Investigations into the shape-preserving interpolants using symbolic computation

Shape representation is a central issue in computer graphics and computer-aided geometric design. Many physical phenomena involve curves and surfaces that are monotone (in some directions) or are convex. The corresponding representation problem is given some monotone or convex data, and a monotone or convex interpolant is found. Standard interpolants need not be monotone or convex even though they may match monotone or convex data. Most of the methods of investigation of this problem involve the utilization of quadratic splines or Hermite polynomials. In this investigation, a similar approach is adopted. These methods require derivative information at the given data points. The key to the problem is the selection of the derivative values to be assigned to the given data points. Schemes for choosing derivatives were examined. Along the way, fitting given data points by a conic section has also been investigated as part of the effort to study shape-preserving quadratic splines

Design and engineering methods for open-rotor nacelle shaping

Due to the growing transport needs in emerging economies and recent success of the low-cost airlines, the demand for short/medium-haul aeroplanes is increasing. Within the next twenty years, the existing single-aisle aircraft are likely to be replaced by new models mounting new propulsion systems. One promising con- figuration being considered is the open-rotor, which is a revision of the propfan. However, further progress has to be done in order to transform propfan engines, whose technology dates back to the 1980s, into viable and feasible open-rotor con- cepts. Among the aspects yet to be investigated in su ficient depth is the de finition of a methodology for the open-rotor nacelle design. The aim of the present research is to help enhance the knowledge in this area. Even if there are a number of important fields of investigation for open-rotor designs, this work is limited to the analysis of the pusher architecture with no exhaust impingement through rotors. The research is initially performed combining both a graphical and a compu- tational approach, investigating the mathematical and physical aspects involved in the de finition of appropriate nacelle pro files, boundary conditions for the CFD analysis and simplifi ed rotor modelling. The first simulations are mainly focused on a typical propfan nacelle, which is taken as a reference model: the computations provide useful results for evaluating its aerodynamic features ... [cont.]

IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains

This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis (IGA) techniques. Introducing IGA solvers to the MISC algorithm is very natural since they are tensor-based PDE solvers, which are precisely what is required by the MISC machinery. Moreover, the combination-technique formulation of MISC allows the straight-forward reuse of existing implementations of IGA solvers. We present numerical results to showcase the effectiveness of the proposed approach.Comment: version 3, version after revisio

Computation of sum of squares polynomials from data points

We propose an iterative algorithm for the numerical computation of sums of squares of polynomials approximating given data at prescribed interpolation points. The method is based on the definition of a convex functional $G$ arising from the dualization of a quadratic regression over the Cholesky factors of the sum of squares decomposition. In order to justify the construction, the domain of $G$, the boundary of the domain and the behavior at infinity are analyzed in details. When the data interpolate a positive univariate polynomial, we show that in the context of the Lukacs sum of squares representation, $G$ is coercive and strictly convex which yields a unique critical point and a corresponding decomposition in sum of squares. For multivariate polynomials which admit a decomposition in sum of squares and up to a small perturbation of size $\varepsilon$, $G^\varepsilon$ is always coercive and so it minimum yields an approximate decomposition in sum of squares. Various unconstrained descent algorithms are proposed to minimize $G$. Numerical examples are provided, for univariate and bivariate polynomials

Parametric Spiral And Its Application As Transition Curve

Lengkung Bezier merupakan suatu perwakilan lengkungan yang paling popular digunakan di dalam applikasi Rekabentuk Berbantukan Komputer (RBK) dan Rekabentuk Geometrik Berbantukan Komputer (RGBK). The Bezier curve representation is frequently utilized in computer-aided design (CAD) and computer-aided geometric design (CAGD) applications. The curve is defined geometrically, which means that the parameters have geometric meaning; they are just points in three-dimensional space

Image segmentation and reconstruction of 3D surfaces from carotid ultrasound images

Tese de doutoramento. Engenharia Electrotécnica e de Computadores. Faculdade de Engenharia. Universidade do Porto. 200