Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

Lines pinning lines

A line g is a transversal to a family F of convex polytopes in 3-dimensional space if it intersects every member of F. If, in addition, g is an isolated point of the space of line transversals to F, we say that F is a pinning of g. We show that any minimal pinning of a line by convex polytopes such that no face of a polytope is coplanar with the line has size at most eight. If, in addition, the polytopes are disjoint, then it has size at most six. We completely characterize configurations of disjoint polytopes that form minimal pinnings of a line.Comment: 27 pages, 10 figure

A 3D descriptor to detect task-oriented grasping points in clothing

© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Manipulating textile objects with a robot is a challenging task, especially because the garment perception is difficult due to the endless configurations it can adopt, coupled with a large variety of colors and designs. Most current approaches follow a multiple re-grasp strategy, in which clothes are sequentially grasped from different points until one of them yields a recognizable configuration. In this work we propose a method that combines 3D and appearance information to directly select a suitable grasping point for the task at hand, which in our case consists of hanging a shirt or a polo shirt from a hook. Our method follows a coarse-to-fine approach in which, first, the collar of the garment is detected and, next, a grasping point on the lapel is chosen using a novel 3D descriptor. In contrast to current 3D descriptors, ours can run in real time, even when it needs to be densely computed over the input image. Our central idea is to take advantage of the structured nature of range images that most depth sensors provide and, by exploiting integral imaging, achieve speed-ups of two orders of magnitude with respect to competing approaches, while maintaining performance. This makes it especially adequate for robotic applications as we thoroughly demonstrate in the experimental section.Peer ReviewedPostprint (author's final draft

Development of Feature Recognition Algorithm for Automated Identification of Duplicate Geometries in CAD Models

This research presents a feature recognition algorithm for the automated identification of duplicate geometries in the CAD assembly. The duplicate geometry is one of the seven indicators of the lazy parts mass reduction method. The lazy parts method is a light weight engineering method that is used for analyzing parts with the mass reduction potential. The duplicate geometry is defined as any geometries lying equal to or within the threshold distance with the user-defined orientation between them and have the percentage similarity that is equal to or greater than the threshold value. The feature recognition system developed in this research for the identification of duplicate geometries is also extended to retrieve the weighted bipartite graph of part connections for the assembly time estimation. The weighted bipartite graph is used as input for the part connectivity based assembly time estimation method. The SolidWorks API software development kit is used in this research to develop a feature recognition system in SolidWorks CAD software package using C++ programming language. The feature recognition system built in the SolidWorks CAD software uses a combination of topology and geometric data for the evaluation of duplicate geometry. The measurement of distances between the sampling points strategy is used for the duplicate geometry feature recognition. The feature recognition algorithm has three phases of evaluation: first, is the evaluation for threshold distance condition of parts in the CAD assembly. Second, the part pairs that have satisfied the threshold distance condition are evaluated for the orientation condition. The threshold distance and orientation are the necessary but not the sufficient conditions for duplicate geometries. In the third phase, the geometries that have satisfied orientation condition are evaluated for the percentage similarity condition. The geometries that satisfy the percentage similarity condition are highlighted in order to help designers review the results of the duplicate geometry analysis. The test cases are used to validate the algorithm against the requirements list. The test cases are designed to check the performance of the algorithm for the evaluation of the threshold distance, orientation, and percentage similarity condition. The results indicate that the duplicate geometry algorithm is able to successfully conduct all the three phases of evaluation. The algorithm is independent of the geometric type and is able to analyze planar, cylindrical, conical, spherical, freeform, and toroidal shapes. The number of sampling points generated on the faces of parts for the orientation and percentage similarity evaluation has the significant effect on the analysis time. The worst case complexity of the algorithm is the big O (nC2x m12 x m22x p4), where n = the number of parts in the assembly m1 = the number of faces in the parts that meet the threshold distance condition m2 = the number of faces that meet the orientation condition p = the number of sampling points on the face The duplicate geometry feature recognition approach is used to demonstrate the applicability in the extraction of assembly relations for the part connectivity based assembly time estimation method. The algorithm is also able to extract part connectivity information for the patterns. Further research is required to automate the identification of other laziness indicators in order to make the lazy parts method a completely automated tool. With regards to the complete automation of part connectivity based assembly time estimation method, the duplicate geometry feature recognition system needs integration with the algorithm for the computation of bipartite graph of part connections for the prediction of assembly time

Simulating Hard Rigid Bodies

Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in condensed matter. The next level of description is to consider particles as rigid objects of generic shape, which would enrich the possible phenomenology enormously. This kind of modeling will prove to be interesting in all those situations in which steric effects play a relevant role. These include biology, soft matter, granular materials and molecular systems. With a view to developing a general recipe for event-driven Molecular Dynamics simulations of hard rigid bodies, two algorithms for calculating the distance between two convex hard rigid bodies and the contact time of two colliding hard rigid bodies solving a non-linear set of equations will be described. Building on these two methods, an event-driven molecular dynamics algorithm for simulating systems of convex hard rigid bodies will be developed and illustrated in details. In order to optimize the collision detection between very elongated hard rigid bodies, a novel nearest-neighbor list method based on an oriented bounding box will be introduced and fully explained. Efficiency and performance of the new algorithm proposed will be extensively tested for uniaxial hard ellipsoids and superquadrics. Finally applications in various scientific fields will be reported and discussed.Comment: 36 pages, 17 figure