The thesis deals with the representation of objects in the solid geometry. The first part contains a summary of theorems and definitions which are needed for understanding problems of mutual position of lines and planes, cut of objects with a plane and intersection of the object with the line. The second part contains a collection of worksheets for students. It has been created a solution for each worksheet. This solution can be used in printed version or in electronic version which is created in the software GeoGebra. This thesis can be used in tuition or self-studying.

The purpose of this thesis work was to develop a Hardware-in-the-Loop imaging setup that enables experimenting with an event-based and frame-based camera under simulated space conditions. The generated data sets were used to compare visual navigation algorithms in terms of an event-based and frame-based feature detection and tracking algorithm. The comparative analyses of the feature detection and tracking algorithms were used to get insights into the feasibility of event-based vision near-space space objects. Event-based cameras differ from frame-based cameras by how they produce an asynchronous and independent stream of events caused by brightness changes at each pixel instead of capturing images at a fixed rate. The setup design is based on a theoretical framework incorporating optical calculations. These calculations indicating the asteroid model needed to be scaled down by a factor of 3192 to fit inside the camera depth-of-view. This resulted in a scaled Bennu asteroid with a size of 16.44 centimeters.The cameras under testing conducted three experiments to generate data sets. The utilization of a feature detection and tracking algorithm on both camera data sets revealed that the absolute number of tracked features, computation time, and robustness in various scenarios of the frame-based camera algorithm outperforms the event-based camera algorithm. However, when considering the percentages of tracked features relative to the total detected features, the event-based algorithm tracks a significantly higher percentage of features for at least one key frame than the frame-based algorithm.  The comparative analysis of the experiments performed in space-simulated conditions during this project showed that the feasibility of an event-based camera using solely events is low compared to the frame-based camera.

Contrairement aux autres biens meubles, les navires, les aéronefs et les objets spatiaux affectés à la navigation internationale sont rattachés à un Etat. Le lien de droit public établi entre ces engins et l’Etat est communément appelé « nationalité ». Mais ce terme n’exprime pas à leur propos une institution à tous égards identique à la nationalité des personnes. Le rattachement examiné ne repose en effet pas sur des éléments de fait (naissance, ascendance etc.), mais uniquement sur un acte administratif interne, l’immatriculation. L’étude de la pratique, notamment des conventions internationales et des législations nationales, montre clairement que – contrairement à ce qu’on soutient souvent – il n’y a pas lieu de subordonner ce rattachement à un lien effectif. Ce qui importe, compte tenu notamment du fait que ces engins évoluent dans des espaces soustraits à toute compétence territoriale, est d’identifier l’Etat qui est seul compétent à l’égard de l’« ensemble organisé » formé par le véhicule, les personnes et la cargaison à bord, et qui est responsable de ses activités. Le droit international interdit dès lors la double immatriculation, mais il laisse aux Etats le pouvoir discrétionnaire de déterminer les conditions d’attribution de leur « nationalité », sans subordonner l’opposabilité internationale de celle-ci à quelque autre exigence que ce soit. Le danger est toutefois que cela favorise un certain laxisme de l’Etat d’immatriculation, ce qui exposerait au risque que des dommages graves soient causés aux personnes impliquées dans les activités de ces engins et – surtout – aux tiers. Mais ce sont les obligations internationales imposées et les droits corrélatifs reconnus dans le chef de l’Etat d’immatriculation qui sont déterminants à cet égard et non quelque mystérieuse « effectivité » du rattachement. Autrement dit, s’il n’est pas nécessaire d’imposer à l’Etat d’immatriculation des conditions internationales limitant sa liberté dans l’attribution de sa « nationalité » aux engins, il est indispensable d’exiger que celui-ci respecte ses obligations, c’est-à-dire exerce effectivement son contrôle et sa juridiction. Cette constatation se vérifie quel que soit l’engin en cause. Le rattachement créé par l’immatriculation constitue donc une institution "sui generis", commune aux navires, aéronefs et objets spatiaux et dont le régime juridique est encadré par le droit international. / Unlike any other movable property, ships, aircraft and space objects that are engaged in international navigation are linked to a State. The legal connection established between these craft/vessels and the State is commonly referred to as “nationality”. However, in this case the term does not represent an institution identical in all respects to the nationality of persons. With regard to vessels, the legal connection to a State is not based on factual elements (such as birth, descent etc.), but merely on the internal administrative act of registration. The study of State practice, notably international conventions and national laws, clearly shows that – contrary to what is often argued – there is no need to make this connection dependent on a pre-existing effective link. What matters most, given that these craft navigate in international space beyond the territorial jurisdiction of sovereign States, is to identify the State that holds sole jurisdiction over said “organized entity” consisting of the vehicle, the persons and the cargo on board and that is responsible for its activities. Public international law therefore prohibits dual registration, but leaves States free to determine the conditions under which they will confer their “nationality”, without imposing any other requirement for the opposability of this legal bond to third States. The danger is that this situation encourages laxity on the part of the States of registry and therefore creates the potential for serious damage incurred by persons involved in these vessels’ activities and – mostly – by third persons. In this regard, it is the international obligations and corresponding rights of the States of registry which are critical, and not a mysterious “effectiveness” of the legal bond. In other words, it is not necessary to impose on the State of registry any international conditions which would limit its freedom with regard to the conferral of its “nationality” upon vessels. It is however indispensable to require that said State complies with its obligations, meaning that it has to effectively exercise its jurisdiction and control over those craft. This statement holds true regardless of the craft concerned. The legal bond created by the registration therefore constitutes a "sui generis" institution, common to ships, aircraft and space objects, and whose legal regime is governed by international law.