technical preferences. Dental morphology and anatomic rules will be embedded into a system with state-of-the-art shape deformation technology. Aim 4: Automatic shape adjustment for manufacturing and insertion. We will numerically analyze the surfaces of the patient's residual tooth and derive restoration surfaces without manufacturing defects; i.e., we will automatically remove preparation undercuts, add draft angles, compensate for cutter radii and determine angular insertion ranges.


Grant
Agency: National Science Foundation | Branch: | Program: SBIR | Phase: Phase II | Award Amount: 489.18K | Year: 2005

This Small Business Innovation Research Phase II project deals with the problems of reconstructing complex free-form shapes from measured data. Raindrop Magic's primary interest is to produce well-structured, high-quality CAD models. Several techniques exist to reach this goal; unfortunately, automatic surfacing systems provide only rough approximations and do not capture the original design intent, while manual segmentation methods are not very stable and require tedious work. Using functional decomposition, objects are built up as a collection of large, independent primary surfaces being connected by smaller, dependent feature surfaces, such as fillets or swept surfaces. In Phase I, semi-automatic methods were elaborated to create good segmenting curve nets. Exploiting the specific properties of different feature types, the research team proposed algorithms to compute optimal surface representations for each. In Phase II, the team envisions transforming and extending their theoretical results into robust and efficient computational algorithms. Five subsystems are proposed: Surface-Indicators, Constrained-Fitting, Curve-Tracing, Fairing, and Feature-Fitting. New core technologies are developed for creating different geometric entities, which are eventually integrated to obtain high-quality surface models. This technology should significantly shorten lead-time in related industrial design and manufacturing processes and produce aesthetic objects, having a positive impact on the whole society. The proffered technology has broader impacts in two key market sectors: reverse engineering and advanced surfacing. At the research front, the proposed project deepens the understanding of computer-aided geometric modeling working with scan data, a field that has not received much attention from the large CAD companies, but is an active area of research. It combines the knowledge of both discrete and continuous mathematics and takes advantage of the strength of both approaches. On the technology front, it introduces a new paradigm that will significantly improve the current commercial systems of reverse engineering with better engineering features and advanced surfacing through simpler operations. The main applications will be product design, including automotive, aerospace, consumer products, and medical devices. The improved product will help the US manufacturing industry to be more competitive in the world market, providing a way to introduce design on demand and engineering on demand services. The proposed project will help US companies to increase customer-focused production and reduce the time between product iterations.


Grant
Agency: National Science Foundation | Branch: | Program: SBIR | Phase: Phase II | Award Amount: 500.00K | Year: 2005

This Small Business Innovation Research (SBIR) Phase II project will investigate applications of Combinatorial Morse Theory in Reverse Engineering, a field that focuses on converting physical objects into a digital representation suitable for CAD, CAM, and CAE. The biggest challenge in this field is to automate the conversion process while producing a model that meets all the requirements of downstream applications. These requirements include both an accurate representation of features and a high degree of smoothness. Combinatorial Morse Theory relies on a single mathematical approach: the definition of a continuous function on a polygonal model and the decomposition of the surface based on the gradient flow of that function. One advantage of this over earlier approaches to the conversion problem is its flexibility obtained by adapting to and combining different analysis criteria. Morse theory is the key to computing patch layouts that naturally adapt to and follow the shape of the surface, a property that is difficult to achieve but necessary to automatically construct high-quality NURBS surfaces of scanned or triangulated CAD models. The proposed algorithms will allow users to easily create accurate representations of scanned physical parts, thereby providing an efficient closed-loop between physical and digital at any phase of a product life cycle. This project will make strong research contributions in computer science and mechanical engineering by dealing with the practical applications of Morse Theory, automatic feature detection and patch layout. It will also make strong advances in the amount of information that can be extracted from a polygonal model. Commercial applications include design and analysis of complex shapes such as turbine blades, transmission housings, and engine blocks, creating digital inventory of legacy parts, historical preservation, mass customization and biometric shape reconstruction. These applications will allow manufacturing companies to be more competitive globally because it enables product differentiations and existing processes to be carried out efficiently, cost-effectively, and automatically. The societal impact of this technology includes the improvement of work environments due to reduction of dust, noise, and work-related injuries associated with traditional processes, prevention of loss of lives and equipment by enabling sampling based inspections as well as improvement of the quality life through customized medical devices, and apparel that conform perfectly to the wearer.

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