NURBS双向蒙皮造型方法的研究与实现

本文通过对ＮＵＲＢＳ造型方法技术的研究，在自主开发的ＳｕｐｅｒＭａｎＣＡＤ／ＣＡＭ集成系统中成功地实现了基于复杂曲线的ＮＵＲＢＳ双向蒙皮曲面的造型功能，从而建立了完全基于ＮＵＲＢＳ方法的ＣＡＤ／ＣＡＭ系统．通过大量的工程应用和实例验证表明所研究的ＮＵＲＢＳ方法是一种适用于复杂外形产品设计与制造的、灵活有效的造型方法．     

Appropriating an architectural design tool for musical ends

NURBS (non-uniform rational b-spline) modelling has become a ubiquitous tool within architectural design praxis. In this article I examine three projects that utilise NURBS modelling as a means for which a musical system's inherent spatiality is visualised. There are numerous precedents for which architectural form is a derivation of a musical system, or a musical system is proportionally informed by architectonic gesture. I propose in this article three NURBS modelling methodologies: for the spatial analysis of Karlheinz Stockhausen's sound projection geometries in Pole für 2; for a spatial realisation of John Cage's indeterminate work Variations III; and for the generation of a surface manifold informed by musically derived soundscape data from the Japanese garden Kyu Furukawa Teien. Rather than seeking to translate music into inhabitable architecture, or architectonic form into music, I highlight an approach that produces an interstitial territory between discourses on architecture and music analysis.     

反向工程中NURBS曲面CAD重构技术研究

CAD几何模型重构技术是反向工程RE(Reverse Engineering)技术的核心,NURBS(Non-Uniform Rational B-Splines)方法因其表示法的形状控制灵活性,在曲面造型和曲面重构中具有重要作用.针对CAD曲面重构技术进行研究,并对NURBS曲面重构提出一种新的构建方法,将每个数据点相对应的有理基函数的参数值最大化,所得函数值作为数据点的参数值来构造NURBS参数曲面.最后通过实例证明了该方法的有效性.     

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.     

Automatic surface modelling of a ship hull

When defining a ship hull surface, the main objective is to obtain a faired surface or surfaces that contain some specific points of the hull, that have been selected in the design process and give the ship its hydrodynamic, stability and other properties. So, the hull surface should be a compromise between fairness and precision, and this is not and easy task. In this paper, authors present a thorough procedure for automatic modelling with a fair NURBS surface, having lists of points on the stations of the vessel as initial data. The construction of spline curves, and their application in the definition of ship lines is 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 increase the accuracy of the splines. NURBS surfaces modelling the hull of the vessel are constructed and the fairing process adapted to maintain certain ship characteristics is described.     

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.     

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.     

基于能量优化的NURBS曲面几何特征修改

NURBS作为曲面造型技术中的重要方法之一,在计算机辅助几何设计和计算机图形学领域中有着广泛的应用。针对NURBS曲面的几何特征修改,提出了基于能量优化的修改方法。通过对NURBS曲面的控制顶点进行扰动,以曲面的应力能改变为目标函数并使之最小化,实现了NURBS曲面上给定多个点处的位置、一阶偏导矢、二阶偏导矢和法矢等几何特征的修改。数值实例表明该方法用于微调时,可实现对曲面局部形状的多种修改效果,便于交互设计。     

插值边界曲线的NURBS 近似极小曲面设计

探索性地设计了一个插值给定边界曲线的NURBS 近似极小曲面算法,弥补了当前NURBS 系统无法有效地设计工程所急需的一般NURBS 极小曲面的缺陷.运用NURBS 曲面的节点插入、Hybrid 多项式逼近等多种技术,将NURBS 曲面转化为相对简单的分片Bézier 曲面求解,并运用各子曲面片的控制顶点优化、整体曲面不断更新的迭代方法,成功地得到高精度的近似分片Bézier 极小曲面.最后,可以按用户的各种要求选择运用相应不同的迭代逼近算法,求取插值给定边界曲线的近似NURBS 极小曲面.     

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.     

Subdivision Surfaces with Creases and Truncated Multiple Knot Lines

We deal with subdivision schemes based on arbitrary degree B‐splines. We focus on extraordinary knots which exhibit various levels of complexity in terms of both valency and multiplicity of knot lines emanating from such knots. The purpose of truncated multiple knot lines is to model creases which fair out. Our construction supports any degree and any knot line multiplicity and provides a modelling framework familiar to users used to B‐splines and NURBS systems.     

Interactive display of large NURBS models

We present algorithms for interactive rendering of large-scale NURBS models. The algorithms convert the NURBS surfaces to Bezier surfaces, tessellate each Bezier surface into triangles, and render them using the triangle-rendering capabilities common to current graphics systems. We present algorithms for computing tight bounds on surface properties in order to generate high quality tessellation of Bezier surfaces. We introduce enhanced visibility determination techniques and present methods to make efficient use of coherence between successive frames. In addition, we also discuss issues in parallelization of these techniques. The algorithm also avoids polygonization anomalies like cracks. Our algorithms work well in practice and, on high-end graphics systems, are able to display models described using thousands of Bezier surfaces at interactive frame rates     

基于NURBS曲面的棉花器官建模

数字农业将工业可控生产和计算机辅助设计的思想引入农业。该文介绍了利用NURBS和OpenGl对虚拟棉花主要器官果枝、铃、主茎叶、果枝叶、花瓣、苞叶等进行建模的方法,得到了逼真的效果。与三维数字化方法相比,省去了大量精确数据的测量和数学表达式的拟合工作。     

复杂地质体NURBS辅助建模及可视化分析

基于NURBS技术提出一种重建复杂三维地质体的建模方法．首先对数字地形模型进行简化处理以满足地质体重建的需要;然后结合地质原始资料和解译数据,拟合构造出更能反映地质规律的地质结构面．在此基础上,利用三维图形学技术重建复杂地质体,并根据实际需要对整体模型实现一系列的三维地质信息可视化分析．实际水电工程应用表明,文中方法可以满足复杂工程地质信息三维可视化研究的实际需要．     

Fitting NURBS spherical patches to measured data

Algorithms and empirical studies for fitting spherical and planar NURBS patches to random data are presented. Algebraic as well as geometric methods are discussed leading to efficient techniques for surface as well as patch fitting. An automatic fitter is also presented that determines whether a plane or a sphere fit is optimal, computes the appropriate entities, and clips the geometry to obtain a NURBS sphere or plane fit. It is argued that patch fitting is necessary in order to avoid numerical problems due to pole and seam problems.     

基于3D曲面模型的数字水印算法

本文给出了一种NURBS曲面模型的三维数字水印算法.该算法不直接将水印信息嵌入到NURBS曲面的参数中,而是对原始NURBS曲面模型进行修改,通过映射成虚拟2D图像,利用已有的DCT域图像水印嵌入算法将信息嵌入到2D图像中,再对2D图像进行提取产生新的NURBS曲面水印模型.该算法对于控制顶点、节点向量的改变以及模型表面的近似等操作具有鲁棒性.     

Multi-degree reduction of NURBS curves based on their explicit matrix representation and polynomial approximation theory

NURBS curve is one of the most commonly used tools in CAD systems and geometric modeling for its various specialties, which means that its shape is locally adjustable as well as its continuity order, and it can represent a conic curve precisely. But how to do degree reduction of NURBS curves in a fast and efficient way still remains a puzzling problem. By applying the theory of the best uniform approximation of Chebyshev polynomials and the explicit matrix representation of NURBS curves, this paper gives the necessary and sufficient condition for degree reducible NURBS curves in an explicit form. And a new way of doing degree reduction of NURBS curves is also presented, including the multi-degree reduction of a NURBS curve on each knot span and the multi-degree reduction of a whole NURBS curve. This method is easy to carry out, and only involves simple calculations. It provides a new way of doing degree reduction of NURBS curves, which can be widely used in computer graphics and industrial design.     

NURBS曲线自动光顺的一种有效算法

提出了一种局部光顺NURBS曲线的算法。算法建立在重复删除和插入节点的过程中，这个重复删除和插入的节点通过一个光顺准则自动选择。此算法自动找出NURBS曲线需要修改的那一点，局部修改控制多边形，使生成的新曲线更加光顺。     

Interactive rendering of NURBS surfaces

NURBS (Non-uniform rational B-splines) surfaces are one of the most useful primitives employed for high quality modeling in CAD/CAM tools and graphics software. Since direct evaluation of NURBS surfaces on the GPU is a highly complex task, the usual approach for rendering NURBS is to perform the conversion into Bézier surfaces on the CPU, and then evaluate and tessellate them on the GPU. In this paper we present a new proposal for rendering NURBS surfaces directly on the GPU in order to achieve interactive and real-time rendering. Our proposal, Rendering Pipeline for NURBS Surfaces (RPNS), is based on a new primitive KSQuad that uses a regular and flexible processing of NURBS surfaces, while maintaining their main geometric properties to achieve real-time rendering. RPNS performs an efficient adaptive discretization to fine tune the density of primitives needed to avoid cracks and holes in the final image, applying an efficient non-recursive evaluation of the basis function on the GPU. An implementation of RPNS using current GPUs is presented, achieving real-time rendering rates of complex parametric models. Our experimental tests show a performance several orders of magnitude higher than traditional approximations based on NURBS to Bézier conversion.