Transactions of the Institute of British Geographers

In this paper we present an automatic algorithm to detect basic shapes in unorganized point clouds. The algorithm decomposes the point cloud into a concise, hybrid structure of inherent shapes and a set of remaining points. Each detected shape serves as a proxy for a set of corresponding points. Our method is based on random sampling and detects planes, spheres, cylinders, cones and tori. For models with surfaces composed of these basic shapes only, for example, CAD models, we automatically obtain a representation solely consisting of shape proxies. We demonstrate that the algorithm is robust even in the presence of many outliers and a high degree of noise. The proposed method scales well with respect to the size of the input point cloud and the number and size of the shapes within the data. Even point sets with several millions of samples are robustly decomposed within less than a minute. Moreover, the algorithm is conceptually simple and easy to implement. Application areas include measurement of physical parameters, scan registration, surface compression, hybrid rendering, shape classification, meshing, simplification, approximation and reverse engineering.

Efficient RANSAC for Point-Cloud Shape Detection

A method for concise, faithful approximation of complex 3D datasets is key to reducing the computational cost of graphics applications. Despite numerous applications ranging from geometry compression to reverse engineering, efficiently capturing the geometry of a surface remains a tedious task. In this paper, we present both theoretical and practical contributions that result in a novel and versatile framework for geometric approximation of surfaces. We depart from the usual strategy by casting shape approximation as a variational geometric partitioning problem. Using the concept of geometric proxies, we drive the distortion error down through repeated clustering of faces into best-fitting regions. Our approach is entirely discrete and error-driven, and does not require parameterization or local estimations of differential quantities. We also introduce a new metric based on normal deviation, and demonstrate its superior behavior at capturing anisotropy.

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Variational shape approximation

We present a review of the state of the art of segmentation and partitioning techniques of boundary meshes. Recently, these have become a part of many mesh and object manipulation algorithms in computer graphics, geometric modelling and computer aided design. We formulate the segmentation problem as an optimization problem and identify two primarily distinct types of mesh segmentation, namely part segmentation and surface-patch segmentation. We classify previous segmentation solutions according to the different segmentation goals, the optimization criteria and features used, and the various algorithmic techniques employed. We also present some generic algorithms for the major segmentation techniques.

A survey on Mesh Segmentation Techniques

Three-dimensional surface registration transforms multiple three-dimensional data sets into the same coordinate system so as to align overlapping components of these sets Recent surveys have covered different aspects of either rigid or nonrigid registration, but seldom discuss them as a whole Our study serves two purposes: 1) To give a comprehensive survey of both types of registration, focusing on three-dimensional point clouds and meshes and 2) to provide a better understanding of registration from the perspective of data fitting Registration is closely related to data fitting in which it comprises three core interwoven components: model selection, correspondences and constraints, and optimization Study of these components 1) provides a basis for comparison of the novelties of different techniques, 2) reveals the similarity of rigid and nonrigid registration in terms of problem representations, and 3) shows how overfitting arises in nonrigid registration and the reasons for increasing interest in intrinsic techniques We further summarize some practical issues of registration which include initializations and evaluations, and discuss some of our own observations, insights and foreseeable research trends

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Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid

In many areas of industry, it is desirable to create geometric models of existing objects for which no such model is available. This paper reviews the process of reverse engineering of shapes. After identifying the purpose of reverse engineering and the main application areas, the most important algorithmic steps are outlined and various reconstruction strategies are presented. Pros and cons of various data acquisition techniques are described with related problems of boundary representation model construction. Specific issues addressed include characterization of geometric models and related surface representations, segmentation and surface fitting for simple and free-form shapes, multiple view combination and creating consistent and accurate B-rep models. The limitations of currently known solutions are also described, and we point out areas in which further work is required before reverse engineering of shape becomes a practical, widely-available engineering tool.

Reverse engineering of geometric models—an introduction

Several methods have been developed for the computerized generation of space-filling curves, but these curves have never been used for NC tool-path generation. The paper discusses the application of space-filling curves as tool paths for sculptured-surface machining. Tool paths that are space-filling curves, single-direction conventional paths, and 2-direction conventional paths are compared. The efficiency ratings of the paths require further testing, but the preliminary conclusions are favourable for space-filling curves.

Space-filling curves in tool-path applications

Special issue: Reverse engineering of geometric models

Applying methods of mass customization to the empirical process can improve product development process efficiency and reduce time and cost. Empirical methods are used to develop predictions of product behavior in conjunction with analytical methods or instead of analytical methods. These empirical methods represent a complete sub-product development process within the overall product development process. Application of process decomposition and planning used in mass customization can improve the efficiency, lower the time and cost of these empirical processes. This paper presents a method for applying principles of mass customization to the empirical sub-processes within a product development process. Two case studies are also presented to demonstrate the method.

Applying principles of mass customization to improve the empirical product development process

Several optimization-based strategies have been proposed for compliant mechanism design that do not rely on the experience or intuition of the designer. This paper demonstrates an optimization-based method wherein compliant mechanisms are modeled parametrically within an optimization and a finite element analysis package. Topological optimization is performed to minimize an objective function representing the fitness of the design. This methodology exploits the nonlinear nature of compliant mechanisms and augments optimization-based methods previously proposed. Using this method, constant-force mechanisms optimized for a displacement from 4% to 25% of the mechanism’s total length were predicted to remain within 3.58% of constant force. Results from the testing of fabricated mechanisms are: for 425% displacement, within 7.5% constant force; for 18-65% displacement, within 2.3%. Path generation mechanisms were designed with similarly encouraging results.

Jordan J. Cox

Papers

Reverse engineering of geometric models—an introduction

Space-filling curves in tool-path applications

Special issue: Reverse engineering of geometric models

Applying principles of mass customization to improve the empirical product development process

A Parametric Approach to the Optimization-Based Design of Compliant Mechanisms