6,431 research outputs found
Generation of three-dimensional body-fitted grids by solving hyperbolic and parabolic partial differential equations
Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations
An efficient method for multiobjective optimal control and optimal control subject to integral constraints
We introduce a new and efficient numerical method for multicriterion optimal
control and single criterion optimal control under integral constraints. The
approach is based on extending the state space to include information on a
"budget" remaining to satisfy each constraint; the augmented
Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our
approach hinges on the causality in that PDE, i.e., the monotonicity of
characteristic curves in one of the newly added dimensions. A semi-Lagrangian
"marching" method is used to approximate the discontinuous viscosity solution
efficiently. We compare this to a recently introduced "weighted sum" based
algorithm for the same problem. We illustrate our method using examples from
flight path planning and robotic navigation in the presence of friendly and
adversarial observers.Comment: The final version accepted by J. Comp. Math. : 41 pages, 14 figures.
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SEGMENT3D: A Web-based Application for Collaborative Segmentation of 3D images used in the Shoot Apical Meristem
The quantitative analysis of 3D confocal microscopy images of the shoot
apical meristem helps understanding the growth process of some plants. Cell
segmentation in these images is crucial for computational plant analysis and
many automated methods have been proposed. However, variations in signal
intensity across the image mitigate the effectiveness of those approaches with
no easy way for user correction. We propose a web-based collaborative 3D image
segmentation application, SEGMENT3D, to leverage automatic segmentation
results. The image is divided into 3D tiles that can be either segmented
interactively from scratch or corrected from a pre-existing segmentation.
Individual segmentation results per tile are then automatically merged via
consensus analysis and then stitched to complete the segmentation for the
entire image stack. SEGMENT3D is a comprehensive application that can be
applied to other 3D imaging modalities and general objects. It also provides an
easy way to create supervised data to advance segmentation using machine
learning models
Subdivision surface fitting to a dense mesh using ridges and umbilics
Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach
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