Meshing Genus-1 Point Clouds Using Discrete One-Forms

We present an algorithm to mesh point clouds sampled from a closed manifold surface of genus 1. The method relies on a doubly periodic global parameterization of the point cloud to the plane, so no segmentation of the point cloud is required. Based on some recent techniques for parameterizing higher genus meshes, when some mild conditions on the sampling density are satisfied, the algorithm generates a closed toroidal manifold which interpolates the input and is geometrically similar to the sampled surface.Engineering and Applied Science

Free-boundary conformal parameterization of point clouds

With the advancement in 3D scanning technology, there has been a surge of interest in the use of point clouds in science and engineering. To facilitate the computations and analyses of point clouds, prior works have considered parameterizing them onto some simple planar domains with a fixed boundary shape such as a unit circle or a rectangle. However, the geometry of the fixed shape may lead to some undesirable distortion in the parameterization. It is therefore more natural to consider free-boundary conformal parameterizations of point clouds, which minimize the local geometric distortion of the mapping without constraining the overall shape. In this work, we develop a free-boundary conformal parameterization method for disk-type point clouds, which involves a novel approximation scheme of the point cloud Laplacian with accumulated cotangent weights together with a special treatment at the boundary points. With the aid of the free-boundary conformal parameterization, high-quality point cloud meshing can be easily achieved. Furthermore, we show that using the idea of conformal welding in complex analysis, the point cloud conformal parameterization can be computed in a divide-and-conquer manner. Experimental results are presented to demonstrate the effectiveness of the proposed method

One machine, one minute, three billion tetrahedra

This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A simple dedicated data structure, an efficient sorting of the points and the optimization of the insertion algorithm have permitted to accelerate reference implementations by a factor three. Our second contribution is a multi-threaded version of the Delaunay kernel that is able to concurrently insert vertices. Moore curve coordinates are used to partition the point set, avoiding heavy synchronization overheads. Conflicts are managed by modifying the partitions with a simple rescaling of the space-filling curve. The performances of our implementation have been measured on three different processors, an Intel core-i7, an Intel Xeon Phi and an AMD EPYC, on which we have been able to compute 3 billion tetrahedra in 53 seconds. This corresponds to a generation rate of over 55 million tetrahedra per second. We finally show how this very efficient parallel Delaunay triangulation can be integrated in a Delaunay refinement mesh generator which takes as input the triangulated surface boundary of the volume to mesh

ImMesh: An Immediate LiDAR Localization and Meshing Framework

In this paper, we propose a novel LiDAR(-inertial) odometry and mapping framework to achieve the goal of simultaneous localization and meshing in real-time. This proposed framework termed ImMesh comprises four tightly-coupled modules: receiver, localization, meshing, and broadcaster. The localization module utilizes the prepossessed sensor data from the receiver, estimates the sensor pose online by registering LiDAR scans to maps, and dynamically grows the map. Then, our meshing module takes the registered LiDAR scan for incrementally reconstructing the triangle mesh on the fly. Finally, the real-time odometry, map, and mesh are published via our broadcaster. The key contribution of this work is the meshing module, which represents a scene by an efficient hierarchical voxels structure, performs fast finding of voxels observed by new scans, and reconstructs triangle facets in each voxel in an incremental manner. This voxel-wise meshing operation is delicately designed for the purpose of efficiency; it first performs a dimension reduction by projecting 3D points to a 2D local plane contained in the voxel, and then executes the meshing operation with pull, commit and push steps for incremental reconstruction of triangle facets. To the best of our knowledge, this is the first work in literature that can reconstruct online the triangle mesh of large-scale scenes, just relying on a standard CPU without GPU acceleration. To share our findings and make contributions to the community, we make our code publicly available on our GitHub: https://github.com/hku-mars/ImMesh

Review of the mathematical foundations of data fusion techniques in surface metrology

The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed

A framework for hull form reverse engineering and geometry integration into numerical simulations

The thesis presents a ship hull form specific reverse engineering and CAD integration framework. The reverse engineering part proposes three alternative suitable reconstruction approaches namely curves network, direct surface fitting, and triangulated surface reconstruction. The CAD integration part includes surface healing, region identification, and domain preparation strategies which used to adapt the CAD model to downstream application requirements. In general, the developed framework bridges a point cloud and a CAD model obtained from IGES and STL file into downstream applications

Sensing of complex buildings and reconstruction into photo-realistic 3D models

The 3D reconstruction of indoor and outdoor environments has received an interest only recently, as companies began to recognize that using reconstructed models is a way to generate revenue through location-based services and advertisements. A great amount of research has been done in the field of 3D reconstruction, and one of the latest and most promising applications is Kinect Fusion, which was developed by Microsoft Research. Its strong points are the real-time intuitive 3D reconstruction, interactive frame rate, the level of detail in the models, and the availability of the hardware and software for researchers and enthusiasts. A representative effort towards 3D reconstruction is the Point Cloud Library (PCL). PCL is a large scale, open project for 2D/3D image and point cloud processing. On December 2011, PCL made available an implementation of Kinect Fusion, namely KinFu. KinFu emulates the functionality provided in Kinect Fusion. However, both implementations have two major limitations: 1. The real-time reconstruction takes place only within a cube with a size of 3 meters per axis. The cube's position is fixed at the start of execution, and any object outside of this cube is not integrated into the reconstructed model. Therefore the volume that can be scanned is always limited by the size of the cube. It is possible to manually align many small-size cubes into a single large model, however this is a time-consuming and difficult task, especially when the meshes have complex topologies and high polygon count, as is the case with the meshes obtained from KinFu. 2. The output mesh does not have any color textures. There are some at-tempts to add color in the output point cloud; however, the resulting effect is not photo-realistic. Applying photo-realistic textures to a model can enhance the user experience, even when the model has a simple topology. The main goal of this project is to design and implement a system that captures large indoor environments and generates 3D photo-realistic large indoor models in real time. This report describes an extended version of the KinFu system. The extensions overcome the scalability and texture reconstruction limitations using commodity hardware and open-source software. The complete hardware setup used in this project is worth €2,000, which is comparable to the cost of a single professional laser scanner. The software is released under BSD license, which makes it completely free to use and commercialize. The system has been integrated into the open-source PCL project. The immediate benefits are three-fold: the system becomes a potential industry standard, it is maintained and extended by many developers around the world with no addition-al cost to the VCA group, and it can reduce the application development time by reusing numerous state-of-the-art algorithms