Sweep Algorithms for Constructing Higher-Dimensional Constrained Delaunay Triangulations

I discuss algorithms for constructing constrained Delaunay triangulations (CDTs) in dimensions higher than two. If the CDT of a set of vertices and constraining simplices exists, it can be constructed in O(n v n s ) time, where n v is the number of input vertices and n s is the number of output d-simplices. The CDT of a starshaped polytope can be constructed in O(n s log n v ) time, yielding an efficient way to delete a vertex from a CDT. 1 Introduction Mesh generation and interpolation can benefit from triangulations that have properties similar to Delaunay triangulations, but are constrained to contain specified faces. These constraints may arise because a mesh must conform to the shape of an object, or because of the desire to interpolate a discontinuous function. The constrained Delaunay triangulation (CDT) [5, 1, 11] is a Delaunay-like triangulation that conforms to constraints. In two dimensions, the input is a planar straight line graph (PSLG) X , which is a set of vertices a..

Random lattice particle modeling of fracture processes in cementitious materials

The capability of representing fracture processes in non-homogeneous media is of great interest among the scientific community for at least two reasons: the first one stems from the fact that the use of composite materials is ubiquitous within structural applications, since the advantages of the constituents can be exploited to improve material performance; the second consists of the need to assess the non-linear post-peak behavior of such structures to properly determine margins of safety with respect to strong excitations (e.g. earthquakes, blast or impact loadings). Different kinds of theories and methodologies have been developed in the last century in order to model such phenomena, starting from linear elastic equivalent methods, then moving to plastic theories and fracture mechanics. Among the different modeling techniques available, in recent years lattice models have established themselves as a powerful tool for simulating failure modes and crack paths in heterogeneous materials. The basic idea dates back to the pioneeristic work of Hrennikoff: a continuum medium can be modeled through the interaction of unidimensional elements (e.g. springs or beams) spatially arranged in different ways. The set of nodes that interconnect the elements can be regularly or irregularly placed inside the domain, leading to regular or random lattices. It has been shown that lattices with regular geometry can strongly bias the direction of cracking, leading to incorrect results. A variety of lattice models have been developed. Such models have seen a wide field of applications, ranging from aerodynamics (using Lattice-Boltzman models) to heat transfer, crystallography and many others. Every material used in civil and infrastructure engineering is constituted of different phases. This is due to the fact that the different features of different elements are usually coupled in order to obtain greater advantages with respect to the original constituents. Even structural steel, which is usually thought of as a homogeneous continuum-type medium, includes carbon particles that can be seen as inhomogeneities at the microscopic level. The mechanical behavior of concrete, which is the main object of the present work, is strongly affected not only by the presence of inclusions (i.e. the aggregates pieces) but also by their arrangement. For this reason, the explicit, statistical representation of their presence is of great interest in the simulations of concrete behavior. Lattice models can directly account for the presence of different phases, and so are advantageous from this perspective. The definition of such models, their implementation in a computer program, together with validation on laboratory tests will be presented. The present work will briefly review the state of the art and the basic principles of these models, starting from the geometrical and computing tools needed to build the simulations. The implementation of this technique in the Matlab environment will be presented, highlighting the theoretical background. The numerical results will be validated based on two complementary experimental campaigns,which focused on the meso- and macro-scales of concrete. Whereas the aim of this work is the representation of the quasi-brittle fracture processes in cementitious materials such as concrete, the discussed approach is general, and therefore valid for the representation of damage and crack growth in a variety of different materials

Segmentation and Deformable Modelling Techniques for a Virtual Reality Surgical Simulator in Hepatic Oncology

Liver surgical resection is one of the most frequently used curative therapies. However, resectability is problematic. There is a need for a computer-assisted surgical planning and simulation system which can accurately and efficiently simulate the liver, vessels and tumours in actual patients. The present project describes the development of these core segmentation and deformable modelling techniques. For precise detection of irregularly shaped areas with indistinct boundaries, the segmentation incorporated active contours - gradient vector flow (GVF) snakes and level sets. To improve efficiency, a chessboard distance transform was used to replace part of the GVF effort. To automatically initialize the liver volume detection process, a rotating template was introduced to locate the starting slice. For shape maintenance during the segmentation process, a simplified object shape learning step was introduced to avoid occasional significant errors. Skeletonization with fuzzy connectedness was used for vessel segmentation. To achieve real-time interactivity, the deformation regime of this system was based on a single-organ mass-spring system (MSS), which introduced an on-the-fly local mesh refinement to raise the deformation accuracy and the mesh control quality. This method was now extended to a multiple soft-tissue constraint system, by supplementing it with an adaptive constraint mesh generation. A mesh quality measure was tailored based on a wide comparison of classic measures. Adjustable feature and parameter settings were thus provided, to make tissues of interest distinct from adjacent structures, keeping the mesh suitable for on-line topological transformation and deformation. More than 20 actual patient CT and 2 magnetic resonance imaging (MRI) liver datasets were tested to evaluate the performance of the segmentation method. Instrument manipulations of probing, grasping, and simple cutting were successfully simulated on deformable constraint liver tissue models. This project was implemented in conjunction with the Division of Surgery, Hammersmith Hospital, London; the preliminary reality effect was judged satisfactory by the consultant hepatic surgeon