Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

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Convex Analysisの二,三の進展について

The k_t and Cambridge/Aachen inclusive jet finding algorithms for hadron-hadron collisions can be seen as belonging to a broader class of sequential recombination jet algorithms, parametrised by the power of the energy scale in the distance measure. We examine some properties of a new member of this class, for which the power is negative. This ``anti-k_t'' algorithm essentially behaves like an idealised cone algorithm, in that jets with only soft fragmentation are conical, active and passive areas are equal, the area anomalous dimensions are zero, the non-global logarithms are those of a rigid boundary and the Milan factor is universal. None of these properties hold for existing sequential recombination algorithms, nor for cone algorithms with split--merge steps, such as SISCone. They are however the identifying characteristics of the collinear unsafe plain ``iterative cone'' algorithm, for which the anti-k_t algorithm provides a natural, fast, infrared and collinear safe replacement.

/pdf/the-anti-k-t-jet-clustering-algorithm-2c4jbguc9f.pdf

The anti-$k_t$ jet clustering algorithm

Different geometric structures are investigated in the context of discrete surface representation. It is shown that minimal representations (i.e., polyhedra) can be provided by a surface-based method using nearest neighbors structures or by a volume-based method using the Delaunay triangulation. Both approaches are compared with respect to various criteria, such as space requirements, computation time, constraints on the distribution of the points, facilities for further calculations, and agreement with the actual shape of the object.

/pdf/geometric-structures-for-three-dimensional-shape-3uyq4t1ogz.pdf

Geometric structures for three-dimensional shape representation

We propose a new solution to the problem of constructing a shape over a set of cross-sectional contours. We construct a volume whose boundary is a polyhedron with triangular faces intersecting the cutting planes along the given contours. This volume is obtained, slice by slice, by pruning the Delaunay triangulations formed between two adjacent cross sections. The Delaunay triangulation can be computed efficiently in this specific situation: an algorithm is presented that is optimal with respect to the input size and the output size and that only uses 2-dimensional operations. The shape reconstruction method extracts, from that triangulation, a maximum solid with no singularity. It can handle the case where the number of contours varies from one cross section to the other and thus, can handle contour-defined objects which are branched and have holes. This algorithm has been fully implemented and tested on various examples; results on medical images are presented.

/pdf/shape-reconstruction-from-planar-cross-sections-4mi4gazm2y.pdf

Shape reconstruction from planar cross sections

What do you do to start reading algorithmic geometry? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their reason of reading a book. Actuary, reading habit must be from earlier. Many people may be love to read, but not a book. It's not fault. Someone will be bored to open the thick book with small words to read. In more, this is the real condition. So do happen probably with this algorithmic geometry.

Algorithmic Geometry

The notion of e-sample, introduced by Amenta and Bern, has proven to be a key concept in the theory of sampled surfaces. Of particular interest is the fact that, if E is an e-sample of a C2-continuous surface S for a sufficiently small e, then the Delaunay triangulation of E restricted to S is a good approximation of S, both in a topological and in a geometric sense. Hence, if one can construct an e-sample, one also gets a good approximation of the surface. Moreover, correct reconstruction is ensured by various algorithms. In this paper, we introduce the notion of loose e-sample. We show that the set of loose e-samples contains and is asymptotically identical to the set of e-samples. The main advantage of loose e-samples over e-samples is that they are easier to check and to construct. We also present a simple algorithm that constructs provably good surface samples and meshes. Given a C2-continuous surface S without boundary, the algorithm generates a sparse e-sample E and at the same time a triangulated surface Dels(E). The triangulated surface has the same topological type as S, is close to S for the Hausdorff distance and can provide good approximations of normals, areas and curvatures. A notable feature of the algorithm is that the surface needs only to be known through an oracle that, given el line segment, detects whether the segment intersects the surface and in the affirmative, returns the intersection points. This makes the algorithm useful in a wide variety of contexts and for a large class of surfaces.

https://hal.archives-ouvertes.fr/hal-00488829/document

Provably good sampling and meshing of surfaces

We present an algorithm to reconstruct smooth surfaces of arbitrary topology from unorganised sample points and normals. The method uses natural neighbour interpolation, works in any dimension and allows to deal with non uniform samples. The reconstructed surface is a smooth manifold passing through all the sample points. This surface is implicitly represented as the zero-set of some pseudo-distance function. It can be meshed so as to satisfy a user-defined error bound. Experimental results are presented for surfaces in R^3.

/pdf/smooth-surface-reconstruction-via-natural-neighbour-3dczqdbs1q.pdf

Jean-Daniel Boissonnat

Papers

Geometric structures for three-dimensional shape representation

Shape reconstruction from planar cross sections

Algorithmic Geometry

Provably good sampling and meshing of surfaces

Smooth surface reconstruction via natural neighbour interpolation of distance functions