Smooth quasi-developable surfaces bounded by smooth curves

Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not adequate for generating smooth quasi-developable surfaces. We propose the first method which is capable of exploring the full solution space of continuous input curves to compute a smooth quasi-developable ruled surface with as large developability as possible. The resulting surface is exactly bounded by the input smooth curves and is guaranteed to have no self-intersections. The main contribution is a variational approach to compute a continuous mapping of parameters of input curves by minimizing a function evaluating surface developability. Moreover, we also present an algorithm to represent a resulting surface as a B-spline surface when input curves are B-spline curves.Comment: 18 page

Geometric Modelling and Deformation for Shape Optimization of Ship Hulls and Appendages

International audienceThe precise control of geometric models plays an important role in many domains such as computer-aided geometric design and numerical simulation. For shape optimization in computational fluid dynamics (CFD), the choice of control parameters and the way to deform a shape are critical.In this article, we describe a skeleton-based representation of shapes adapted for CFD simulation and automatic shape optimization. Instead of using the control points of a classic B-spline representation, we control the geometry in terms of architectural parameters. We assure valid shapeswith a strong shape consistency control. Deformations of the geometry are performed by solving optimization problems on the skeleton. Finally, a surface reconstruction method is proposed to evaluate the shape's performances with CFD solvers. We illustrate the approach on two problems: thefoil of an AC45 racing sail boat and the bulbous bow of a fishing trawler. For each case, we obtained a set of shape deformations and then we evaluated and analyzed the performances of the different shapes with CFD computations

An approach to construct a three-dimensional isogeometric model from µ-CT scan data with an application to the bridge of a violin

We present an algorithm to build a ready to use isogeometric model from scan data gained by a µ-CT scan. Based on a three-dimensional multi-patch reference geometry, which includes the major topological features, we fit the outline, then the cross-section and finally the three-dimensional geometry. The key step is to fit the outline, where a non-linear least squares problem is solved with a Gauss-Newton approach presented by Borges and Pastva (2002). We extend this approach by a regularisation and a precise interpolation of selected data points. The resulting NURBS geometry is ready for applying isogeometric analysis tools for efficient numerical simulations. As a particular example we examine the scan data of a violin bridge and present the complete workflow from the µ-CT scan up to the numerical simulation based on isogeometric mortar methods. We illustrate the relevance of the constructed geometry with a vibro-acoustical application

The missing link in as-built 3D modeling: geometrical labeling of segmented point clouds for fitting geometrical surface

Modeling of the built environment is used in a variety of engineering analysis scenarios. Significant applications include monitoring of construction work in progress, quality control of on-site assemblies, building energy diagnostics, and structural integrity evaluation. The modeling process mainly consists of three sequential steps: data collection, modeling, and analysis. In current practice, these steps are performed manually which are time-consuming, prohibitively expensive, and prone to errors. While the analysis stage is fairly quick, taking several hours to complete, data collection and modeling can be the bottlenecks of the process: the first can spread over a few days, and the latter can span over multiple weeks or even months. In consequence, the applicability of as-built modeling has been traditionally restricted to high latency analysis, where the model need not be updated frequently. In fast changing environments such as construction sites, due to the difficulty in rapidly updating 3D models, model-based assessment methods for purposes such as progress or quality monitoring have had very limited applications. There is a need for a low-cost, reliable, and automated method for as-built modeling. This method should quickly generate and update accurate and complete semantically-rich models in a master format that is translatable to any engineering scenario and can be widely applied across all construction projects. To address these limitations, recent research efforts have focused on developing methods to (1) segment point cloud models at user’s desired level of abstraction; and (2) fit surface topologies such as NURBS into the segmented point clouds. While these methods exhibit flexibility in accounting for the user desired level of abstraction, yet they still result in over segmentation. Even if properly segmented, there is still a need to merge several segmented point clouds to create continuous surface models. The geometrical labels can also be used to better populate the scene with distinct surface objects based on the segmented subsets. To address current needs, this thesis focused on automatically labeling each segmented point cloud based on their geometrical properties as wall, floor, ceiling, and pipe, and fits in cylindrical and planar surfaces into the labeled point cloud models. To do so, the method detects and characterizes various types of geometrical features for each segment (e.g. density of the point cloud segment, curvature, height distributions, etc.) and infers their geometrical labels (wall, floor, ceiling, and pipe) using multiple one-vs.-all discriminative machine learning classifiers. Next, the most appropriate type of surface is fitted into the point cloud segments. The experiment results from applying the introduced method on real world point clouds – with an average accuracy of 89% in geometrical labeling – show promise in defining the relationship among segments, improve the accuracy of segmentation process, and can ultimately assist with populating the scene with distinct surface objects based on the segmented subsets

A revisit to fitting parametric surfaces to point clouds

We study the performance of algorithms for freeform surface fitting when different error terms are used as quadratic approximations to the squared orthogonal distances from data points to the fitting surface. We review the TD error term and the SD error term in surface fitting to point clouds, present robust surface fitting algorithms using the TD error term and a new variant of the SD error term. We report experimental results on comparing them with the prevailing PD error term in the setting of fitting B-spline surfaces to point cloud data. We conclude that using the TD error term and the SD error term leads to surface fitting algorithms that converge much faster than using the PD error term. © 2012 Elsevier Ltd. All rights reserved.link_to_subscribed_fulltex