14,962 research outputs found
Revisión de literatura de jerarquía volúmenes acotantes enfocados en detección de colisiones
(Eng) A bounding volume is a common method to simplify object representation by using the composition of geometrical shapes that enclose the object; it encapsulates complex objects by means of simple volumes and it is widely useful in collision detection applications and ray tracing for rendering algorithms. They are popular in computer graphics and computational geometry. Most popular bounding volumes are spheres, Oriented-Bounding Boxe s (OBB’ s), Axis-Align ed Bound ing Boxes (AABB’ s); moreover , the literature review includes ellipsoids, cylinders, sphere packing, sphere shells , k-DOP’ s, convex hulls, cloud of points, and minimal bounding boxe s, among others. A Bounding Volume Hierarchy is ussualy a tree in which the complete object is represented thigter fitting every level of the hierarchy. Additionally, each bounding volume has a cost associated to construction, update, and interference te ts. For instance, spheres are invariant to rotation and translations, then they do not require being updated ; their constructions and interference tests are more straightforward then OBB’ s; however, their tightness is lower than other bounding volumes. Finally , three comparisons between two polyhedra; seven different algorithms were used, of which five are public libraries for collision detection.(Spa) Un volumen acotante es un método común para simplificar la representación de los objetos por medio de composición
de formas geométricas que encierran el objeto; estos encapsulan objetos complejos por medio de volúmenes simples y
son ampliamente usados en aplicaciones de detección de colisiones y trazador de rayos para algoritmos de renderización.
Los volúmenes acotantes son populares en computación gráfica y en geometría computacional; los más populares son las
esferas, las cajas acotantes orientadas (OBB’s) y las cajas acotantes alineadas a los ejes (AABB’s); no obstante, la literatura
incluye elipses, cilindros empaquetamiento de esferas, conchas de esferas, k-DOP’s, convex hulls, nubes de puntos y cajas
acotantes mínimas, entre otras. Una jerarquía de volúmenes acotantes es usualmente un árbol, en el cual la representación
de los objetos es más ajustada en cada uno de los niveles de la jerarquía. Adicionalmente, cada volumen acotante tiene
asociado costos de construcción, actualización, pruebas de interferencia. Por ejemplo, las esferas so invariantes a rotación
y translación, por lo tanto no requieren ser actualizadas en comparación con los AABB no son invariantes a la rotación.
Por otro lado la construcción y las pruebas de solapamiento de las esferas son más simples que los OBB’s; sin embargo, el
ajuste de las esferas es menor que otros volúmenes acotantes. Finalmente, se comparan dos poliedros con siete algoritmos
diferentes de los cuales cinco son librerías públicas para detección de colisiones
Isotropic Dynamic Hierarchical Clustering
We face a need of discovering a pattern in locations of a great number of
points in a high-dimensional space. Goal is to group the close points together.
We are interested in a hierarchical structure, like a B-tree. B-Trees are
hierarchical, balanced, and they can be constructed dynamically. B-Tree
approach allows to determine the structure without any supervised learning or a
priori knowlwdge. The space is Euclidean and isotropic. Unfortunately, there
are no B-Tree implementations processing indices in a symmetrical and
isotropical way. Some implementations are based on constructing compound
asymmetrical indices from point coordinates; and the others split the nodes
along the coordinate hyper-planes. We need to process tens of millions of
points in a thousand-dimensional space. The application has to be scalable.
Ideally, a cluster should be an ellipsoid, but it would require to store O(n2)
ellipse axes. So, we are using multi-dimensional balls defined by the centers
and radii. Calculation of statistical values like the mean and the average
deviation, can be done in an incremental way. While adding a point to a tree,
the statistical values for nodes recalculated in O(1) time. We support both,
brute force O(2n) and greedy O(n2) split algorithms. Statistical and aggregated
node information also allows to manipulate (to search, to delete) aggregated
sets of closely located points. Hierarchical information retrieval. When
searching, the user is provided with the highest appropriate nodes in the tree
hierarchy, with the most important clusters emerging in the hierarchy
automatically. Then, if interested, the user may navigate down the tree to more
specific points. The system is implemented as a library of Java classes
representing Points, Sets of points with aggregated statistical information,
B-tree, and Nodes with a support of serialization and storage in a MySQL
database.Comment: 6 pages with 3 example
Hierarchical bounding structures for efficient virial computations: Towards a realistic molecular description of cholesterics
We detail the application of bounding volume hierarchies to accelerate
second-virial evaluations for arbitrary complex particles interacting through
hard and soft finite-range potentials. This procedure, based on the
construction of neighbour lists through the combined use of recursive
atom-decomposition techniques and binary overlap search schemes, is shown to
scale sub-logarithmically with particle resolution in the case of molecular
systems with high aspect ratios. Its implementation within an efficient
numerical and theoretical framework based on classical density functional
theory enables us to investigate the cholesteric self-assembly of a wide range
of experimentally-relevant particle models. We illustrate the method through
the determination of the cholesteric behaviour of hard, structurally-resolved
twisted cuboids, and report quantitative evidence of the long-predicted phase
handedness inversion with increasing particle thread angles near the
phenomenological threshold value of . Our results further highlight
the complex relationship between microscopic structure and helical twisting
power in such model systems, which may be attributed to subtle geometric
variations of their chiral excluded-volume manifold
Planning 3-D collision-free paths using spheres
A scheme for the representation of objects, the Successive Spherical Approximation (SSA), facilitates the rapid planning of collision-free paths in a 3-D, dynamic environment. The hierarchical nature of the SSA allows collision-free paths to be determined efficiently while still providing for the exact representation of dynamic objects. The concept of a freespace cell is introduced to allow human 3-D conceptual knowledge to be used in facilitating satisfying choices for paths. Collisions can be detected at a rate better than 1 second per environment object per path. This speed enables the path planning process to apply a hierarchy of rules to create a heuristically satisfying collision-free path
Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma
Dickson's Lemma is a simple yet powerful tool widely used in termination
proofs, especially when dealing with counters or related data structures.
However, most computer scientists do not know how to derive complexity upper
bounds from such termination proofs, and the existing literature is not very
helpful in these matters.
We propose a new analysis of the length of bad sequences over (N^k,\leq) and
explain how one may derive complexity upper bounds from termination proofs. Our
upper bounds improve earlier results and are essentially tight
A Proposal for Semantic Map Representation and Evaluation
Semantic mapping is the incremental process of “mapping” relevant information of the world (i.e., spatial information, temporal events, agents and actions) to a formal description supported by a reasoning engine. Current research focuses on learning the semantic of environments based on their spatial location, geometry and appearance. Many methods to tackle this problem have been proposed, but the lack of a uniform representation, as well as standard benchmarking suites, prevents their direct comparison. In this paper, we propose a standardization in the representation of semantic maps, by defining an easily extensible formalism to be used on top of metric maps of the environments. Based on this, we describe the procedure to build a dataset (based on real sensor data) for benchmarking semantic mapping techniques, also hypothesizing some possible evaluation metrics. Nevertheless, by providing a tool for the construction of a semantic map ground truth, we aim at the contribution of the scientific community in acquiring data for populating the dataset
Few smooth d-polytopes with n lattice points
We prove that, for fixed n there exist only finitely many embeddings of
Q-factorial toric varieties X into P^n that are induced by a complete linear
system. The proof is based on a combinatorial result that for fixed nonnegative
integers d and n, there are only finitely many smooth d-polytopes with n
lattice points. We also enumerate all smooth 3-polytopes with at most 12
lattice points. In fact, it is sufficient to bound the singularities and the
number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result
Open questions about Ramsey-type statements in reverse mathematics
Ramsey's theorem states that for any coloring of the n-element subsets of N
with finitely many colors, there is an infinite set H such that all n-element
subsets of H have the same color. The strength of consequences of Ramsey's
theorem has been extensively studied in reverse mathematics and under various
reducibilities, namely, computable reducibility and uniform reducibility. Our
understanding of the combinatorics of Ramsey's theorem and its consequences has
been greatly improved over the past decades. In this paper, we state some
questions which naturally arose during this study. The inability to answer
those questions reveals some gaps in our understanding of the combinatorics of
Ramsey's theorem.Comment: 15 page
Fixed-Dimensional Energy Games are in Pseudo-Polynomial Time
We generalise the hyperplane separation technique (Chatterjee and Velner,
2013) from multi-dimensional mean-payoff to energy games, and achieve an
algorithm for solving the latter whose running time is exponential only in the
dimension, but not in the number of vertices of the game graph. This answers an
open question whether energy games with arbitrary initial credit can be solved
in pseudo-polynomial time for fixed dimensions 3 or larger (Chaloupka, 2013).
It also improves the complexity of solving multi-dimensional energy games with
given initial credit from non-elementary (Br\'azdil, Jan\v{c}ar, and
Ku\v{c}era, 2010) to 2EXPTIME, thus establishing their 2EXPTIME-completeness.Comment: Corrected proof of Lemma 6.2 (thanks to Dmitry Chistikov for spotting
an error in the previous proof
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