Non-Uniform Offsetting and its Applications in Laser Path Planning of Sterolithography Machine

Laser path planning is an important step in solid freeform fabrication processes such as Stereolithography (SLA). An important consideration in the laser path planning is to compensate the shape of laser beam. Currently the compensation is divided into two steps, Z-compensation and X-Y compensation, and the shape of laser beam is assumed to be uniform for the whole platform. In this research, we present a sampling based non-uniform offsetting method which accounts for the different shapes of laser beam at various locations. We discuss the related steps and algorithms. We demonstrate its effectiveness by using various test cases. Besides improving the accuracy of SLA machine, non-uniform offsetting can also be applied to address other accuracy issues caused by thermal and structural variationsMechanical Engineerin

Algorithms for LiDAR Based Traffic Tracking: Development and Demonstration

The current state of the art of traffic tracking is based on the use of video, and requires extensive manual intervention for it to work, including hours of painstaking human examination of videos frame by frame which also make the acquisition of data extremely expensive. Fundamentally, this is because we do not have observability of the actual scene from a camera which captures a 2D projection of the 3D world. Even if video were to be automated, it would involve such algorithms as RANSACK for outlier elimination while matching features across frames or across multiple cameras. This results in algorithms without stationary relationships between input and output statistics, i.e., between sensing resolution and error and estimated positions and velocities. LiDAR directly provides 3D point clouds, giving a one-one mapping between the scene from the physical world and data. However, available eye-safe lidars have been developed for autonomous vehicles, and provide only sparse point clouds when used for longer range data acquisition. Our experimental results use the Velodyne HDL 64E lidar. The sparse nature of data points returned by the Velodyne LiDAR rendered most of the algorithms for object identification and tracking using 3D point clouds at the point cloud library (PCL), a leading multi-agency open source research initiative focused on 3D point cloud processing ineffective for our work. Hence I developed a comprehensive set of algorithms developed to identify and remove background; detect objects through clustering of remaining points; associate detected objects across frames, track the detected objects, and estimate the dimension of objects. Two different complementary algorithms based on, surface equation (in 3D Cartesian coordinates) and LiDAR spherical coordinates were developed for background identification and removal. Delaunay triangulation based clustering is performed to identify objects. Kalman filter and Hungarian assignment algorithm are used in tandem to track multiple objects simultaneously. A novel bounding box algorithm was devised taking advantage of the way LiDAR scans the environment to predict the orientation and estimate dimension of objects. Trajectory analysis is performed to identify and split any wrong associations, join trajectories belonging to same object and stitch partial trajectories. Finally, the results are stored in a format usable by various transportation or traffic engineering applications. The algorithms were tested by peers with data collected at three intersections. Detection rate and counting accuracy are above 95% which is on par with commercial video solutions that employ humans to varying degrees. While prototyping for the algorithms was done it MATLAB, preliminary tests of conversion to C++ showed that the developed algorithms can be executed in real time on standard computer hardware

Comparison of methods for curvature estimation from volume fractions

This paper evaluates and compares the accuracy and robustness of curvature estimation methods for three-dimensional interfaces represented implicitly by discrete volume fractions on a Cartesian mesh. The height function (HF) method is compared to three paraboloid fitting methods: fitting to the piecewise linear interface reconstruction centroids (PC), fitting to the piecewise linear interface reconstruction volumetrically (PV), and volumetrically fitting (VF) the paraboloid directly to the volume fraction field. The numerical studies presented in this work find that while the curvature error from the VF method converges with second-order accuracy as with the HF method for static interfaces represented by exact volume fractions, the PV method best balances low curvature errors with low computational cost for dynamic interfaces when the interface reconstruction and advection are coupled to a two-phase Navier-Stokes solver

TScan: Stationary LiDAR for Traffic and Safety Studies—Object Detection and Tracking

The ability to accurately measure and cost-effectively collect traffic data at road intersections is needed to improve their safety and operations. This study investigates the feasibility of using laser ranging technology (LiDAR) for this purpose. The proposed technology does not experience some of the problems of the current video-based technology but less expensive low-end sensors have limited density of points where measurements are collected that may bring new challenges. A novel LiDAR-based portable traffic scanner (TScan) is introduced in this report to detect and track various types of road users (e.g., trucks, cars, pedestrians, and bicycles). The scope of this study included the development of a signal processing algorithm and a user interface, their implementation on a TScan research unit, and evaluation of the unit performance to confirm its practicality for safety and traffic engineering applications. The TScan research unit was developed by integrating a Velodyne HDL-64E laser scanner within the existing Purdue University Mobile Traffic Laboratory which has a telescoping mast, video cameras, a computer, and an internal communications network. The low-end LiDAR sensor’s limited resolution of data points was further reduced by the distance, the light beam absorption on dark objects, and the reflection away from the sensor on oblique surfaces. The motion of the LiDAR sensor located at the top of the mast caused by wind and passing vehicles was accounted for with the readings from an inertial sensor atop the LiDAR. These challenges increased the need for an effective signal processing method to extract the maximum useful information. The developed TScan method identifies and extracts the background with a method applied in both the spherical and orthogonal coordinates. The moving objects are detected by clustering them; then the data points are tracked, first as clusters and then as rectangles fit to these clusters. After tracking, the individual moving objects are classified in categories, such as heavy and non-heavy vehicles, bicycles, and pedestrians. The resulting trajectories of the moving objects are stored for future processing with engineering applications. The developed signal-processing algorithm is supplemented with a convenient user interface for setting and running and inspecting the results during and after the data collection. In addition, one engineering application was developed in this study for counting moving objects at intersections. Another existing application, the Surrogate Safety Analysis Model (SSAM), was interfaced with the TScan method to allow extracting traffic conflicts and collisions from the TScan results. A user manual also was developed to explain the operation of the system and the application of the two engineering applications. Experimentation with the computational load and execution speed of the algorithm implemented on the MATLAB platform indicated that the use of a standard GPU for processing would permit real-time running of the algorithms during data collection. Thus, the post-processing phase of this method is less time consuming and more practical. Evaluation of the TScan performance was evaluated by comparing to the best available method: video frame-by-frame analysis with human observers. The results comparison included counting moving objects; estimating the positions of the objects, their speed, and direction of travel; and counting interactions between moving objects. The evaluation indicated that the benchmark method measured the vehicle positions and speeds at the accuracy comparable to the TScan performance. It was concluded that the TScan performance is sufficient for measuring traffic volumes, speeds, classifications, and traffic conflicts. The traffic interactions extracted by SSAM required automatic post-processing to eliminate vehicle interactions at too low speed and between pedestrians – events that could not be recognized by SSAM. It should be stressed that this post processing does not require human involvement. Nighttime conditions, light rain, and fog did not reduce the quality of the results. Several improvements of this new method are recommended and discussed in this report. The recommendations include implementing two TScan units at large intersections and adding the ability to collect traffic signal indications during data collection

Planar hexagonal meshing for architecture

published_or_final_versio

Scene reconstruction using accumulated line-of-sight

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (leaves 49-52).by Christopher P. Stauffer.M.S

Iterating evolutes and involutes

This paper concerns iterations of two classical geometric constructions, the evolutes and involutes of plane curves, and their discretizations: evolutes and involutes of plane polygons. In the continuous case, our main result is that the iterated involutes of closed locally convex curves with rotation number one (possibly, with cusps) converge to their curvature centers (Steiner points), and their limit shapes are hypocycloids, generically, astroids. As a consequence, among such curves only the hypocycloids are homothetic to their evolutes. The bulk of the paper concerns two kinds of discretizations of these constructions: the curves are replaced by polygons, and the evolutes are formed by the circumcenters of the triples of consecutive vertices ( PP - evolutes), or by the incenters of the triples of consecutive sides ( AA -evolutes). For equiangular polygons, the theory is parallel to the continuous case: we define discrete hypocycloids (equiangular polygons whose sides are tangent to hypocycloids) and a discrete Steiner point. The space of polygons is a vector bundle over the space of the side directions; our main result here is that both kinds of evolutes define vector bundle morphisms. In the case of PP -evolutes, the induced map of the base is 4-periodic, and the dynamics reduces to the linear maps on the fibers. We prove that the spectra of these linear maps are symmetric with respect to the origin. The asymptotic dynamics of linear maps is determined by their eigenvalues with the maximum modulus, and we show that all types of behavior can occur: in particular, hyperbolic, when this eigenvalue is real, and elliptic, when it is complex. We also study PP - and AA -involutes and prove that the side directions of iterated AA -involutes of polygons with odd number of sides behave ergodically; this generalizes well-known results concerning iterations of the construction of the pedal triangle. In addition to the theoretical study, we performed numerous computer experiments; some of the observations remain unexplained

Wire mesh design

We present a computational approach for designing wire meshes, i.e., freeform surfaces composed of woven wires arranged in a regular grid. To facilitate shape exploration, we map material properties of wire meshes to the geometric model of Chebyshev nets. This abstraction is exploited to build an efficient optimization scheme. While the theory of Chebyshev nets suggests a highly constrained design space, we show that allowing controlled deviations from the underlying surface provides a rich shape space for design exploration. Our algorithm balances globally coupled material constraints with aesthetic and geometric design objectives that can be specified by the user in an interactive design session. In addition to sculptural art, wire meshes represent an innovative medium for industrial applications including composite materials and architectural façades. We demonstrate the effectiveness of our approach using a variety of digital and physical prototypes with a level of shape complexity unobtainable using previous methods

Probabilistic and parallel algorithms for centroidal Voronoi tessellations with application to meshless computing and numerical analysis on surfaces

Centroidal Voronoi tessellations (CVT) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions. Such tessellations are of use in very diverse applications, including data compression, clustering analysis, cell biology, territorial behavior of animals, optimal allocation of resources, and grid generation. A detailed review is given in chapter 1. In chapter 2, some probabilistic methods for determining centroidal Voronoi tessellations and their parallel implementation on distributed memory systems are presented. The results of computational experiments performed on a CRAY T3E-600 system are given for each algorithm. These demonstrate the superior sequential and parallel performance of a new algorithm we introduce. Then, new algorithms are presented in chapter 3 for the determination of point sets and associated support regions that can then be used in meshless computing methods. The algorithms are probabilistic in nature so that they are totally meshfree, i.e., they do not require, at any stage, the use of any coarse or fine boundary conforming or superimposed meshes. Computational examples are provided that show, for both uniform and non-uniform point distributions that the algorithms result in high-quality point sets and high-quality support regions. The extensions of centroidal Voronoi tessellations to general spaces and sets are also available. For example, tessellations of surfaces in a Euclidean space may be considered. In chapter 4, a precise definition of such constrained centroidal Voronoi tessellations (CCVT\u27s) is given and a number of their properties are derived, including their characterization as minimizers of a kind of energy. Deterministic and probabilistic algorithms for the construction of CCVT\u27s are presented and some analytical results for one of the algorithms are given. Some computational examples are provided which serve to illustrate the high quality of CCVT point sets. CCVT point sets are also applied to polynomial interpolation and numerical integration on the sphere. Finally, some conclusions are given in chapter 5