A Review of 3D Point Clouds Parameterization Methods

3D point clouds parameterization is a very important research topic in the fields of computer graphics and computer vision, which has many applications such as texturing, remeshing and morphing, etc. Different from mesh parameterization, point clouds parameterization is a more challenging task in general as there is normally no connectivity information between points. Due to this challenge, the papers on point clouds parameterization are not as many as those on mesh parameterization. To the best of our knowledge, there are no review papers about point clouds parameterization. In this paper, we present a survey of existing methods for parameterizing 3D point clouds. We start by introducing the applications and importance of point clouds parameterization before explaining some relevant concepts. According to the organization of the point clouds, we first divide point cloud parameterization methods into two groups: organized and unorganized ones. Since various methods for unorganized point cloud parameterization have been proposed, we further divide the group of unorganized point cloud parameterization methods into some subgroups based on the technique used for parameterization. The main ideas and properties of each method are discussed aiming to provide an overview of various methods and help with the selection of different methods for various applications

Local Energy Fairing of B-Spline Curves

An automatic algorithm for fairing B-spline curves of general order is presented. This work was motivated by a method of Farin and Sapidis about fairing planar cubic B-spline curves by subsequently removing and reinserting knots. Instead our new algorithm is based on the idea of subsequently changing one control point of a given B-spline curve so that the new curve minimizes the integral of the squared l-th derivative of the B-spline curve. How to proceed, if a tolerance is given and must be kept, is also discussed

Variational based analysis and modelling using B-splines

The use of energy methods and variational principles is widespread in many fields of engineering of which structural mechanics and curve and surface design are two prominent examples. In principle many different types of function can be used as possible trial solutions to a given variational problem but where piecewise polynomial behaviour and user controlled cross segment continuity is either required or desirable, B-splines serve as a natural choice. Although there are many examples of the use of B-splines in such situations there is no common thread running through existing formulations that generalises from the one dimensional case through to two and three dimensions. We develop a unified approach to the representation of the minimisation equations for B-spline based functionals in tensor product form and apply these results to solving specific problems in geometric smoothing and finite element analysis using the Rayleigh-Ritz method. We focus on the development of algorithms for the exact computation of the minimisation matrices generated by finding stationary values of functionals involving integrals of squares and products of derivatives, and then use these to seek new variational based solutions to problems in the above fields. By using tensor notation we are able to generalise the methods and the algorithms from curves through to surfaces and volumes. The algorithms developed can be applied to other fields where a variational form of the problem exists and where such tensor product B-spline functions can be specified as potential solutions.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Automatic parametric digital design of custom-fit bicycle helmets based on 3D anthropometry and novel clustering algorithm

Bicycle helmets can provide valuable protective effects to the wearer’s head in the event of a crash. However, the level of protection that helmets offer varies greatly between the users for similar impacts. Although these discrepancies can be due to many causes, several researchers highlighted the poor fit of helmets experienced by some users as a possible explanation. Poor helmet fit may be attributed to two main causes. First, the helmet could be worn incorrectly, with the helmet either worn back to front, or tilted forward or backward. The chin strap could also be unfastened. Second, helmet sizes and shapes available to the public might not be suitable for the full range of head morphologies observed in the population. Indeed, for some users, there could either be a large gap and/or pressure points between the inner surfaces of the helmet and the head, or a low coverage of the skull area with significant unprotected regions of the head. While the poorly informed usage of bicycle helmets is partly rectifiable through education programs, the mismatch between the head and the helmet’s inside surfaces primarily relates to the conventional design method and manufacturing techniques used in the industry today. In addition to the safety concerns described above, poorly fitted helmets can cause significant discomfort and may lead people to cycle infrequently or even not cycle altogether. Such a reaction could be somewhat detrimental to the user since the health benefits of regular cycling are significant. Some organisations and institutions even believe that the risks involved in cycling without a helmet (in not-extreme practices such as mountain biking) might be outweighed by the health benefits of consistent physical workout that the activity procures. However, this is impractical in countries such as Australia where mandatory helmet laws (MHL) are in place. Improper helmet fit coupled with MHL might be the reason why Australians cycle less than formerly, despite many initiatives undertaken by the government to grow the activity. In summary, current commercially available bicycle helmets suffer from the lack of fit accuracy, are uncomfortable, and consequently can discourage riding activities in the community, especially in populations like Australia where MHL exist. Therefore, the main purpose of this research has been to develop an innovative method to produce bicycle helmet models that provide a highly accurate fit to the wearer’s head. To achieve this goal, a mass customisation (MC) framework was initiated. MC systems enable the association of the small unit costs of mass production with the compliance of individual customisation. Although MC is defined as the use of both computer-aided design and manufacturing systems to produce custom output, it was decided to focus exclusively, in this study, on the design part of the MC framework of bicycle helmets. More specifically, I tried to answer the following central research question: How can one automatically create commercially ready, custom-fit digital 3D models of bicycle helmets based on 3D anthropometric data? One objective was to create certified design models, since helmets must comply with relevant safety regulations to be sold in a country. Safety standards generally determine the amount of energy a helmet must absorb during a crash, which mostly affects the thickness of its foam liner. Since customisation plays a major role in the helmet liner’s thickness, special considerations on how the automatic process should affect the helmet’s shape were provided. Contrary to conventional helmet production techniques, this method was based on state of the art technologies and techniques, such as three-dimensional (3D) anthropometry, supervised and unsupervised machine-learning methods, and fully parametric design models. Indeed, until today, traditional 1D anthropometric data (e.g., head circumference, head length, and head breath) have been the primary sources of information used by ergonomists for the design of user-centred products such as helmets. Although these data are simple to use and understand, they only provide univariate measures of key dimensions, and these tend to only partially represent the actual shape characteristics of the head. However, 3D anthropometric data can capture the full shape of a scanned surface, thereby providing meaningful information for the design of properly fitted headgear. However, the interpretation of these data can be complicated due to the abundance of information they contain (i.e., a 3D head scan can contain up to several million data points). In recent years, the use of 3D measurements for product design has become more appealing thanks to the advances in mesh parameterization, multivariate analyses, and clustering algorithms. Such analyses and algorithms have been adopted in this project. To the author’s knowledge, this is the first time that these methods have been applied to the design of helmets within a mass customisation framework. As a result, a novel method has been developed to automatically create a complete, certified custom-fit 3D model of a bicycle helmet based on the 3D head scan of a specific individual. Even though the manufacturing of the generated customised helmets is not discussed in detail in this research, it is envisaged that the models could be fabricated using either advanced subtractive and additive manufacturing technologies (e.g., numerical control machining and 3D printing.), standard moulding techniques, or a combination of both. The proposed design framework was demonstrated using a case study where customised helmet models were created for Australian cyclists. The computed models were evaluated and validated using objective (digital models) fit assessments. Thus, a significant improvement in terms of fit accuracy was observed compared to commercially available helmet models. More specifically, a set of new techniques and algorithms were developed, which successively: (i) clean, repair, and transform a digitized head scan to a registered state; (ii) compare it to the population of interest and categorize it into a predefined group; and (iii) modify the group’s generic helmet 3D model to precisely follow the head shape considered. To successfully implement the described steps, a 3D anthropometric database comprising 222 Australian cyclists was first established using a cutting edge handheld white light 3D scanner. Subsequently, a clustering algorithm, called 3D-HEAD-CLUSTERING, was introduced to categorize individuals with similar head shapes into groups. The algorithm successfully classified 95% of the sample into four groups. A new supervised learning method was then developed to classify new customers into one of the four computed groups. It was named the 3D-HEAD-CLASSIFIER. Generic 3D helmet models were then generated for each of the computed groups using the minimum, maximum, and mean shapes of all the participants classified inside a group. The generic models were designed specifically to comply with the relevant safety standard when accounting for all the possible head shape variations within a group. Furthermore, a novel quantitative method that investigates the fit accuracy of helmets was presented. The creation of the new method was deemed necessary, since the scarce computational methods available in the literature for fit assessment of user-centred products were inadequate for the complex shapes of today’s modern bicycle helmets. The HELMET-FIT-INDEX (HFI) was thus introduced, providing a fit score ranging on a scale from 0 (excessively poor fit) to 100 (perfect fit) for a specific helmet and a specific individual. In-depth analysis of three commercially available helmets and 125 participants demonstrated a consistent correlation between subjective assessment of helmet fit and the index. The HFI provided a detailed understanding of helmet efficiency regarding fit. For example, it was shown that females and Asians experience lower helmet fit accuracy than males and Caucasians, respectively. The index was used during the MC design process to validate the high fit accuracy of the generated customised helmet models. As far as the author is aware, HFI is the first method to successfully demonstrate an ability to evaluate users’ feelings regarding fit using computational analysis. The user-centred framework presented in this work for the customisation of bicycle helmet models is proved to be a valuable alternative to the current standard design processes. With the new approach presented in this research study, the fit accuracy of bicycle helmets is optimised, improving both the comfort and the safety characteristics of the headgear. Notwithstanding the fact that the method is easily adjustable to other helmet types (e.g., motorcycle, rock climbing, football, military, and construction), the author believes that the development of similar MC frameworks for user-centred products such as shoes, glasses and gloves could be adapted effortlessly. Future work should first emphasise the fabrication side of the proposed MC system and describe how customised helmet models can be accommodated in a global supply chain model. Other research projects could focus on adjusting the proposed customisation framework to other user-centred products