Rapid wavelet construction of multi-resolution fairing for curves and surfaces with any number of control vertices

In the field of curves and surfaces fairing, arbitrary resolution wavelet fairing algorithm made wavelet fairing technology widely extended to general curves and surfaces, which are determined by any number of control vertices. Unfortunately, accurate wavelet construction algorithm for general curves and surfaces still has not been perfect now. In this article, a concrete algorithm for reconstruction matrix and wavelet construction was emphatically studied, which would be used in the multi-resolution fairing process for curves and surfaces with any number of control vertices. The essence of this algorithm is to generalize wavelet construction into the solution of null space, which could be solved gradually and rapidly by the procedures of decomposition and simplification of coefficient matrix. Certainly, the related compactly supported wavelets could be constructed efficiently and accurately, too. In the last of the article, a complex curve and a complex surface case were provided to verify the stability, high performance, and robustness of this algorithm.

Shipboard Fairing Process Improvement and Testing

The flame straightening process has been developed since 1940; however, the process at Ingalls Shipbuilding (Ingalls) was loosely controlled with the majority of procedural steps governed by the flame straightener performing the operation. Findings from initial research showed excessive heat, both in the size and temperature of the heat spots as well as the quantity of spots used to achieve flatness. The amount of heat involved drastically increased paint rework, delayed schedules, and affected the surrounding structural members causing crippled structures that must be cut out and replaced. Between operators or applications, the process also varied greatly which provided no measureable work scope and led to the tendency of the straighteners to apply far more heat than necessary to achieve panel flatness tolerances. The Ingalls research team executed tasking that analyzed the current flame straightening process, quantified issues associated with overheating, tested a variety of different straightening patterns, and ultimately implemented a revised procedure. The new, more efficient procedure reduces the amount of heat spots required to achieve flatness tolerance with and thus decreases the process cost, minimizes heat input, and prevents damage caused by past practices.

Inverse-Problem-Based Accuracy Control for Arbitrary-Resolution Fairing of Quasiuniform Cubic B-Spline Curves

In the process of curves and surfaces fairing with multiresolution analysis, fairing accuracy will be determined by final fairing scale. On the basis of Dyadic wavelet fairing algorithm (DWFA), arbitrary resolution wavelet fairing algorithm (ARWFA), and corresponding software, accuracy control of multiresolution fairing was studied for the uncertainty of fairing scale. Firstly, using the idea of inverse problem for reference, linear hypothesis was adopted to predict the corresponding wavelet scale for any given fairing error. Although linear hypothesis has error, it can be eliminated by multiple iterations. So faired curves can be determined by a minimum number of control vertexes and have the best faring effect under the requirement of accuracy. Secondly, in consideration of efficiency loss caused by iterative algorithm, inverse calculation of fairing scale was presented based on the least squares fitting. With the increase of order of curves, inverse calculation accuracy becomes higher and higher. Verification results show that inverse calculation scale can meet the accuracy requirement when fitting curve is sextic. In the whole fairing process, because there is no approximation algorithm such as interpolation and approximation, faired curves can be reconstructed again exactly. This algorithm meets the idea and essence of wavelet analysis well.

Experimental Research on Effect of Hot Works on Mechanical Performance of Ship Steel Plate

Hot works is an important method for fairing the ship steel plate to improve the quality of shipbuilding, while the mechanical performance of the ship steel plate may be affected during the fairing process, which could result to some safe problems on the structural strength. DH32 high-strength ship steel plate, which is a kind of widely used material in shipbuilding industry, is taken as an object of the present experimental study. Some main parameters of the plate’s mechanical property through hot-works treatment for different times are investigated systematically. Through analyzing the variation of the mechanical properties, some conclusions are drawn and some useful suggestions put forward.

Parametric Generation, Modeling, and Fairing of Simple Hull Lines With the Use of Nonuniform Rational B-Spline Surfaces

This paper deals with the use of a simple parametric design method applied to simple hull lines, such as sailing ship hulls and round bilge hulls. The described method allows the generation of hull lines that meet hydrodynamic coefficients imposed by the designer, obtaining more flexibility than with normal affine transformations of a parent hull. First, a wire model of the ship stations is made with the use of explicit curves. The method is completed with an automatic surface modeling of the previ¬ously generated offsets. The construction of spline curves and their application in the definition of ship lines are reviewed. Approximation of spline curves fitting the data on the stations is made, with special emphasis on the choice of parametrization, which is relevant to increasing the accuracy of the splines. B-spline surface modeling of the hull and the fairing process adapted to maintain certain ship characteristics are described. Some examples of the generation, lofting, and fairing process are pre¬sented.

Construction of Fair Surfaces Over Irregular Meshes

This paper describes the process of constructing a fair, open or closed C1 surface over a given irregular curve mesh. The input to the surface construction consists of point and/or curve data which are individually marked to be interpolated or approximated and are arranged according to an arbitrary irregular curve mesh topology (Fig. 1). The surface constructed from these data will minimize flexibly chosen fairness criteria. The set of available fairness criteria is able to measure surface characteristics related to curvature, variation of curvature, and higher order surface derivatives based on integral functionals of quadratic form derived from the second, third and higher order parametric derivatives of the surface. The choice is based on the desired shape character. The construction of the surface begins with a midpoint refinement decomposition of the irregular mesh into aggregates of patch complexes in which the only remaining type of building block is the quadrilateral Be´zier patch of degrees 4 by 4. The fairing process may be applied regionally or to the entire surface. The fair surface is built up either in a single global step or iteratively in a three stage local process, successively accounting for vertex, edge curve and patch interior continuity and fairness requirements. This surface fairing process will be illustrated by two main examples, a benchmark test performed on a topological cube, resulting in many varieties of fair shapes for a closed body, and a practical application to a ship hull surface for a modern container ship, which is subdivided into several local fairing regions with suitable transition pieces. The examples will demonstrate the capability of the fairing approach of contending with irregular mesh topologies, dealing with multiple regions, applying global and local fairing processes and will illustrate the influence of the choice of criteria upon the character of the resulting shapes.