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

Best data-dependent triangulations

AbstractWhen reconstructing a surface from irregularly spaced data we need to decide how to identify a good triangulation. As a measure of quality we consider various differential geometrical properties, namely integral absolute Gaussian curvature, integral absolute mean curvature and area. A comparison is made with data-dependent triangulation methods that exist in the literature

Regularized Optimal Transport and the Rot Mover's Distance

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences. Our framework thus naturally generalizes a previously proposed regularization based on the Boltzmann-Shannon entropy related to the Kullback-Leibler divergence, and solved with the Sinkhorn-Knopp algorithm. We call the regularized optimal transport distance the rot mover's distance in reference to the classical earth mover's distance. We develop two generic schemes that we respectively call the alternate scaling algorithm and the non-negative alternate scaling algorithm, to compute efficiently the regularized optimal plans depending on whether the domain of the regularizer lies within the non-negative orthant or not. These schemes are based on Dykstra's algorithm with alternate Bregman projections, and further exploit the Newton-Raphson method when applied to separable divergences. We enhance the separable case with a sparse extension to deal with high data dimensions. We also instantiate our proposed framework and discuss the inherent specificities for well-known regularizers and statistical divergences in the machine learning and information geometry communities. Finally, we demonstrate the merits of our methods with experiments using synthetic data to illustrate the effect of different regularizers and penalties on the solutions, as well as real-world data for a pattern recognition application to audio scene classification

Automatic tailoring and cloth modelling for animation characters.

The construction of realistic characters has become increasingly important to the production of blockbuster films, TV series and computer games. The outfit of character plays an important role in the application of virtual characters. It is one of the key elements reflects the personality of character. Virtual clothing refers to the process that constructs outfits for virtual characters, and currently, it is widely used in mainly two areas, fashion industry and computer animation. In fashion industry, virtual clothing technology is an effective tool which creates, edits and pre-visualises cloth design patterns efficiently. However, using this method requires lots of tailoring expertises. In computer animation, geometric modelling methods are widely used for cloth modelling due to their simplicity and intuitiveness. However, because of the shortage of tailoring knowledge among animation artists, current existing cloth design patterns can not be used directly by animation artists, and the appearance of cloth depends heavily on the skill of artists. Moreover, geometric modelling methods requires lots of manual operations. This tediousness is worsen by modelling same style cloth for different characters with different body shapes and proportions. This thesis addresses this problem and presents a new virtual clothing method which includes automatic character measuring, automatic cloth pattern adjustment, and cloth patterns assembling. There are two main contributions in this research. Firstly, a geodesic curvature flow based geodesic computation scheme is presented for acquiring length measurements from character. Due to the fast growing demand on usage of high resolution character model in animation production, the increasing number of characters need to be handled simultaneously as well as improving the reusability of 3D model in film production, the efficiency of modelling cloth for multiple high resolution character is very important. In order to improve the efficiency of measuring character for cloth fitting, a fast geodesic algorithm that has linear time complexity with a small bounded error is also presented. Secondly, a cloth pattern adjusting genetic algorithm is developed for automatic cloth fitting and retargeting. For the reason that that body shapes and proportions vary largely in character design, fitting and transferring cloth to a different character is a challenging task. This thesis considers the cloth fitting process as an optimization procedure. It optimizes both the shape and size of each cloth pattern automatically, the integrity, design and size of each cloth pattern are evaluated in order to create 3D cloth for any character with different body shapes and proportions while preserve the original cloth design. By automating the cloth modelling process, it empowers the creativity of animation artists and improves their productivity by allowing them to use a large amount of existing cloth design patterns in fashion industry to create various clothes and to transfer same design cloth to characters with different body shapes and proportions with ease

Computational Aspects of the Hausdorff Distance in Unbounded Dimension

We study the computational complexity of determining the Hausdorff distance of two polytopes given in halfspace- or vertex-presentation in arbitrary dimension. Subsequently, a matching problem is investigated where a convex body is allowed to be homothetically transformed in order to minimize its Hausdorff distance to another one. For this problem, we characterize optimal solutions, deduce a Helly-type theorem and give polynomial time (approximation) algorithms for polytopes

Developing a Semantic-Driven Hybrid Segmentation Method for Point Clouds of 3D Shapes

With the rapid development of point cloud processing technologies and the availability of a wide range of 3D capturing devices, a geometric object from the real world can be directly represented digitally as a dense and fine point cloud. Decomposing a 3D shape represented in point cloud into meaningful parts has very important practical implications in the fields of computer graphics, virtual reality and mixed reality. In this paper, a semantic-driven automated hybrid segmentation method is proposed for 3D point cloud shapes. Our method consists of three stages: semantic clustering, variational merging, and region remerging. In the first stage, a new feature of point cloud, called Local Concave-Convex Histogram, is introduced to first extract saddle regions complying with the semantic boundary feature. All other types of regions are then aggregated according to this extracted feature. This stage often leads to multiple over-segmentation convex regions, which are then remerged by a variational method established based on the narrow-band theory. Finally, in order to recombine the regions with the approximate shapes, order relation is introduced to improve the weighting forms in calculating the conventional Shape Diameter Function. We have conducted extensive experiments with the Princeton Dataset. The results show that the proposed algorithm outperforms the state-of-the-art algorithms in this area. We have also applied the proposed algorithm to process the point cloud data acquired directly from the real 3D objects. It achieves excellent results too. These results demonstrate that the method proposed in this paper is effective and universal

In Perfect Shape: Certifiably Optimal 3D Shape Reconstruction from 2D Landmarks

We study the problem of 3D shape reconstruction from 2D landmarks extracted in a single image. We adopt the 3D deformable shape model and formulate the reconstruction as a joint optimization of the camera pose and the linear shape parameters. Our first contribution is to apply Lasserre's hierarchy of convex Sums-of-Squares (SOS) relaxations to solve the shape reconstruction problem and show that the SOS relaxation of minimum order 2 empirically solves the original non-convex problem exactly. Our second contribution is to exploit the structure of the polynomial in the objective function and find a reduced set of basis monomials for the SOS relaxation that significantly decreases the size of the resulting semidefinite program (SDP) without compromising its accuracy. These two contributions, to the best of our knowledge, lead to the first certifiably optimal solver for 3D shape reconstruction, that we name Shape*. Our third contribution is to add an outlier rejection layer to Shape* using a truncated least squares (TLS) robust cost function and leveraging graduated non-convexity to solve TLS without initialization. The result is a robust reconstruction algorithm, named Shape#, that tolerates a large amount of outlier measurements. We evaluate the performance of Shape* and Shape# in both simulated and real experiments, showing that Shape* outperforms local optimization and previous convex relaxation techniques, while Shape# achieves state-of-the-art performance and is robust against 70% outliers in the FG3DCar dataset.Comment: Camera-ready, CVPR 2020. 18 pages, 5 figures, 1 tabl