Solid reconstruction using recognition of quadric surfaces from orthographic views

International audienceThe reconstruction of 3D objects from 2D orthographic views is crucial for maintaining and further developing existing product designs. A B-rep oriented method for reconstructing curved objects from three orthographic views is presented by employing a hybrid wire-frame in place of an intermediate wire-frame. The Link-Relation Graph (LRG) is introduced as a multi-graph representation of orthographic views, and quadric surface features (QSFs) are defined by special basic patterns of LRG as well as aggregation rules. By hint-based pattern matching in the LRGs of three orthographic views in an order of priority, the corresponding QSFs are recognized, and the geometry and topology of quadric surfaces are recovered simultaneously. This method can handle objects with interacting quadric surfaces and avoids the combinatorial search for tracing all the quadric surfaces in an intermediate wire-frame by the existing methods. Several examples are provided

Constructing a wire-frame from views on arbitrary view planes for objects with conic sections inclined to all view planes

A new and efficient approach to construct a 3D wire-frame of an object from its orthographic projections is described. The input projections can be two or more and can include regular and complete auxiliary views. Each view may contain linear, circular and other conic sections. The output is a 3D wire-frame that is consistent with the input views. The approach can handle auxiliary views containing curved edges. This generality derives from a new technique to construct 3D vertices from the input 2D vertices (as opposed to matching coordinates that is prevalent in current art). 3D vertices are constructed by projecting the 2D vertices in a pair of views on the common line of the two views. The construction of 3D edges also does not require the addition of silhouette and tangential vertices and subsequently splitting edges in the views. The concepts of complete edges and n-tuples are introduced to obviate this need. Entities corresponding to the 3D edge in each view are first identified and the 3D edges are then constructed from the information available with the matching 2D edges. This allows the algorithm to handle conic sections that are not parallel to any of the viewing directions. The localization of effort in constructing 3D edges is the source of efficiency of the construction algorithm as it does not process all potential 3D edges. Working of the algorithm on typical drawings is illustrated. (C) 2011 Elsevier Ltd. All rights reserved

A research on a reconfigurable hypar structure for architectural applications

Thesis (Master)--İzmir Institute of Technology, Architecture, İzmir, 2013Includes bibliographical references (leaves: 102-108)Text in English; Abstract: Turkish and Englishxii, 108 leavesKinetic design strategy is a way to obtain remarkable applications in architecture. These kinetic designs can offer more advantages compared to conventional ones. Basic knowledge of different disciplines is necessary to generate kinetic designs. In other words, interdisciplinary studies are critical. Therefore, architect's knowledge must be wide-ranging in order to increase novel design approaches and applications. The resulting rich hybrid products increase the potential of the disciplines individually. Research on kinetic structures shows that the majority of kinetic structures are deployable. However, deployable structures can only be transformed from a closed compact configuration to a predetermined expanded form. The motivation of the present dissertation is generating a novel 2 DOF 8R reconfigurable structure which can meet different hyperbolic paraboloid surfaces for architectural applications. In order to obtain this novel structure; the integration between the mechanism science and architecture is essential. The term reconfigurable will be used in the present dissertation to describe deployable structures with various configurations. The novel reconfigurable design utilizes the overconstrained Bennett linkage and the production principals of ruled surfaces. The dissertation begins with a brief summary of deployable structures to show their shortcomings and their lack of form flexibility. Afterward, curved surfaces, basic terms in mechanisms and overconstrained mechanisms were investigated. Finally, a proposed novel mechanism which is inspired from the basic design principles of Bennett linkage and the fundamentals of ruled surfaces are explained with the help of kinematic diagrams and models

Non-contact free-form shape measurement for coordinate measuring machines

Precision measurement of manufactured parts commonly uses contact measurement methods. A Coordinate Measuring Machine (CMM) mounted probe touches the surface of the part, recording the probe’s tip position at each contact. Recently, devices have been developed that continuously scan the probe tip across the surface, allowing points to be measured more quickly. Contact measurement is accurate and fast for shapes that are easily parameterized such as a sphere or a plane, but is slow and requires considerable user input for more general objects such as those with free-form surfaces. Phase stepping fringe projection and photogrammetry are common non-contact shape measurement methods. Photogrammetry builds a 3D model of feature points from images of an object taken from multiple perspectives. In phase stepping fringe projection a series of sinusoidal patterns, with a phase shift between each, is projected towards an object. A camera records a corresponding series of images. The phase of the pattern at each imaged point is calculated and converted to a 3D representation of the object’s surface. Techniques combining phase stepping fringe projection and photogrammetry were developed and are described here. The eventual aim is to develop an optical probe for a CMM to enable non-contact measurement of objects in an industrial setting. For the CMM to accurately report its position the probe must be small, light, and robust. The methods currently used to provide a phase shift require either an accurately calibrated translation stage to move an internal component, or a programmable projector. Neither of these implementations can be practically mounted on a CMM due to size and weight limits or the delicate parts required. A CMM probe consisting of a single camera and a fringe projector was developed. The fringe projector projects a fixed fringe pattern. Phase steps are created by moving the CMM mounted probe, taking advantage of the geometry of the fringe projection system. New techniques to calculate phase from phase stepped images created by relative motion of probe and object are proposed, mathematically modelled, and tested experimentally. Novel techniques for absolute measurement of surfaces by viewing an object from different perspectives are developed. A prototype probe is used to demonstrate measurements of a variety of objects.Engineering and Physical Sciences Research Council (EPSRC) Grant No. GR/T11289/0

Logic and intuition in architectural modelling: philosophy of mathematics for computational design

This dissertation investigates the relationship between the shift in the focus of architectural modelling from object to system and philosophical shifts in the history of mathematics that are relevant to that change. Particularly in the wake of the adoption of digital computation, design model spaces are more complex, multidimensional, arguably more logical, less intuitive spaces to navigate, less accessible to perception and visual comprehension. Such spatial issues were encountered much earlier in mathematics than in architectural modelling, with the growth of analytical geometry, a transition from Classical axiomatic proofs in geometry as the basis of mathematics, to analysis as the underpinning of geometry. Can the computational design modeller learn from the changing modern history, philosophy and psychology of mathematics about the construction and navigation of computational geometrical architectural system model space? The research is conducted through a review of recent architectural project examples and reference to three more detailed architectural modelling case studies. The spatial questions these examples and case studies raise are examined in the context of selected historical writing in the history, philosophy and psychology of mathematics and space. This leads to conclusions about changes in the relationship of architecture and mathematics, and reflections on the opportunities and limitations for architectural system models using computation geometry in the light of this historical survey. This line of questioning was motivated as a response to the experience of constructing digital associative geometry models and encountering the apparent limits of their flexibility as the graph of dependencies grew and the messiness of the digital modelling space increased. The questions were inspired particularly by working on the Narthex model for the Sagrada Família church, which extends to many tens of thousands of relationships and constraints, and which was modelled and repeatedly partially remodelled over a very long period. This experience led to the realisation that the limitations of the model were not necessarily the consequence of poor logical schema definition, but could be inevitable limitations of the geometry as defined, regardless of the means of defining it, the ‘shape’ of the multidimensional space being created. This led to more fundamental questions about the nature of Space, its relationship to geometry and the extent to which the latter can be considered simply as an operational and notational system. This dissertation offers a purely inductive journey, offering evidence through very selective examples in architecture, architectural modelling and in the philosophy of mathematics. The journey starts with some questions about the tendency of the model space to break out and exhibit unpredictable and not always desirable behaviour and the opportunities for geometrical construction to solve these questions is not conclusively answered. Many very productive questions about computational architectural modelling are raised in the process of looking for answers

ACS Without an Attitude

The book (ACS without an Attitude) is an introduction to spacecraft attitude control systems. It is based on a series of lectures that Dr. Hallock presented in the early 2000s to members of the GSFC flight software branch, the target audience being flight software engineers (developers and testers), fairly new to the field that desire an introductory understanding of spacecraft attitude determination and control

3D reconstruction of coronary arteries from angiographic sequences for interventional assistance

Introduction -- Review of literature -- Research hypothesis and objectives -- Methodology -- Results and discussion -- Conclusion and future perspectives

Mathematical surfaces models between art and reality

In this paper, I want to document the history of the mathematical surfaces models used for the didactics of pure and applied “High Mathematics” and as art pieces. These models were built between the second half of nineteenth century and the 1930s. I want here also to underline several important links that put in correspondence conception and construction of models with scholars, cultural institutes, specific views of research and didactical studies in mathematical sciences and with the world of the figurative arts furthermore. At the same time the singular beauty of form and colour which the models possessed, aroused the admiration of those entirely ignorant of their mathematical attraction

The benefits of an additional practice in descriptive geomerty course: non obligatory workshop at the Faculty of Civil Engineering in Belgrade

At the Faculty of Civil Engineering in Belgrade, in the Descriptive geometry (DG) course, non-obligatory workshops named “facultative task” are held for the three generations of freshman students with the aim to give students the opportunity to get higher final grade on the exam. The content of this workshop was a creative task, performed by a group of three students, offering free choice of a topic, i.e. the geometric structure associated with some real or imagery architectural/art-work object. After the workshops a questionnaire (composed by the professors at the course) is given to the students, in order to get their response on teaching/learning materials for the DG course and the workshop. During the workshop students performed one of the common tests for testing spatial abilities, named “paper folding". Based on the results of the questionnairethe investigation of the linkages between:students’ final achievements and spatial abilities, as well as students’ expectations of their performance on the exam, and how the students’ capacity to correctly estimate their grades were associated with expected and final grades, is provided. The goal was to give an evidence that a creative work, performed by a small group of students and self-assessment of their performances are a good way of helping students to maintain motivation and to accomplish their achievement. The final conclusion is addressed to the benefits of additional workshops employment in the course, which confirmhigherfinal scores-grades, achievement of creative results (facultative tasks) and confirmation of DG knowledge adaption