Simple and Robust Boolean Operations for Triangulated Surfaces

Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two stages: (1) We firstly find out candidate intersected-triangles pairs based on Octree and then compute the inter-section lines for all pairs of triangles with parallel algorithm; (2) We form closed or open intersection-loops, sub-surfaces and sub-blocks quite robustly only according to the cleared and updated topology of meshes while without coordinate computations for geometric enti-ties. A novel technique instead of inside/outside classification is also proposed to distinguish the resulting union, subtraction and intersection. Several examples have been given to illus-trate the effectiveness of our approach.Comment: Novel method for determining Union, Subtraction and Intersectio

The Double Hierarchy Method: a parallel 3D contact method for the interaction of spherical particles with rigid FE boundaries using the DEM

The final publication is available at Springer via http://dx.doi.org/10.1007/s40571-016-0109-4In this work, we present a new methodology for the treatment of the contact interaction between rigid boundaries and spherical discrete elements (DE). Rigid body parts are present in most of large-scale simulations. The surfaces of the rigid parts are commonly meshed with a finite element-like (FE) discretization. The contact detection and calculation between those DE and the discretized boundaries is not straightforward and has been addressed by different approaches. The algorithm presented in this paper considers the contact of the DEs with the geometric primitives of a FE mesh, i.e. facet, edge or vertex. To do so, the original hierarchical method presented by Horner et al. (J Eng Mech 127(10):1027–1032, 2001) is extended with a new insight leading to a robust, fast and accurate 3D contact algorithm which is fully parallelizable. The implementation of the method has been developed in order to deal ideally with triangles and quadrilaterals. If the boundaries are discretized with another type of geometries, the method can be easily extended to higher order planar convex polyhedra. A detailed description of the procedure followed to treat a wide range of cases is presented. The description of the developed algorithm and its validation is verified with several practical examples. The parallelization capabilities and the obtained performance are presented with the study of an industrial application example.Peer ReviewedPostprint (author's final draft

QuickCSG: Fast Arbitrary Boolean Combinations of N Solids

QuickCSG computes the result for general N-polyhedron boolean expressions without an intermediate tree of solids. We propose a vertex-centric view of the problem, which simplifies the identification of final geometric contributions, and facilitates its spatial decomposition. The problem is then cast in a single KD-tree exploration, geared toward the result by early pruning of any region of space not contributing to the final surface. We assume strong regularity properties on the input meshes and that they are in general position. This simplifying assumption, in combination with our vertex-centric approach, improves the speed of the approach. Complemented with a task-stealing parallelization, the algorithm achieves breakthrough performance, one to two orders of magnitude speedups with respect to state-of-the-art CPU algorithms, on boolean operations over two to dozens of polyhedra. The algorithm also outperforms GPU implementations with approximate discretizations, while producing an output without redundant facets. Despite the restrictive assumptions on the input, we show the usefulness of QuickCSG for applications with large CSG problems and strong temporal constraints, e.g. modeling for 3D printers, reconstruction from visual hulls and collision detection

Dense Piecewise Planar RGB-D SLAM for Indoor Environments

The paper exploits weak Manhattan constraints to parse the structure of indoor environments from RGB-D video sequences in an online setting. We extend the previous approach for single view parsing of indoor scenes to video sequences and formulate the problem of recovering the floor plan of the environment as an optimal labeling problem solved using dynamic programming. The temporal continuity is enforced in a recursive setting, where labeling from previous frames is used as a prior term in the objective function. In addition to recovery of piecewise planar weak Manhattan structure of the extended environment, the orthogonality constraints are also exploited by visual odometry and pose graph optimization. This yields reliable estimates in the presence of large motions and absence of distinctive features to track. We evaluate our method on several challenging indoors sequences demonstrating accurate SLAM and dense mapping of low texture environments. On existing TUM benchmark we achieve competitive results with the alternative approaches which fail in our environments.Comment: International Conference on Intelligent Robots and Systems (IROS) 201

Towards Full Automated Drive in Urban Environments: A Demonstration in GoMentum Station, California

Each year, millions of motor vehicle traffic accidents all over the world cause a large number of fatalities, injuries and significant material loss. Automated Driving (AD) has potential to drastically reduce such accidents. In this work, we focus on the technical challenges that arise from AD in urban environments. We present the overall architecture of an AD system and describe in detail the perception and planning modules. The AD system, built on a modified Acura RLX, was demonstrated in a course in GoMentum Station in California. We demonstrated autonomous handling of 4 scenarios: traffic lights, cross-traffic at intersections, construction zones and pedestrians. The AD vehicle displayed safe behavior and performed consistently in repeated demonstrations with slight variations in conditions. Overall, we completed 44 runs, encompassing 110km of automated driving with only 3 cases where the driver intervened the control of the vehicle, mostly due to error in GPS positioning. Our demonstration showed that robust and consistent behavior in urban scenarios is possible, yet more investigation is necessary for full scale roll-out on public roads.Comment: Accepted to Intelligent Vehicles Conference (IV 2017

A Novel Self-Intersection Penalty Term for Statistical Body Shape Models and Its Applications in 3D Pose Estimation

Statistical body shape models are widely used in 3D pose estimation due to their low-dimensional parameters representation. However, it is difficult to avoid self-intersection between body parts accurately. Motivated by this fact, we proposed a novel self-intersection penalty term for statistical body shape models applied in 3D pose estimation. To avoid the trouble of computing self-intersection for complex surfaces like the body meshes, the gradient of our proposed self-intersection penalty term is manually derived from the perspective of geometry. First, the self-intersection penalty term is defined as the volume of the self-intersection region. To calculate the partial derivatives with respect to the coordinates of the vertices, we employed detection rays to divide vertices of statistical body shape models into different groups depending on whether the vertex is in the region of self-intersection. Second, the partial derivatives could be easily derived by the normal vectors of neighboring triangles of the vertices. Finally, this penalty term could be applied in gradient-based optimization algorithms to remove the self-intersection of triangular meshes without using any approximation. Qualitative and quantitative evaluations were conducted to demonstrate the effectiveness and generality of our proposed method compared with previous approaches. The experimental results show that our proposed penalty term can avoid self-intersection to exclude unreasonable predictions and improves the accuracy of 3D pose estimation indirectly. Further more, the proposed method could be employed universally in triangular mesh based 3D reconstruction