Intelligent sampling for the measurement of structured surfaces

Uniform sampling in metrology has known drawbacks such as coherent spectral aliasing and a lack of efficiency in terms of measuring time and data storage. The requirement for intelligent sampling strategies has been outlined over recent years, particularly where the measurement of structured surfaces is concerned. Most of the present research on intelligent sampling has focused on dimensional metrology using coordinate-measuring machines with little reported on the area of surface metrology. In the research reported here, potential intelligent sampling strategies for surface topography measurement of structured surfaces are investigated by using numerical simulation and experimental verification. The methods include the jittered uniform method, low-discrepancy pattern sampling and several adaptive methods which originate from computer graphics, coordinate metrology and previous research by the authors. By combining the use of advanced reconstruction methods and feature-based characterization techniques, the measurement performance of the sampling methods is studied using case studies. The advantages, stability and feasibility of these techniques for practical measurements are discussed

Mobile Paving System (MPS): A New Large Scale Freeform Fabrication Method

In the last decade, significant opportunities for automation have been identified in the area of construction. Soaring labor and material costs have driven multiple research efforts in construction automation. In this paper, we present a novel means for construction automation that involves the fusion of the rapid prototyping, controls and mechatronics technologies. The resultant autonomous construction mechanism has been designed for commercial applications. Mobile Paving System (MPS) is a new freeform fabrication process which is capable of rapidly producing variable profiles such as curbs and sidewalks out of materials like cement and asphalt. Path generation and guidance of the construction operation is controlled by a mobile robot. This article presents an overview of research and development efforts that are aimed at establishing the feasibility and the potential of the process.Mechanical Engineerin

Optimized normal and distance matching for heterogeneous object modeling

This paper presents a new optimization methodology of material blending for heterogeneous object modeling by matching the material governing features for designing a heterogeneous object. The proposed method establishes point-to-point correspondence represented by a set of connecting lines between two material directrices. To blend the material features between the directrices, a heuristic optimization method developed with the objective is to maximize the sum of the inner products of the unit normals at the end points of the connecting lines and minimize the sum of the lengths of connecting lines. The geometric features with material information are matched to generate non-self-intersecting and non-twisted connecting surfaces. By subdividing the connecting lines into equal number of segments, a series of intermediate piecewise curves are generated to represent the material metamorphosis between the governing material features. Alternatively, a dynamic programming approach developed in our earlier work is presented for comparison purposes. Result and computational efficiency of the proposed heuristic method is also compared with earlier techniques in the literature. Computer interface implementation and illustrative examples are also presented in this paper

Discrete algorithms for morphological filters in geometrical metrology

In geometrical metrology, morphological filters are useful tools for the surface texture analysis and functional prediction. Although they are generally accepted and regarded as the complement to mean-line based filters, they are not universally adopted in practice due to a number of fatal limitations in their implementations —they are restricted to planar surfaces, uniform sampled surfaces, time-consuming and suffered from end distortions and limited sizes of structuring elements. A novel morphological method is proposed based on the alpha shape with the advantages over traditional methods that it enables arbitrary large ball radii, and applies to freeform surfaces and non-uniform sampled surfaces. A practical algorithm is developed based on the theoretical link between the alpha hull and morphological envelopes. The performance bottleneck due to the costly 3D Delaunay triangulation is solved by the divide-and-conquer optimization. Aiming to overcome the deficits of the alpha shape method that the structuring element has to be circular and the computation relies on the Delaunay triangulation, a set of definitions, propositions and comments for searching contact points is proposed and mathematically proved based on alpha shape theory, followed by the construction of a recursive algorithm. The algorithm could precisely capture contact points without performing the Delaunay triangulation. By correlating the convex hull and morphological envelopes, the Graham scan algorithm, originally developed for the convex hull, is modified to compute morphological profile envelopes with an excellent performance achieved. The three novel methods along with the two traditional methods are compared and analyzed to evaluate their advantages and disadvantages. The end effects of morphological filtration on open surfaces are discussed and four end effect correction methods are explored. Case studies are presented to demonstrate the feasibility and capabilities of using the proposed discrete algorithms

Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces

We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature directions and closely approximate the curved parts of the input developable, and planar polygons representing the flat parts of the input. Developable PQ-strip meshes are useful in many areas of shape modeling, thanks to the simplicity of fabrication from flat sheet material. Unfortunately, they are difficult to model due to their restrictive combinatorics and locking issues. Other representations of developable surfaces, such as arbitrary triangle or quad meshes, are more suitable for interactive freeform modeling, but generally have non-planar faces or are not aligned to principal curvatures. Our method leverages the modeling flexibility of non-ruling based representations of developable surfaces, while still obtaining developable, curvature aligned PQ-strip meshes. Our algorithm optimizes for a scalar function on the input mesh, such that its level sets are extrinsically straight and align well to the locally estimated ruling directions. The condition that guarantees straight level sets is nonlinear of high order and numerically difficult to enforce in a straightforward manner. We devise an alternating optimization method that makes our problem tractable and practical to compute. Our method works automatically on any developable input, including multiple patches and curved folds, without explicit domain decomposition. We demonstrate the effectiveness of our approach on a variety of developable surfaces and show how our remeshing can be used alongside handle based interactive freeform modeling of developable shapes

LiDAR-Based Object Tracking and Shape Estimation

Umfeldwahrnehmung stellt eine Grundvoraussetzung für den sicheren und komfortablen Betrieb automatisierter Fahrzeuge dar. Insbesondere bewegte Verkehrsteilnehmer in der unmittelbaren Fahrzeugumgebung haben dabei große Auswirkungen auf die Wahl einer angemessenen Fahrstrategie. Dies macht ein System zur Objektwahrnehmung notwendig, welches eine robuste und präzise Zustandsschätzung der Fremdfahrzeugbewegung und -geometrie zur Verfügung stellt. Im Kontext des automatisierten Fahrens hat sich das Box-Geometriemodell über die Zeit als Quasistandard durchgesetzt. Allerdings stellt die Box aufgrund der ständig steigenden Anforderungen an Wahrnehmungssysteme inzwischen häufig eine unerwünscht grobe Approximation der tatsächlichen Geometrie anderer Verkehrsteilnehmer dar. Dies motiviert einen Übergang zu genaueren Formrepräsentationen. In der vorliegenden Arbeit wird daher ein probabilistisches Verfahren zur gleichzeitigen Schätzung von starrer Objektform und -bewegung mittels Messdaten eines LiDAR-Sensors vorgestellt. Der Vergleich dreier Freiform-Geometriemodelle mit verschiedenen Detaillierungsgraden (Polygonzug, Dreiecksnetz und Surfel Map) gegenüber dem einfachen Boxmodell zeigt, dass die Reduktion von Modellierungsfehlern in der Objektgeometrie eine robustere und präzisere Parameterschätzung von Objektzuständen ermöglicht. Darüber hinaus können automatisierte Fahrfunktionen, wie beispielsweise ein Park- oder Ausweichassistent, von einem genaueren Wissen über die Fremdobjektform profitieren. Es existieren zwei Einflussgrößen, welche die Auswahl einer angemessenen Formrepräsentation maßgeblich beeinflussen sollten: Beobachtbarkeit (Welchen Detaillierungsgrad lässt die Sensorspezifikation theoretisch zu?) und Modell-Adäquatheit (Wie gut bildet das gegebene Modell die tatsächlichen Beobachtungen ab?). Auf Basis dieser Einflussgrößen wird in der vorliegenden Arbeit eine Strategie zur Modellauswahl vorgestellt, die zur Laufzeit adaptiv das am besten geeignete Formmodell bestimmt. Während die Mehrzahl der Algorithmen zur LiDAR-basierten Objektverfolgung ausschließlich auf Punktmessungen zurückgreift, werden in der vorliegenden Arbeit zwei weitere Arten von Messungen vorgeschlagen: Information über den vermessenen Freiraum wird verwendet, um über Bereiche zu schlussfolgern, welche nicht von Objektgeometrie belegt sein können. Des Weiteren werden LiDAR-Intensitäten einbezogen, um markante Merkmale wie Nummernschilder und Retroreflektoren zu detektieren und über die Zeit zu verfolgen. Eine ausführliche Auswertung auf über 1,5 Stunden von aufgezeichneten Fremdfahrzeugtrajektorien im urbanen Bereich und auf der Autobahn zeigen, dass eine präzise Modellierung der Objektoberfläche die Bewegungsschätzung um bis zu 30%-40% verbessern kann. Darüber hinaus wird gezeigt, dass die vorgestellten Methoden konsistente und hochpräzise Rekonstruktionen von Objektgeometrien generieren können, welche die häufig signifikante Überapproximation durch das einfache Boxmodell vermeiden

Virtual prototyping with surface reconstruction and freeform geometric modeling using level-set method

More and more products with complex geometries are being designed and manufactured by computer aided design (CAD) and rapid prototyping (RP) technologies. Freeform surface is a geometrical feature widely used in modern products like car bodies, airfoils and turbine blades as well as in aesthetic artifacts. How to efficiently design and generate digital prototypes with freeform surfaces is an important issue in CAD. This paper presents the development of a Virtual Sculpting system and addresses the issues of surface reconstruction from dexel data structures and freeform geometric modeling using the level-set method from distance field structure. Our virtual sculpting method is based on the metaphor of carving a solid block into a 3D freeform object using a 3D haptic input device integrated with the computer visualization. This dissertation presents the result of the study and consists primarily of four papers --Abstract, page iv

Modeling planar 3-valence meshes

In architectural and sculptural practice, the eventual goal is constructing the shapes that have been designed. Due to fabrication considerations, shapes with planar faces are in demand for these practices. In this thesis, a novel computational modeling approach to design constructible shapes is introduced. This method guarantees that the resulting shapes are planar meshes with 3-valence vertices, which can always be physically constructed using planar or developable materials such as glass, sheet metal or plywood. The method introduced is inspired by the traditional sculpture and is based on the idea of carving a mesh by using slicing planes. The process of determining the slicing planes can either be interactive or automated. A framework is developed which allows user to sculpt shapes by using the in- teractive and automated processes. The framework allows user to cut a source mesh based on its edges, faces or vertices. The user can sculpt various kinds of developable surfaces by cutting the parallel edges of the mesh. The user can also introduce in- teresting conical patterns by cutting dierent vertex, edge, face combinations of the mesh

Parametric Deformation of Discrete Geometry for Aerodynamic Shape Design

We present a versatile discrete geometry manipulation platform for aerospace vehicle shape optimization. The platform is based on the geometry kernel of an open-source modeling tool called Blender and offers access to four parametric deformation techniques: lattice, cage-based, skeletal, and direct manipulation. Custom deformation methods are implemented as plugins, and the kernel is controlled through a scripting interface. Surface sensitivities are provided to support gradient-based optimization. The platform architecture allows the use of geometry pipelines, where multiple modelers are used in sequence, enabling manipulation difficult or impossible to achieve with a constructive modeler or deformer alone. We implement an intuitive custom deformation method in which a set of surface points serve as the design variables and user-specified constraints are intrinsically satisfied. We test our geometry platform on several design examples using an aerodynamic design framework based on Cartesian grids. We examine inverse airfoil design and shape matching and perform lift-constrained drag minimization on an airfoil with thickness constraints. A transport wing-fuselage integration problem demonstrates the approach in 3D. In a final example, our platform is pipelined with a constructive modeler to parabolically sweep a wingtip while applying a 1-G loading deformation across the wingspan. This work is an important first step towards the larger goal of leveraging the investment of the graphics industry to improve the state-of-the-art in aerospace geometry tools

Triangulation of uniform particle systems: its application to the implicit surface texturing

Particle systems, as originally presented by Witkin and Heckbert [32], offer an elegant solution to sample implicit surfaces of arbitrary genus, while providing an extremely regular distribution of samples over the surface. In this paper, we present an ef cient technique that uses particle systems to rapidly generate a triangular mesh over an implicit surface, where each triangle is almost equilateral. The major advantage of such a triangulation is that it minimizes the deformations between the mesh and the underlying implicit surface. We exploit this property by using few triangular texture samples mapped in a non-periodic fashion as presented by Neyret and Cani [16]. The result is a pattern-based texturing method that maps homogeneous non-periodic textures to arbitrary implicit surfaces, with almost no deformation