„… vertex normals of the nominal model and those of the Skin Model Shape. Indeed, this approach should not …” „… by a vector f (t) at certain discrete points in T . A straightforward approach to perform this is to …” „… Shapes is conceptualised, before approaches for the virtual representation, the visualisation, and the …”

„… , . . . , n; j = 1, . . . , F , (5.5) and its normal vector is denoted by nfj∗ . In contrast to other …” „… plane is shiqed in the direction of its normal vector nfj∗ along the flatness value. By doing so, a …” „… normal vector of the flatness tolerance zone nfj∗ is equal to the normal of the associated plane of the …”

„… this, the worst-case limits of the vector loop approach can be found as max(pos) = 4.00. In contrast to …” „… ‡ G using the vector loop approach. It can be found, that Table 7.3: Considered Tolerances in the …” „… different tolerance analysis approaches, such as the vector loop approach, the variational model, the matrix …”

„… (Point-wise), Height lρ Correlation Length m Module n (Vertex) Normal Vector X Abbreviations and Symbols p …” „… Tolerance Analysis based on Skin Model Shapes 3 1.4 7e Approach: Scope and Outline of the Work …” „… regarding the GPS Standards . . . . . . . . . . . . . . . 26 2.2.4 Further Approaches for the Specification …”

„… approaches, that have been proposed during the last decades. 7e aim of this chapter is to provide an overview …” „… approaches and tools for the computer-aided tolerancing with a focus on the computer-aided tolerance analysis …” „… development approaches, concurrent engineering workflows [RLW91, Soh92, GRDN97, Smi97], and predictive …”

„… loss-cost of a non-symmetrical functional requirement with a statistical tolerancing approach. In Giordano …” „… Production CPI 2001, Fez (Maroc), Paper No. 8, 2001. [And96] Andersson, P. A semi-analytic approach to robust …” „… Approach. In Houten, F. and Kals, H., editors, Global Consistency of Tolerances: Proceedings of the 6th …”

„… , identically-distributed random variables results in a normal distribution, when n approaches infinity. During practical …” „… of the main reasons for this is that this approach to problem solving has been very successful for a …” „… lot of applications in everyday life. In this approach artificial information carriers are connected …”

„… the input vectors, single measuring values, packets of spectral measuring data and other data sources …” „… vectors should have a limitedmaximum distance to their nearest neighbors (NN). This and a continuous …” „… wavelet transform (WT) in the form of spectral components, at the end of the DV, as a vector, which is …”

„… . Each normal feature vector extracted from network traffic was represented by a hypersphere with fix …” „… . The result also illustrated that themodified approach still had the best performance. 1 Introduction …” „… , GAs have been proposed as hybrids by combining to various approaches such as PSO, Ant Colony, and …”

„… – Partitioned Solution Approach – Maritime Applications – Floating Offshore Wind Turbines – Landing Maneuver of …” „… multifield phenomena. In this thesis, a partitioned solution approach is followed to solve these kind of …” „… . . . . . . . . . . . . . . . 84 4.7.3 Vector ε-Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.7.4 …”

„… contrast, follows a material particle as it moves through space. The latter approach is commonly used in …” „… row-vector of all zeros the length of which matches the number of columns in the spatial derivative ∂x/∂χ …” „… outer unit surface normal of the surface Γt. In essence, this equation states that the variation of the …”

„… now focus on the interaction of multiple fields in the framework of a partitioned solution approach …” „… contrast a monolithic solution procedure with a partitioned approach, which is pursued in this work …” „… written as g(u) = 0 on Ω . (4.3) In a monolithic approach, Equation (4.3) is solved by applying a …”

„… VertexCoordinates, class LocalPoint1> static DoubleVector computeNormal( const …” „… . Consider, for example, a std::vector that is returned from a function. In the absence of return value …” „… std::vector until C++03 [79]. In C++11, this copy is avoided due to the fact that std::vector defines a …”

„… illustrate the effectiveness of the partitioned solution approach. Depending on the particular problem under …” „… Aitken relaxation, the vector-ε algorithm, and the modification of the conventional Aitken relaxation …” „… approach. Furthermore, it is interesting to note that the CPU time spent on the solution of the fluid and …”

„… pi,xp̃i,x + pi,y p̃i,y (A.18) B Normal Vector of 3D Points In Ch. 4 vector normals are applied based on …” „… set of points, the normal vector for one point pk ∈ R3 is defined based on its six neighbors, which …” „… are then used to estimate a local plane. This plane has a well-defined normal vector, which represents …”

„… Computing Optimal Angles . . . . . . . . . 179 B Normal Vector of 3D Points …” „… different modes of individual shape and expression compared to traditional approaches based on 2D data …” „… values: s ∈ R. v lower case bold letters define column vectors: v ∈ RN×1 M upper case bold letters define …”

„… criteria: e.g. if a triangle has a large edge length and a low z-value, or if the normal vector is oriented …” „… triangular information, the normal vectors of triangles of the deformable set before Y and after Ŷ …” „… ) , (4.48) where ni ∈ RD refers to the normal vector of triangle i of the set Y . Another measure for …”

„… parameters at once. As we aim to use an alternating least squares approach to estimate the parameter vectors …” „… network approach for 3D face reconstruction from a single image, based on an image-to-image framework …” „… estimated from the image and then used to change the position of each vertex along its normal. The …”

„… search dimensions in ES z Random mutation vector C Covariance matrix of ES mutation operator N Normal …” „… distribution σ Standard deviation of normal distribution, global step size σ Vector of strategy parameters z …” „… optimization is studied in conjunction with statistical models such as neural networks or support vector …”

„… optimization can be differentiated into continuum and discrete approaches. Discrete topology optimization …” „… topology optimization, although the presented approaches that are discussed hereafter are transferable to …” „… the state vector, and G0 and Gl are optimization constraints with the target volume V0. In topology …”

„… , gradient-based approaches also utilize this state vector to compute the sensitivities of the objective function …” „… feature vector s. The generic topology optimization approach with linear regression model is referred to …” „… , evolutionary computation approaches for topology optimization come with the need of an appropriate …”

„… , R., Ramakrishnan, C., and Swaminathan, N. A two phase approach based on skeleton convergence and …” „… ., Aulig, N., Olhofer, M., and Duddeck, F. Hybrid evolutionary approach for level set topology optimization …” „… , July 2016. [35] Bujny, M. Development of a hybrid evolutionary approach for level set topology …”