TITLE: Tools for 3D modelling in teaching solid geometry AUTHOR: Bc. Jana Taušová DEPARTMENT: Department of Information Technology and Technology Education SUPERVISOR: PhDr. Josef Procházka, Ph.D. ABSTRACT: The key topic of the thesis is the possibility of enhancement of the teaching of solid geometry through a 3D modelling program of choice. The theoretical part of the work defines solid geometry as a branch of mathematics. It furthermore investigates spatial visualization ability as a crucial one for understanding this particular area; and also explains the possibilities of computer program usage. The practical part starts with an inquiry into the use of ICT tools at secondary schools in the Czech Republic. Then there is an overview of the programs suitable for teaching, and methodology for a particular section of solid geometry curriculum. The suggestions mentioned in the methodology section have been used during class work (the 7th year students of an 8-year comprehensive grammar school), as specified in the last part of the work. Thus we have researched the actual practical use of our theoretical inferences. KEY WORDS: Tools for 3D modelling, ICT support for education, spatial visualization ability, solid geometry

In this thesis we develop a 3D soft object modeling system with implicit functions. Our system provides implicit functions including the primitive functions and blending functions to modeling soft object. The system satisfies some requirements, such as intuitive operating environment, the Model-View-Controller (MVC) system architecture, and extensibility, etc. The system consists of four major parts: (1) the graphical user interface (GUI); (2) the constructive tree viewing Subsystem; (3) the implicit function operating Subsystem; (4) the 3D scene graph rendering Subsystem. The GUI initializes the window frame and responds to the event messages dispatched from the OS or applications. The constructive tree viewing Subsystem presents the composition of the object modal with the tree structure. The implicit function operating system accomplishes the polygon tessellation, that is, it translates the blending tree with the implicit functions to polygon meshes. The 3D scene graph rendering system renders the polygon mesh and provides 3D scene graph manipulations.

In recent years, it is becoming more and more common to utilize 3D modeling technology to reconstruct cultural heritages. The most common way to deliver the 3D model of an existing object is based on hands-on surveys and CAD tools which could be impractical for large or complex structure in term of time consumption and cost. Recently, laser scanning technology and more automated photogrammetric modeling methods become available, and making the 3D reconstruction process of real world objects easier. Photogrammetry is one of the most cost-effective approaches we could use to gather the physical information of an object, such as size, location, and appearance. Also, the operation of the equipment of photogrammetry, which is a camera, is very easy and cost-effective. However, it also has its drawback, which is mainly caused the outcome’s low accuracy level. Accurate drawings or models only have been achieved with other approaches, such as 3D laser scanning or total station. The 3D model of the Francis Hall at Texas A&M University, which will be renovated soon, was created in order to investigate whether the image-based 3D model produced using photogrammetry technology would be acceptable or not for the use in renovation projects. For this investigation, the elapsed time for data acquisition and 3D modeling was measured. The accuracy level of the image-based 3D model and the deficiencies of this approach were also recorded. Then, the image-based 3D model of Francis Hall was presented in the BIM CAVE to four industry professionals and one graduate student. The regular 3D model of the Francis Hall, which was created, using dimensions extracted from 2D drawings, was also presented to the interviewees in the BIM CAVE. After watching two different 3D models (image-based 3D model and regular 3D model) of the same Francis Hall, five interviewees were requested to describe the differences they noticed between image-based 3D model and regular 3D model presented in the BIM CAVE. By reviewing and analyzing the data from interviews. Following conclusions could be made. First, the image-based 3D model of Francis Hall gave people more feeling of reality than the traditional CAD drawings or BIM models. Second, the image-based 3D model could be used for saving travels, showing details, improving coordination, improving design, facilities management tool, and marketing tool. Third, in order to make it practical for the industry, the time consumption and cost of generating the image-based 3D model should be at least equivalent to time consumption and cost for architects to conduct survey and generate CAD drawings or BIM model.

Three-dimensional (3D) visualization is rapidly becoming an important tool for many engineering projects. Accurate digital representations of terrain and ground features are extremely useful for efficient design, communication and data representation in projects involving land development, transportation planning, hydrologic analysis, environmental impact studies, and much more. Within the scope of terrain modeling lie a wide variety of techniques used to build digital elevation models (DEMs). Each approach has inherent problems and difficulties that can alter the accuracy and usability of the DEM produced. The main objectives of this study are to examine the various methods used for the creation of digital elevation models and make recommendations as to the appropriate techniques to use depending on specific project circumstances. Data sets generated using two of the methods, photogrammetry and LIDAR, are used to build digital terrain models in various software packages for an analysis of data usability and function. The key results of this research project are two DEMs of a real-world transportation study area and a set of conclusions and recommendations that give insight into the exact methods to be used on various projects. The paper ends with two short appendices, the first of which discusses several software packages and their effectiveness in DEM creation and 3-D modeling. The final appendix is a flow chart summarizing the recommendations for the seven DEM creation methods. / Master of Science

This work goes through the mindset and ways of analyzing the problem of realizing 2D concept art into the 3D game model used in game. Specifically targeted for top down games and the effects the top down view have on the 3D game model. Studies in Principles and design concepts are used to create a 3D game character that works well for the top down view. The method used where an experimental study which resulted in a 3D model and implementation of principles and design concepts.  Based on the results it is concluded that it could be a useful tool. In the discussion a deeper analysis is conducted and it´s concluded that further research are necessary and the purpose and questions were answered.

Neste estudo é apresentado um procedimento de análise de dados magnéticos em casos de presença de magnetização remanente para, ao final do processo, a realização de uma inversão mais rápida e fiel ao comportamento do alvo em sub-superfície. O procedimento é composto por seis passos: (1) Delimitação lateral do alvo; (2) Estimativa de suas profundidades; (3) Estimativa das direções de inclinação e declinação aparentes de seu vetor de magnetização total; (4) Modelagem inicial com inferência de valores de susceptibilidades oriundos de estudos geológicos anteriores sobre o alvo e/ou sua região; (5) Inversão dos dados magnéticos utilizando o modelo inicial; e (6) atribuição das características magnéticas do passo (3) sobre o modelo de contraste de susceptibilidade magnética obtido com a inversão para a modelagem final do alvo, conhecendo-se seus vetores de magnetização induzida, total e, por subtração vetorial de ambos, remanente. Este procedimento foi aplicado a 108 casos sintéticos e a 8 casos reais pertencentes às províncias ígneas do Alto do Paranaíba e Rondoniana-San-Ignácio. Os resultados do uso deste procedimento indicaram uma recuperação das direções das componentes de magnetização com erro menor que 10%, em casos sintéticos, uma redução de mais de 20% no tempo de inversão com o uso de modelos iniciais, e qualitativamente, apresentaram modelos mais próximos dos originais (nos casos sintéticos) e geologicamente factíveis nos casos reais. / In this study, we present a procedure of analysis of magnetic data when remanence is present in order to, at the end of the process, obtain an inversion faster and more reliable inversion. The procedure is composed of six steps: (1) Estimation of the borders of the target; (2) Estimation of its depths; (3) A sweeping for the total apparent inclination and declination directions; (4) Initial modeling of a synthetic body, based on the recovered geometry and depth, on the directions of inclination and declination of the total magnetic field, and on previous analysis of the target and/or its region; (5) Inversion of magnetic data using the initial model; and (6) Attribution of the magnetic features of step (3) to the model recovered by the inversion for a final modeling of the target, estimating as well its remanent magnetization; the last through the vectorial resultant of the induction and total magnetization subtraction. This procedure was applied to 108 synthetic and to 8 real cases from the Alto do Paranaíba and Rondonian-San Ignacio Igneous Provinces. Their results pointed out that the error between the recovered directions of the magnetization components and the original values, in synthetic cases, was smaller than 10%; The inversions had their processing-time reduced in more than 20% and, qualitatively, presented models were more similar to the original (synthetic cases) and geologically feasible (real cases).

In order for a system to learn a model for object recognition, it must have a lot of positive images to learn from. Because of this, datasets of similar objects are built to train the model. These object datasets used for learning models are best when large, diverse and have annotations. But the process of obtaining the images and creating the annotations often times take a long time, and are costly. We use a method that obtains many images of the same objects in different angles very quickly and then reconstructs those images into a 3D model. We then use the 3D reconstruction of these images of an object to connect information about the different images of the same object together. We use that information to annotate all of the images taken very quickly and cheaply. These annotated images are then used to train the model.

We propose three biometric systems for performing 1) Multi-modal Three-Dimensional (3D) ear + Two-Dimensional (2D) face recognition, 2) 3D face recognition, and 3) hybrid 3D ear recognition combining local and holistic features. For the 3D ear component of the multi-modal system, uncalibrated video sequences are utilized to recover the 3D ear structure of each subject within a database. For a given subject, a series of frames is extracted from a video sequence and the Region-of-Interest (ROI) in each frame is independently reconstructed in 3D using Shape from Shading (SFS). A fidelity measure is then employed to determine the model that most accurately represents the 3D structure of the subject’s ear. Shape matching between a probe and gallery ear model is performed using the Iterative Closest Point (ICP) algorithm. For the 2D face component, a set of facial landmarks is extracted from frontal facial images using the Active Shape Model (ASM) technique. Then, the responses of the facial images to a series of Gabor filters at the locations of the facial landmarks are calculated. The Gabor features are stored in the database as the face model for recognition. Match-score level fusion is employed to combine the match scores obtained from both the ear and face modalities. The aim of the proposed system is to demonstrate the superior performance that can be achieved by combining the 3D ear and 2D face modalities over either modality employed independently. For the 3D face recognition system, we employ an Adaboost algorithm to builda classifier based on geodesic distance features. Firstly, a generic face model is finely conformed to each face model contained within a 3D face dataset. Secondly, the geodesic distance between anatomical point pairs are computed across each conformed generic model using the Fast Marching Method. The Adaboost algorithm then generates a strong classifier based on a collection of geodesic distances that are most discriminative for face recognition. The identification and verification performances of three Adaboost algorithms, namely, the original Adaboost algorithm proposed by Freund and Schapire, and two variants – the Gentle and Modest Adaboost algorithms – are compared. For the hybrid 3D ear recognition system, we propose a method to combine local and holistic ear surface features in a computationally efficient manner. The system is comprised of four primary components, namely, 1) ear image segmentation, 2) local feature extraction and matching, 3) holistic feature extraction and matching, and 4) a fusion framework combining local and holistic features at the match score level. For the segmentation component, we employ our method proposed in [111], to localize a rectangular region containing the ear. For the local feature extraction and representation component, we extend the Histogram of Categorized Shapes (HCS) feature descriptor, proposed in [111], to an object-centered 3D shape descriptor, termed Surface Patch Histogram of Indexed Shapes (SPHIS), for surface patch representation and matching. For the holistic matching component, we introduce a voxelization scheme for holistic ear representation from which an efficient, element-wise comparison of gallery-probe model pairs can be made. The match scores obtained from both the local and holistic matching components are fused to generate the final match scores. Experimental results conducted on the University of Notre Dame (UND) collection J2 dataset demonstrate that theproposed approach outperforms state-of-the-art 3D ear biometric systems in both accuracy and efficiency.

The research evaluates the feasibility of assisting orthodontists to treat irregularities in teeth by computing the transformations to move each tooth to its ideal position. The intent is to help orthodontists craft a precise and specific treatment plan for each patient. Computation of the transformations is achieved through the use of a reverse engineering package, Geomagic Studio, and a three dimensional modeling program, Rhino3D. The inputs for finding the transformation are the patient's teeth mold and dental arch templates. A 3D laser scanner is used to form a point cloud data representation of the patient's teeth mold. Geomagic is used to construct a Non-Uniform Rational B-Spline surface for the mold. Rhino3D is used to manipulate this surface and compute the required transformations using the scripting platform, Rhinoscript, in Rhino3D. The steps in the process and the algorithms developed in Rhinoscript to compute the transformations are discussed. Three case studies are presented to demonstrate the process. / text

The goal of this research is to develop new, interactive methods for creating very high genus 2-manifold meshes. The various approaches investigated in this research can be categorized into two groups -- interactive methods, where the user primarily controls the creation of the high-genus mesh, and automatic methods, where there is minimal user interaction and the program automatically creates the high-genus mesh. In the interactive category, two different methods have been developed. The first allows the creation of multi-segment, curved handles between two different faces, which can belong to the same mesh or to geometrically distinct meshes. The second method, which is referred to as ``rind modeling'', provides for easy creation of surfaces resembling peeled and punctured rinds. The automatic category also includes two different methods. The first one automates the process of creating generalized Sierpinski polyhedra, while the second one allows the creation of Menger sponge-type meshes. Efficient and robust algorithms for these approaches and user-friendly tools for these algorithms have been developed and implemented.