On the medial surface approximations of extrusions

Generating the medial surface for a general boundary representation model raises several difficulties. Problems might emerge from the complexity of the resulting equations, singularities caused by unforeseen relative boundary element positions and orientations, etc. The majority of the current algorithms are based on the topology of the boundary representation model and produce wireframes composed of straight lines regardless of the real medial surfaces. Many of the solids used in engineering can be represented by extrusions, delimited by a cross-section and an extrusion distance. This paper develops a fast and efficient method for creating the facetted approximations of the medial surfaces of extrusions generated by sweeping along the normal direction to the generating cross-sectio

Restricted Constrained Delaunay Triangulations

We introduce the restricted constrained Delaunay triangulation (restricted CDT), a generalization of both the restricted Delaunay triangulation and the constrained Delaunay triangulation. The restricted CDT is a triangulation of a surface whose edges include a set of user-specified constraining segments. We define the restricted CDT to be the dual of a restricted Voronoi diagram defined on a surface that we have extended by topological surgery. We prove several properties of restricted CDTs, including sampling conditions under which the restricted CDT contains every constraining segment and is homeomorphic to the underlying surface

Unstructured and semi-structured hexahedral mesh generation methods

Discretization techniques such as the finite element method, the finite volume method or the discontinuous Galerkin method are the most used simulation techniques in ap- plied sciences and technology. These methods rely on a spatial discretization adapted to the geometry and to the prescribed distribution of element size. Several fast and robust algorithms have been developed to generate triangular and tetrahedral meshes. In these methods local connectivity modifications are a crucial step. Nevertheless, in hexahedral meshes the connectivity modifications propagate through the mesh. In this sense, hexahedral meshes are more constrained and therefore, more difficult to gener- ate. However, in many applications such as boundary layers in computational fluid dy- namics or composite material in structural analysis hexahedral meshes are preferred. In this work we present a survey of developed methods for generating structured and unstructured hexahedral meshes.Peer ReviewedPostprint (published version

From 3D Models to 3D Prints: an Overview of the Processing Pipeline

Due to the wide diffusion of 3D printing technologies, geometric algorithms for Additive Manufacturing are being invented at an impressive speed. Each single step, in particular along the Process Planning pipeline, can now count on dozens of methods that prepare the 3D model for fabrication, while analysing and optimizing geometry and machine instructions for various objectives. This report provides a classification of this huge state of the art, and elicits the relation between each single algorithm and a list of desirable objectives during Process Planning. The objectives themselves are listed and discussed, along with possible needs for tradeoffs. Additive Manufacturing technologies are broadly categorized to explicitly relate classes of devices and supported features. Finally, this report offers an analysis of the state of the art while discussing open and challenging problems from both an academic and an industrial perspective.Comment: European Union (EU); Horizon 2020; H2020-FoF-2015; RIA - Research and Innovation action; Grant agreement N. 68044

Vascular Hemodynamics CFD Modeling

Three dimensional pulsatile blood flow CFD simulations in geometrically genuine normal and non-normal (aneurysm) human neck-head vascular systems nominally spanning the aortic arch to the circle of Willis has been performed and studied. CT scans of the human aortic arch and the carotid arteries were interpreted to obtain geometric data defining the boundary for a vascular CFD simulation. This was accomplished by reconstructing the surface from the anatomical slices and by imposing pertinent boundary conditions at the various artery termini. Following automated formation of a non-conformal CFD mesh, steady and unsteady laminar and low turbulent simulations were performed both for the normal and aneurysm models. Atherosclerosis and atherosclerotic induced aneurysms can occur in the ascending aorta. The results showed marked differences in the flow dynamics for the two models. Secondary flow is induced in both of the models due to the curvature of the aortic arch which is distorted in three dimensions. Counter clockwise rotating vortex formation was seen at the aneurysm segment in the ascending aorta for the aneurysm model which was absent for the normal case. The effect of the aneurysm bulge was seen in regions proximal to it at peak reverse flow causing secondary flow. These secondary aortic blood flows are though to have an effect on the wall shear stress distribution. Maximum pressure regions for the aneurysm were observed at regions distal to it indicating the possible location for rupture. Wall shear force (WSF) values for the normal case at the aortic bend were low indicating the possible reason for the formation of the aneurysm in the first place. The WSF values at the aneurysm segment for the aneurysm case were also low supporting the low shear stress induced atherosclerotic aneurysms theory. These results may act as a precursor for a multiscale Large eddy simulation model (LES) for pulsatile blood flow eliminating the need for a priori definition of the flow as laminar or turbulent

A theoretical model for the formation of Ring Moat Dome Structures:Products of second boiling in lunar basaltic lava flows

Newly documented Ring Moat Dome Structures (RMDSs), low mounds typically several hundred meters across with a median height of ~3.5 m and surrounded by moats, occur in the lunar maria. They appear to have formed synchronously with the surrounding mare basalt deposits. It has been hypothesized that they formed on the surfaces of lava flows by the extrusion of magmatic foams generated in the flow interiors as the last stage of the eruption and flow emplacement process. We develop a theoretical model for the emplacement and cooling of mare basalts in which the molten cores of cooling flows are inflated during the late stages of eruptions by injection of additional hot lava containing dissolved volatiles. Crystallization of this lava causes second boiling (an increase in vapor pressure to the point of supersaturation due to crystallization of the melt), generating copious quantities of vesicles (magmatic foam layers) at the top and bottom of the central core of the flow. Flow inflation of many meters is predicted to accompany the formation of the foam layers, flexing the cooled upper crustal layer, and forming fractures that permit extrusions of the magmatic foams onto the surface to form domes, with subsidence of the subjacent and surrounding surface forming the moats. By modeling the evolution of the internal flow structure we predict the properties of RMDSs and the conditions in which they are most likely to form. We outline several tests of this hypothesis

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop