BSP-fields: An Exact Representation of Polygonal Objects by Differentiable Scalar Fields Based on Binary Space Partitioning

The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modeling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples

Microfluidic multipoles: theory and applications

Microfluidic multipoles (MFMs) have been realized experimentally and hold promise for "open-space" biological and chemical surface processing. Whereas convective flow can readily be predicted using hydraulic-electrical analogies, the design of advanced MFMs is constrained by the lack of simple, accurate models to predict mass transport within them. In this work, we introduce the first exact solutions to mass transport in multipolar microfluidics based on the iterative conformal mapping of 2D advection-diffusion around a simple edge into dipoles and multipolar geometries, revealing a rich landscape of transport modes. The models were validated experimentally with a library of 3D printed MFM devices and found in excellent agreement. Following a theory-guided design approach, we further ideated and fabricated two new classes of spatiotemporally reconfigurable MFM devices that are used for processing surfaces with time-varying reagent streams, and to realize a multistep automated immunoassay. Overall, the results set the foundations for exploring, developing, and applying open-space MFMs.Comment: 16 pages, 5 figure

Geometric Convolutional Neural Network for Analyzing Surface-Based Neuroimaging Data

The conventional CNN, widely used for two-dimensional images, however, is not directly applicable to non-regular geometric surface, such as a cortical thickness. We propose Geometric CNN (gCNN) that deals with data representation over a spherical surface and renders pattern recognition in a multi-shell mesh structure. The classification accuracy for sex was significantly higher than that of SVM and image based CNN. It only uses MRI thickness data to classify gender but this method can expand to classify disease from other MRI or fMRI dataComment: 29 page

Discrete curvature approximations and segmentation of polyhedral surfaces

The segmentation of digitized data to divide a free form surface into patches is one of the key steps required to perform a reverse engineering process of an object. To this end, discrete curvature approximations are introduced as the basis of a segmentation process that lead to a decomposition of digitized data into areas that will help the construction of parametric surface patches. The approach proposed relies on the use of a polyhedral representation of the object built from the digitized data input. Then, it is shown how noise reduction, edge swapping techniques and adapted remeshing schemes can participate to different preparation phases to provide a geometry that highlights useful characteristics for the segmentation process. The segmentation process is performed with various approximations of discrete curvatures evaluated on the polyhedron produced during the preparation phases. The segmentation process proposed involves two phases: the identification of characteristic polygonal lines and the identification of polyhedral areas useful for a patch construction process. Discrete curvature criteria are adapted to each phase and the concept of invariant evaluation of curvatures is introduced to generate criteria that are constant over equivalent meshes. A description of the segmentation procedure is provided together with examples of results for free form object surfaces

Convolution filtering of continuous signed distance fields for polygonal meshes

Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C1 discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance function and to apply a smoothing filter to it while preserving the shape of the initial mesh. The resulting function is smooth almost everywhere, while preserving the exact shape of the polygonal mesh. Due to its low complexity, the proposed filtering technique remains fast compared to its main alternatives providing C1-continuous distance field approximation. Several applications are presented such as blending, metamorphosis and heterogeneous modelling with polygonal meshes

The Double Hierarchy Method: a parallel 3D contact method for the interaction of spherical particles with rigid FE boundaries using the DEM

The final publication is available at Springer via http://dx.doi.org/10.1007/s40571-016-0109-4In this work, we present a new methodology for the treatment of the contact interaction between rigid boundaries and spherical discrete elements (DE). Rigid body parts are present in most of large-scale simulations. The surfaces of the rigid parts are commonly meshed with a finite element-like (FE) discretization. The contact detection and calculation between those DE and the discretized boundaries is not straightforward and has been addressed by different approaches. The algorithm presented in this paper considers the contact of the DEs with the geometric primitives of a FE mesh, i.e. facet, edge or vertex. To do so, the original hierarchical method presented by Horner et al. (J Eng Mech 127(10):1027–1032, 2001) is extended with a new insight leading to a robust, fast and accurate 3D contact algorithm which is fully parallelizable. The implementation of the method has been developed in order to deal ideally with triangles and quadrilaterals. If the boundaries are discretized with another type of geometries, the method can be easily extended to higher order planar convex polyhedra. A detailed description of the procedure followed to treat a wide range of cases is presented. The description of the developed algorithm and its validation is verified with several practical examples. The parallelization capabilities and the obtained performance are presented with the study of an industrial application example.Peer ReviewedPostprint (author's final draft

A geometric-based method for recognizing overlapping polygonal-shaped and semi-transparent particles in gray tone images

International audienceA geometric-based method is proposed to recognize the overlapping particles of different polygonal shapes such as rectangular, regular and/or irregular prismatic particles in a gray tone image. The first step consists in extracting the salient corners, identified by their locations and orientations, of the overlapping particles. Although there are certain difficulties like the perspective geometric projection, out of focus, transparency and superposition of the studied particles. Then, a new clustering technique is applied to detect the shape by grouping its correspondent salient corners according to the geometric properties of each shape. A simulation process is carried out for evaluating the performance of the proposed method. Then, it is particularly applied on a real application of batch cooling crystallization of the ammonium oxalate in pure water. The experimental results show that the method is efficient to recognize the overlapping particles of different shapes and sizes