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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

It is a challenging task to visualize the behavior of time-dependent 3D vector fields. Most of the time an overview of unsteady fields is provided via animations, but, unfortunately, animations provide only transient impressions of momentary flow. In this paper we present two approaches to visualize time varying fields with fixed geometry. Path lines and streak lines represent such a steady visualization of unsteady vector fields, but because of occlusion and visual clutter it is useless to draw them all over the spatial domain. A selection is needed. We show how bundles of streak lines and path lines, running at different times through one point in space, like through an eyelet, yield an insightful visualization of flow structure ('eyelet lines'). To provide a more intuitive and appealing visualization we also explain how to construct a surface from these lines. As second approach, we use a simple measurement of local changes of a field over time to determine regions with strong changes. We visualize these regions with isosurfaces to give an overview of the activity in the dataset. Finally we use the regions as a guide for placing eyelets.

This thesis is concerned with the utilization of object symmety as a cue for segmentation and object recognition. In particular it investigates the problem of detecting 3D bilaterally symmetric objects from affine views. The first part of the thesis investigates the problem of detecting 3D bilateral symmetry within a scene from known point correspondences across two or more affine views. We begin by extending the notion of skewed symmetry to three dimensions, and give a definition in terms of degenerate structure that applies equally to an affine 3D structure or to point correspondences across two or more affine views. We then consider the effects of measurement errors on symmetry detection, and derive an optimal statistical test of degenerate structure, and thereby of 3D-skewed symmetry. We then move on to the problem of searching for 3D skewed symmetric sets within a larger scene. We discuss two approaches to the problem, both of which we have implemented, and we demonstrate fully automatic detection of 3D skewed symmetry on images of uncluttered scenes. We conclude the first part by investing means of verifying the presence of bilateral rather than skewed symmetry in the Euclidean space, by enforcing mutual consistency between multiple skewed symmetric sets, and by drawing on partial knowledge about the camera calibration. The second part of the thesis is concerned with the problem of obtaining feature correspondences across multiple affine views, as required for the detection of symmetry. In particular we investigate the geometric matching constraints that exist between affine views. We start by specilizing the four projective multifocal tensors to the affine case, and use these to carry the bulk of all known projective multi-view matching relations to affine views, unearthing some new relations in the process. Having done that, we address the problem of estimating the affine tensors. We provide a minimal set of constraints on the affine trifocal tensor, and search for ways of estimating the affine tensors from point and line correspondences.

This work deals with an efficient and robust technique of performing Boolean operations on polygonal models. Full robustness is achieved within an internal representation based on planes and BSP (binary space partitioning) trees, in which operations can be carried out exactly in mere fixed precision arithmetic. Necessary conversions from the usual representation to the inner one and back, including their consequences are analyzed in detail. The performance of the method is optimized by a localization scheme in the form of an adaptive octree. The resulting implementation RazeCSG is experimentally compared with implementations used in practice Carve and Maya, which are not fully robust. For large models, RazeCSG shows only twice lower performance in the worst case than Carve, and is at least 130 times faster than Maya.

In this thesis, opti-acoustic stereo imaging, which is the deployment of two-dimensional (2D) high frequency imaging sonar with the electro-optical camera in calibrated stereo configuration, is studied. Optical cameras give detailed images in clear waters. However, in dark or turbid waters, information coming from electro-optical sensor is insufficient for accurate scene perception. Imaging sonars, also known as acoustic cameras, can provide enhanced target details under these scenarios. To illustrate these visibility conditions, a 2D high frequency imaging sonar simulator as well as an underwater optical image simulator is developed. A computationally efficient algorithm is also proposed for the post-processing of the returned sonar signals. Where optical visibility allows, integration of the sonar and optical images effectively provides binocular stereo vision capability and enables the recovery of three-dimensional (3D) structural information. This requires solving the feature correspondence problem for these completely different sensing modalities. Geometrical interpretation of this problem is examined on the simulated optical and sonar images. Matching the features manually, 3D reconstruction performance of opti-acoustic system is also investigated. In addition, motion estimation from opti-acoustic image sequences is studied. Finally, a method is proposed to improve the degraded optical images with the help of sonar images. First, a nonlinear mapping is found to match local the features in opti-acoustical images. Next, features in the sonar image is mapped to the optical image using the transformation. Performance of the mapping is evaluated for different scene geometries.

This work describes 3D reconstruction using stereo vision. It presents methods for automatic localization of corresponding points in both images and their reprojection into 3D space. Application created can be used for navigation of a robot and object avoidance. Second part of the document describes chosen components of the robot. Path finding algorithms are also discussed, particulary Voronoi's diagram.