Convex Grid Drawings of Plane Graphs with Rectangular Contours

In a convex drawing of a plane graph, all edges are drawn as straight-line segments without any edge-intersection and all facial cycles are drawn as convex polygons. In a convex grid drawing, all vertices are put on grid points. A plane graph G has a convex drawing if and only if G is internally triconnected, and an internally triconnected plane graph G has a convex grid drawing on an n × n grid if G is triconnected or the triconnected component decomposition tree T (G) of G has two or three leaves, where n is the number of vertices in G. In this paper, we show that an internally triconnected plane graph G has a convex grid drawing on a 2n × n 2 grid if T (G) has exactly four leaves. We also present an algorithm to find such a drawing in linear time. Our convex grid drawing has a rectangular contour, while most of the known algorithms produce grid drawings having triangular contours

The role of computer-aided design in the learning of practical 3D-descriptive geometry: a case study

There are a number of problems surrounding the teaching of practical 3-D descriptive geometry to children in secondary education, notably the difficulty pupils have with visualising an object's form from orthographic views, and the interpretation of an object's geometric attributes into the descriptive geometry representation. The purpose of the current research is to evaluate the use of computer-aided design in this area of the curriculum and is based upon work undertaken in a North London comprehensive school. The school and its context is described and evaluated. Theories of child development and educational psychology of relevance to the study are reviewed, notably the work of Piaget, Bryant, Gagne, and Freeman. The history and nature of 3-D descriptive geometry is reviewed in practice and in education, with special reference to various methods employed in instruction. Dr. J. Vince's PICASO SYSTEM of computer subroutines and functions written in FORTRAN for graphic applications is explained as a means of teaching the subject, with special reference to the researcher's own instructional material and computer programs. The use and effectiveness of these teaching materials are related and evaluated in the light of students' performance and results. The research concludes that the special benefits of computer graphics in this field are: the economic production of appropriate didactic material under the direct control of the teacher, increased pupil motivation due to the use of better illustration and the interest generated by computer-aided design project work. and an opportunity to employ analytic geometry to support learning. Its limitations include: the high cost of the computer and peripheral devices, and the lack of a facility for modelling objects by the removal of solid volumes in the existing software. Further research is recommended in the areas of computer graphics, descriptive geometry, and psychology

A system that learns to recognize 3-D objects

A system that learns to recognize 3-D objects from single and multiple views is presented. It consists of three parts: a simulator of 3-D figures, a Learner, and a recognizer. The 3-D figure simulator generates and plots line drawings of certain 3-D objects. A series of transformations leads to a number of 2-D images of a 3-D object, which are considered as different views and are the basic input to the next two parts. The learner works in three stages using the method of Learning from examples. In the first stage an elementary-concept learner learns the basic entities that make up a line drawing. In the second stage a multiple-view learner learns the definitions of 3-D objects that are to be recognized from multiple views. In the third stage a single-view learner learns how to recognize the same objects from single views. The recognizer is presented with line drawings representing 3-D scenes. A single-view recognizer segments the input into faces of possible 3-D objects, and attempts to match the segmented scene with a set of single-view definitions of 3-D objects. The result of the recognition may include several alternative answers, corresponding to different 3-D objects. A unique answer can be obtained by making assumptions about hidden elements (e. g. faces) of an object and using a multiple-view recognizer. Both single-view and multiple-view recognition are based on the structural relations of the elements that make up a 3-D object. Some analytical elements (e. g. angles) of the objects are also calculated, in order to determine point containment and conveziti. The system performs well on polyhedra with triangular and quadrilateral faces. A discussion of the system's performance and suggestions for further development is given at the end. The simulator and the part of the recognizer that makes the analytical calculations are written in C. The learner and the rest of the recognizer are written in PROLOG

Evaluation of lntelligent Medical Systems

This thesis presents novel, robust, analytic and algorithmic methods for calculating Bayesian posterior intervals of receiver operating characteristic (ROC) curves and confusion matrices used for the evaluation of intelligent medical systems tested with small amounts of data. Intelligent medical systems are potentially important in encapsulating rare and valuable medical expertise and making it more widely available. The evaluation of intelligent medical systems must make sure that such systems are safe and cost effective. To ensure systems are safe and perform at expert level they must be tested against human experts. Human experts are rare and busy which often severely restricts the number of test cases that may be used for comparison. The performance of expert human or machine can be represented objectively by ROC curves or confusion matrices. ROC curves and confusion matrices are complex representations and it is sometimes convenient to summarise them as a single value. In the case of ROC curves, this is given as the Area Under the Curve (AUC), and for confusion matrices by kappa, or weighted kappa statistics. While there is extensive literature on the statistics of ROC curves and confusion matrices they are not applicable to the measurement of intelligent systems when tested with small data samples, particularly when the AUC or kappa statistic is high. A fundamental Bayesian study has been carried out, and new methods devised, to provide better statistical measures for ROC curves and confusion matrices at low sample sizes. They enable exact Bayesian posterior intervals to be produced for: (1) the individual points on a ROC curve; (2) comparison between matching points on two uncorrelated curves; . (3) the AUC of a ROC curve, using both parametric and nonparametric assumptions; (4) the parameters of a parametric ROC curve; and (5) the weight of a weighted confusion matrix. These new methods have been implemented in software to provide a powerful and accurate tool for developers and evaluators of intelligent medical systems in particular, and to a much wider audience using ROC curves and confusion matrices in general. This should enhance the ability to prove intelligent medical systems safe and effective and should lead to their widespread deployment. The mathematical and computational methods developed in this thesis should also provide the basis for future research into determination of posterior intervals for other statistics at small sample sizes

Characteristics of flight simulator visual systems

The physical parameters of the flight simulator visual system that characterize the system and determine its fidelity are identified and defined. The characteristics of visual simulation systems are discussed in terms of the basic categories of spatial, energy, and temporal properties corresponding to the three fundamental quantities of length, mass, and time. Each of these parameters are further addressed in relation to its effect, its appropriate units or descriptors, methods of measurement, and its use or importance to image quality

Object Recognition

Vision-based object recognition tasks are very familiar in our everyday activities, such as driving our car in the correct lane. We do these tasks effortlessly in real-time. In the last decades, with the advancement of computer technology, researchers and application developers are trying to mimic the human's capability of visually recognising. Such capability will allow machine to free human from boring or dangerous jobs

Designing aesthetically pleasing freeform surfaces in a computer environment

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, February 2001.Includes bibliographical references (p. 151-160).Statement: If computational tools are to be employed in the aesthetic design of freeform surfaces, these tools must better reflect the ways in which creative designers conceive of and develop such shapes. In this thesis, I studied the design of aesthetically constrained freeform surfaces in architecture and industrial design, formulated a requirements list for a computational system that would aid in the creative design of such surfaces, and implemented a subset of the tools that would comprise such a system. This work documents the clay modeling process at BMW AG., Munich. The study of that process has led to a list of tools that would make freeform surface modeling possible in a computer environment. And finally, three tools from this system specification have been developed into a proof-of-concept system. Two of these tools are sweep modification tools and the third allows a user to modify a surface by sketching a shading pattern desired for the surface. The proof-of-concept tools were necessary in order to test the validity of the tools being presented and they have been used to create a number of example objects. The underlying surface representation is a variational expression which is minimized using the finite element method over an irregular triangulated mesh.by Evan P. Smyth.Ph.D