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Durch die Zunahme von fl��chenhaften Messtechniken ist besonders in der Ingenieurgeod��sie eine genaue Approximation von gro��en Punktwolken f��r sp��tere Anwendungszwecke notwendig. Hierf��r bieten sich im Speziellen B-Spline Kurven bzw. BSpline Fl��chen an, welche sich bei einer geeigneten Parameterwahl an lokale Gegebenheiten geometrisch bestm��glich anpassen k��nnen. Das Anpassungsverm��gen von B-Splines ist dabei im Wesentlichen von zwei Parameters��tzen, den Kontrollpunkten und den Knoten, abh��ngig. Das gleichzeitige Sch��tzen dieser Parameter f��hrt zu einem hochgradig nichtlinearen Gleichungssystem. Deshalb werden typischerweise die Kontrollpunkte in einem linearen Ausgleichungsmodell gesch��tzt, nachdem zuvor die Knoten bestimmt wurden. Vor allem die Anzahl an Knoten als auch die Verteilung dieser im Parameterraum hat einen gro��en Einfluss auf das Approximationsergebnis. Im ersten Teil dieser Arbeit werden deshalb, neben einem Grundlagenkapitel zu B-Splines und vorstellen der benutzten Daten, insgesamt drei unterschiedliche Methoden f��r das Auffinden geeigneter Knotenpositionen untersucht und die erzielten Ergebnisse pr��sentiert. Zur Evaluierung der Methoden stehen vier, aus B-Spline Kurven, extrahierte Punktmengen zur Verf��gung, bei denen die Parameter (Kontrollpunkte und Knoten) bekannt sind. Die Vorteile und Nachteile der einzelnen Methoden bei der Knotenauffindung k��nnen somit durch das Vorhandensein einer Soll-Form und den bekannten Parametern aufgezeigt werden. Am Schluss dieses Evaluierungsprozesses zeigt sich eine klare Pr��ferenz f��r jene Methode, welche einen Teil des nat��rlichen Immunsystems nachahmt und sich auf die Clonal Selection Theorie st��tzt. Im zweiten Teil der Arbeit wird untersucht, ob mit Hilfe von unterschiedlichen Informationskriterien (AIC, BIC) die Anzahl an Knoten und somit die ben��tigte Anzahl an Parametern f��r ein zufriedenstellendes Approximationsergebnis bestimmt werden k��nnen. Es stellt sich heraus, dass mit der Kombination aus Clonal Selection Algorithmus und dem Bayesianischen Informationskriterium BIC die besten Ergebnisse erzielt werden. Alle gewonnen Erkenntnisse werden schlussendlich ebenfalls an realen Daten erprobt., As a result of the increase of areal measurement techniques, an accurate approximation of large point clouds for future applications is necessary. This is particularly true in the engineering geodesy. Suitable for this purpose are B-spline curves and B-spline surfaces, which provide with a suitable choice of the parameters a good fit to local features of the terrain. The adaptability of B-splines is essentially depending on two parameter sets, namely the control points and the knots. The simultaneous estimation of these parameters results in a highly non-linear system of equations. Therefore, in most applications, the knots are determined first. Subsequently the control points are estimated by solving a linear system of equations. The number of knots and their distribution of these in the parameter space have a significant impact on the quality of the approximation result. At the beginning of the first part of this work, an introduction to the B-spline approximation and the data set used in the present work is given. Then three different methods for finding appropriate knot positions are analyzed and the corresponding results are presented. To evaluate these methods four point sets have been constructed from a given B-spline curve. Since the parameters, i.e. the control points and knots, of these approximations are known, the advantages and disadvantages of each method in identifying appropriate knots can be quantified. The evaluation process shows that the method which mimics a part of the natural immune system and is based on the clonal selection theory is superior among the methods considered here. In the second part of this work different information criteria (AIC, BIC) are used in order to evaluate if it is possible to estimate the number of knots required to obtain a sufficiently accurate approximation result. It turns out that the best results are achieved with the combination of clonal selection algorithm and the bayesian information criterion BIC. Finally, all findings are validated against the results obtained from a realistic data set.

Different macrocycles can be synthesized by using template directed synthesis. The template connects the building blocks of the macrocycle, so that the cyclization step between these building blocks can be performend easier. Well defined cyclic dimers can be synthesized using a bifunctional template. The ring closing step occurred by metathesis of the preorganized building blocks. The preorganization of the two building blocks simplifies the cyclisation step. After removal of the template the macrocycle can be obtained. Symmetric cyclophanes which possess internal amine groups can be synthesized by using symmetric templates as terephthaldialdehyd. The imine bonds are easy to prepare and to remove and therefore they are a good choice for introducing and removing of the template. Furthermore they don’t disturb the ring closing metathesis. If two different bulding blocks were used to prepare the cyclophane precursor an unsymmetrical cyclophane can be prepared. Another possibility to prepare the unsymmetrical diamine cyclophane is the template free preorganization of the building blocks. The prepared cyclophanes exhibit at least one functional group e.g. an amine group. These groups offer the opportunity to bind guests inside the macrocycles. Via protonation of these amines it should be possible to bind anions inside the macrocyle, too. Further on it was tried to prepare a molecular knot by using a metal ion as template. For this reason ligands were prepared which are composed of two different building blocks. The design of this ligand is of crucial importance. The subunits should be orthogonal to each other and one of the subunits has to contain to terminal double bonds and the other one has to possess a functionality which can bind to the metal ion. The linkage between the building blocks was performed via an imine or amide bond. The complexation of the ligand and titanium(IV) ions leads to the precursor of the molecular knot. Unfortunately the ring closing metathesis didn’t work in the desired way, so that the molecular knot couldn’t be prepared. An alternative which is based on triformylphloroglucinol was tried at the same time. In this case the precursor contains an organic template with three imine bridges which are additionally stabilized by three hydrogen bridges. However the ring closing metathesis hasn’t successfully performed yet.