A multi-level optimization technique based on fuel consumption and energy index in early-stage ship design

Reducing lifetime fuel consumption (LFC) and energy efficiency design index (EEDI) are two of the main concerns of shipping industry in recent years. This paper presents a multi-disciplinary and multi-level optimization scheme-based software (HPS-MOP2) to design a hull–propeller system simultaneously from the LFC and EEDI point of view in early-stage ship design. Calculations of the ship resistance and propeller performance are essential to optimize the ship hull–propeller system. Two numerical methods with variable fidelity, non-uniform rational basis spline (NURBS) geometry modelling technique and new version of multi-objective evolutionary algorithm based on decomposition (MOEA/D) are three main parts of the proposed methodology. A bulk carrier propelled by a well-known propeller is used as a base model in three different study cases based on specific fuel oil consumption (SFOC) curves provided by the engine manufacturers Wartsila, MAN and Caterpillar. The presented results illustrate that the employed approach may achieve cost- and energy-efficient designs.

     

Accurate parametrization of conics by NURBS

One argument often given to explain the popularity of NURBS (nonuniform rational B-spline) is that it permits the definition of free-form curves and surfaces (as do most spline models). It also provides an exact representation of conic sections and thus of a large set of curves and surfaces used intensively in CAD: circular arcs, circles, cylinders, cones, spheres, surfaces of revolution and so forth. Nevertheless, few published works discuss the mathematical properties behind the representation of conics by NURBS except for two monographs by Piegl and Tiller (1995) and Farin (1995). The article does not pretend to fill this theoretical lack but rather deals with the following problems: all known NURBS representations of curves and surfaces based on conics have only a C^l continuity. Moreover, no technique exists that would eventually allow us to find a parametrization with a higher level of continuity. The parametrization resulting from the NURBS representation of conics can deviate significantly from the ideal are length (that is, uniform) parametrization. The only known solution to reduce this deviation is to increase the number of control points of the spline by using refinement algorithms, for instance, but such a process converges only slowly to the uniform parametrization. The solution proposed uses an original reparametrization process called zigzag reparametrization, based on a specific family of rational polynomials     

基于OpenGL的NURBS曲面的绘制

通过VC 环境下的编程实践,介绍基于OpenGL技术实现NURBS曲面绘制的基本步骤和方法,介绍NURBS的结构特点,给出了用NURBS生成船体曲面的实例.     

Control vectors for splines

Traditionally, modelling using spline curves and surfaces is facilitated by control points. We propose to enhance the modelling process by the use of control vectors. This improves upon existing spline representations by providing such facilities as modelling with local (semi-sharp) creases, vanishing and diagonal features, and hierarchical editing. While our prime interest is in surfaces, most of the ideas are more simply described in the curve context. We demonstrate the advantages provided by control vectors on several curve and surface examples and explore avenues for future research on control vectors in the contexts of geometric modelling and finite element analysis based on splines, and B-splines and subdivision in particular.     

3D geometric modelling based on NURBS: a review

This article reviews the prevailing geometric modelling techniques, based on Non-Uniform Rational B-Splines (NURBS). Emphasis is placed on the most important properties of NURBS surfaces and the available techniques for modelling real natural or artificial objects given a cloud of three-dimensional data points on their surface, possibly taken from a scanning device.     

NURBS曲线曲面的显式矩阵表示及其算法

从 B样条的差商定义出发 ,提出差商展开系数的概念 ,通过差商展开系数显式解析表示式的导出 ,得到任意次 NU RBS曲线曲面系数矩阵的显式解析表示式 ,并给出了求差商展开系数和 NURBS曲线曲面系数矩阵的数值算法 .文中给出的方法适用于一切 NU RBS曲线曲面 ,包括有理和非有理的 Bézier、均匀和非均匀的 B样条曲线曲面 .相应的数值算法计算简单 ,易于实现 .差商展开系数解析表示式为 NU RBS曲线曲面的表示、转换和节点插入、升阶等基本运算以及与差商相关的问题的研究提供了一个统一的构造性工具和应用方法 .     

基于NURBS的扭变曲面的计算机建模方法研究

本文首先介绍了扭变曲面CAD在国内外的发展情况和NURBS方法的概念,通过推导曲面初始二维数据向三维数据的转换关系,提出一种将NURBS曲线曲面反求算法用于叶片曲面的构造,完成叶片的计算机建模方法,有效地提高了此类曲面在实际生产中的设计精度.     

A Blend of Subdivision Surfaces and NURBS

In present paper, the contour deletion method is developed both to blend surfaces and to fill N-sided holes, which is used for subdividing the NURBS surface. First, according to the non-uniform Catmull-Clark subdivision principle, surfaces are blended. The non-uniform Catmull-Clark subdivision method is constructed, which build the surface through interpolating corner vertices and boundary curves. Then the contour deletion method is adapted to remove the controlling mesh boundary contour in the process of segmentation iteration. Last, N sided-hole is filled to generate a integral smooth continuous surface. This method not only guarantee that the blending surface and base surface patches have C2 continuity at the boundary, but also greatly improve the smoothness of the N-side hole filling surface. The results show that, this method simplifies the specific computer-implemented process, broads the scope of application of subdivision surfaces, and solves the incompatible problem between the subdivision surface and classical spline. The resulting surface has both advantages of the subdivision surface and classical spline, and also has better filling effect.     

船体曲面矩形块按参考线敷设法关键技术研究

以船体曲面敷设矩形块为背景,针对现行按肋骨线方向单向展开后进行矩形块敷设设计的不足,提出了矩形块按参考线敷设法及其流程。提出了曲面线偏移的概念和正交线离散点算法。矩形块敷设参考线沿船长方向延伸,按肋骨线方向布置偏移点,在MDT系统中进行二次开发,选取船体典型曲面进行了敷设设计。经验证,该方法满足工程使用要求。     

基于最佳圆弧样条逼近的快速距离曲面计算

距离曲面是一种常用的隐式曲面,它在几何造型和计算机动画中具有重要的应用价值,但以往往在对距离曲面进行多边形化时速较慢,为了提高点到曲线最近距离计算的效率,提出了一种基于最佳圆弧样条逼近的快速线骨架距离曲面计算方法,该算法对于一条任意的二维NURBS曲线,在用户给定的误差范围内,先用最少量的圆弧样条来逼近给定的曲线,从而把点到NURBS曲线最近距离的计算问题转化为点到圆弧样条最近距离的计算问题,由于在对曲面进行多边形化时,需要大量的点到曲线最近距离的计算,而该处可以将点到圆弧样条最近距离很少的计算量来解析求得,故该算法效率很高,该实验表明,算法简单实用,具有很大的应用价值。     

Nonuniform B-spline Mesh Fairing Method

A method for fairing a surface composed of a set of discrete data points distributed in anonrectangular topological mesh is presented.All curves are expressed by nonuniform cubic B-splinecurves.The fairing method is minimizing the elastic strain energy of mesh curves and of springs at-tached to the data points.The fairing surface can be generated by interpolating through the meshcurves.The generation and fairing of a ship hull surface is given as an example.     

玻璃瓶样的设计及参数化实现

对玻璃瓶样的造型方法进行了探讨,建立了瓶样的参数化造型模型,提出了以体积为控制条件的变动设计方法：构造瓶样造型的控制曲线,淫解析几何的方法得到瓶体表面上的坐标点,由坐标点得到满足使用要求的Ｂ样条瓶体表面,并通过对控制曲线的调整来完成瓶容量的调整。这种设计方法,较好地解决了一般性瓶样的设计问题,实现设计的高效性。     

一种B样条表面插值控制点的缩减方法

研究了从给定节点向量中选择节点进行B样条曲线插值的方法，并将此方法应用到行数据点不相同的B样条曲面插值，得到了一个通过对行节点矢量调整传递的曲面插值方法，理论分析和实验表明该方法可大量减少曲面控制点的数目．     

Interactive Rendering of Deforming NURBS Surfaces

Non-uniform rational B-splines (NURBS) has been widely accepted as a standard tool for geometry representation and design. Its rich geometric properties allow it to represent both analytic shapes and free-form curves and surfaces precisely. Moreover, a set of tools is available for shape modification or more implicitly, object deformation. Existing NURBS rendering methods include de Boor algorithm, Oslo algorithm, Shantz’s adaptive forward differencing algorithm and Silbermann’s high speed implementation of NURBS. However, these methods consider only speeding up the rendering process of individual frames. Recently, Kumar et al. proposed an incremental method for rendering NURBS surfaces, but it is still limited to static surfaces. In real-time applications such as virtual reality, interactive display is needed. If a virtual environment contains a lot of deforming objects, these methods cannot provide a good solution. In this paper, we propose an efficient method for interactive rendering of deformable objects by maintaining a polygon model of each deforming NURBS surface and adaptively refining the resolution of the polygon model. We also look at how this method may be applied to multi-resolution modelling.     

Direct boolean intersection between acquired and designed geometry

In this paper, a new shape modeling approach that can enable direct Boolean intersection between acquired and designed geometry without model conversion is presented. At its core is a new method that enables direct intersection and Boolean operations between designed geometry (objects bounded by NURBS and polygonal surfaces) and scanned geometry (objects represented by point cloud data).We use the moving least-squares (MLS) surface as the underlying surface representation for acquired point-sampled geometry. Based on the MLS surface definition, we derive closed formula for computing curvature of planar curves on the MLS surface. A set of intersection algorithms including line and MLS surface intersection, curvature-adaptive plane and MLS surface intersection, and polygonal mesh and MLS surface intersection are successively developed. Further, an algorithm for NURBS and MLS surface intersection is then developed. It first adaptively subdivides NURBS surfaces into polygonal mesh, and then intersects the mesh with the MLS surface. The intersection points are mapped to the NURBS surface through the Gauss-Newton method.Based on the above algorithms, a prototype system has been implemented. Through various examples from the system, we demonstrate that direct Boolean intersection between designed geometry and acquired geometry offers a useful and effective means for the shape modeling applications where point-cloud data is involved.     

自然地形环境下移动机器人的一种路径规划方法

本文给出了一种规划移动机器人在自然地形中运动的新方法，该方法利用ＮＵＲＢＳ曲面模拟自然地形地貌，以ＴｒｉｍｍｅｄＮＵＲＢＳ曲面描述带有障碍物或不可逾越区域的地形，在综合考虑机器人动力学、地形及障碍描述和曲面特性等各方面因素的情形下，运用测地线的概念和计算方法以及Ａ＊搜索算法，获得了在自然地形环境下任意两点间的距离最短路径和时间最优路径，所有的路径均由ＮＵＲＢＳ曲线表示，实验结果表明，该方法在性能与效率上均十分令人满意．     

基于C-B 样条的三角形和四边形曲面生成

文章给出了基于C-B 样条的由网格数据产生三角形和四边形曲面片的方 法,C-B 样条是由基底函数{sin t, cos t, t, 1}导出的一种新型样条曲线,它可以克服现在正在 使用的B 样条和有理B 样条为了满足数据网格的拓扑结构而增加多余的控制点,求导求积 分复杂繁琐,阶数过高,从而讨论其连续拼接时增加了困难等缺点,如何将它推广成曲面就 成为一个重要问题。作者利用边-顶点方法构造插值算子,再将这些算子进行凸性组合,将 C-B 样条曲线推广成三角形曲面片和四边形曲面片,它可以用于CAD 的逆向工程中散乱数 据的曲面重构。     

Image‐based modeling of 3D objects with curved surfaces

This paper addresses an image‐based method for modeling 3D objects with curved surfaces based on the non‐uniform rational B‐splines (NURBS) representation. The user fits the feature curves on a few calibrated images with 2D NURBS curves using the interactive user interface. Then, 3D NURBS curves are constructed by stereo reconstruction of the corresponding feature curves. Using these as building blocks, NURBS surfaces are reconstructed by the known surface building methods including bilinear surfaces, ruled surfaces, generalized cylinders, and surfaces of revolution. In addition to them, we also employ various advanced techniques, including skinned surfaces, swept surfaces, and boundary patches. Based on these surface modeling techniques, it is possible to build various types of 3D shape models with textured curved surfaces without much effort. Copyright © 2007 John Wiley & Sons, Ltd.     

NURBS扫描体的逼近算法研究

提供了一种NURBS扫描体的逼近方法。该方法主要步骤：(1)通过系列平面切割，把NURBS曲面(实体)进行降维处理，变成平面曲线；(2)为曲线设置局部标架；(3)在局部标架下求出每一曲线在每一时刻的极值点后将其转换成原曲线的奇异点；(4)使用marching cubes算法剔除扫描体内部点，保留扫描体边界上的奇异点；(5)由所有保留点拟合成奇异曲面。本算法能较好地逼近NURBS扫描体，其逼近精度可通过控制切割精度和扫描过程中时间间隔的选取而得到有效控制。