TiGL - An Open Source Computational Geometry Library for Parametric Aircraft Design

This paper introduces the software TiGL: TiGL is an open source high-fidelity geometry modeler that is used in the conceptual and preliminary aircraft and helicopter design phase. It creates full three-dimensional models of aircraft from their parametric CPACS description. Due to its parametric nature, it is typically used for aircraft design analysis and optimization. First, we present the use-case and architecture of TiGL. Then, we discuss it's geometry module, which is used to generate the B-spline based surfaces of the aircraft. The backbone of TiGL is its surface generator for curve network interpolation, based on Gordon surfaces. One major part of this paper explains the mathematical foundation of Gordon surfaces on B-splines and how we achieve the required curve network compatibility. Finally, TiGL's aircraft component module is introduced, which is used to create the external and internal parts of aircraft, such as wings, flaps, fuselages, engines or structural elements

Parametric Representation of Part Contours in SLS Process

Current layer-based SFF technologies process faceted geometric input data to produce polygonal contours of the part's boundary in each layer. However, for improved part quality, other more accurate representations of part contours are desirable. Likewise, implementation of Wu's minimum time optimal laser tracking control method for selective laser sintering (SLS) requires contour curves that exhibit higher order continuity. In this paper, we first analyze the requirements of optimal laser tracking to develop evaluation criteria for choosing a contour representation. Several possible representation methods are reviewed. We show that the NonUniform Rational B-Spline (NURBS) curve meets the criteria. A demonstration program illustrates the advantages of NURBS curves for representing contours with uniform point distributions. The results can be used in other control areas where uniform point distribution or constant velocity is required.Mechanical Engineerin

Comparison and Evaluation of Didactic Methods in Numerical Analysis for the Teaching of Cubic Spline Interpolation

In mathematical education it is crucial to have a good teaching plan and to execute it correctly. In particular, this is true in the field of numerical analysis. Every teacher has a different style of teaching. This thesis studies how the basic material of a particular topic in numerical analysis was developed in four different textbooks. We compare and evaluate this process in order to achieve a good teaching strategy. The topic we chose for this research is cubic spline interpolation. Although this topic is a basic one in numerical analysis it may be complicated for students to understand. The aim of the thesis is to analyze the effectiveness of different approaches of teaching cubic spline interpolation and then use this insight to write our own chapter. We intend to channel every-day thinking into a more technical/practical presentation of a topic in numerical analysis. The didactic methodology that we use here can be extended to cover other topics in numerical analysis.Methods of teaching mathematics are different for several reasons, for example, the presentation style of teacher of a particular topic. In several books we can observe a different approach of presentation material of a topic, and at the end we can produce a unique way of teaching but in a different way. In our thesis we study different approaches to teaching in a several numerical analysis books in the topic of cubic spline interpolation. What is cubic spline interpolation? Cubic spline interpolation is a type of interpolation of data points. Interpolation is a method of constructing a curve between some data points. We chose cubic spline interpolation because it is better than other kinds of interpolation. Cubic spline interpolation has a smaller curvature compared with other types of interpolation. Therefore, cubic spline interpolation produces a smooth curve. In this research we study different approaches of teaching cubic spline interpolation to find a good way for presenting the cubic spline interpolation topic, because this topic may be complicated for students to understand. To reach a good process of presentation of cubic spline interpolation we compare each part of different approaches in the books we have studied for teaching cubic spline interpolation by asking questions and then answering those questions. In this way we will show how we can evaluate each answer. Evaluating each answer we will obtain a good result which will prepare us for writing our own chapter in order to present cubic spline interpolation in our way

Spline network modeling and fault classification of a heating ventilation and air-conditioning system

A spline network, that is an alternative to artificial neural networks, is introduced in this dissertation. This network has an input layer, a single hidden layer, and an output layer. Spline basis functions, with small support, are used as the activation functions. The network is used to model the steady state operation of a complex Heating Ventilation and Air-conditioning (HVAC) system. Real data was used to train the spline network. A neural network was also trained on the same set of data. Based on the training process, it is possible to conclude that when compared to artificial neural networks, the spline network is much faster to train, needed fewer input-output pairs, and had no convergence problems. The weights of the spline network are obtained by solving a set of linear equations;The spline network model of the HVAC system is used to detect faulty operation of the actual system. Once abnormal operation of the system is monitored, a fuzzy neural network is used to locate the faulty component. The fuzzy neural network is trained on data obtained by simulating fault scenarios. This network minimizes ambiguities at decision boundaries. The results of fault classification are presented in the dissertation

Solutions of Inequality Constrained Spline Optimization Problems with the Active Set Method

We solve the problem of finding a near-interpolant curve, subject to constraints, which minimizes the bending energy of the curve. Using B-splines as our tools, we give a brief overview of spline properties and develop several different cases of inequality constrained optimization problems of this type. In particular, we develop the active set method and use it to solve these problems, emphasizing the fact that this algorithm will converge to a solution in finite iterations. Our solution will solve an open problem regarding near-interpolant spline curves. Furthermore, we supplement this with an iterative technique for better choosing data sites so as to further minimize the bending energy of the spline curve, offering an easy solution to the problem of free data sites

Approximation of CNC part program within a given tolerance band

Freeform surfaces are widely used in various fields of engineering design such as automotive, aerospace and mold and die industries. With the geometric model designed by freeform surfaces in the CAD system, the tool path will be next constructed and sampled by the CAM system according to the predefined chordal deviation. The sequentially sampled short linear blocks are stored in the file called the part program, which is later interpreted by the CNC system to control the machine tool and mill the workpiece. In order to deliver the desired motion smoothly and rapidly, the short linear blocks in the part program will be approximated with smooth spline curves within a specified tolerance band. With spline curves, which consist of longer polynomial pieces, the attainable feed rate of the machine tool can be greatly enhanced. In addition, with minimization of curvature variation, velocity and acceleration jumps in the relevant machine axes and undesired mechanical oscillation of the machine can be reduced significantly. This allows higher traversing speeds and reduces the vibration of the machine, thus improves the surface quality