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机械毕业设计英文翻译文献翻译
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机械毕业设计英文外文翻译35变动的曲面造型,机械毕业设计英文翻译文献翻译
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附录 A1 译文 变动的曲面造型 我们提出了一种新的手段，能使自由行态的曲面造型相互影响。这种造型方法提供给用户们的是一种无限的，柔顺的，没有固定控制的曲面，从而取代了那种固定的网状控制点。用户们自由地实施那些经过处理的适合操作指令的控制点和曲线。这些复杂的曲面形状也许会因为增加更多的控制点和曲面而变得没有明显的界限。在利用那些控制的约束，这些曲面的形状会在一种或多种的简单的标准下而变得十分确定，就比如光滑度。我们解决导致强迫变形的最优化问题的方法停留在一个允许不一致的 B型活动曲线规曲面细分曲面描写上。自动细分是用来确保那些约束是满足要求， 而不去执行错误的领域。高效的数字化表示会在公式和描述问题上的线性开发中获得。 相互影响的自由形态曲面设计的最基本目标是能使用户能简单的控制曲面的形状。一般来说，这个目标的追寻已经由一种寻找“正确”的曲面描述所构成，对于用户来说，他们的自由程度是足以控制指挥操作的。处理曲面造型的要素，是用控制操作 B型活动曲线规的啮合或其他曲面制作的张力，清楚得地反映这种看法。 这种控制啮合处理出现在大型的测量上，因为曲面控制点转移的响应是直观的：拉或推一个控制点会造成那些本来能轻易地通过良好的相互影响位置的确定来控制的形状， 发生一个局部撞击或凹陷。不nts幸的是，那些局部撞击或凹陷不会只对想创作的人起重要作用。举例来说，尽管几乎任何用控制啮合面方法的人都有试着去做一个概念化的简单变化的失败经验，但是最后他们强迫去精确地复位许多甚至是全部图形，通过控制点去实现所希望的外形。 这种问题的性质是有限制的。在没有设置固定的控制就有希望达到用户要求的预期之前，提升任何时候这种为用户准备的控制是与自由度描述精密结合的能力是有限制的。 这种我们将在纸上描述的工作表明了一个通过切断控制与描述之间联系来避开不可弯曲性的能力。我们想象着提供给用户的造型 是一块无限的柔性片状光滑曲面它本身没有固定的控制或构造，按它的复杂性和能力性决定细节方面也没有前端限制。对这块曲面来说，用户也许能很自由地附加一种特征变化，就像那些为了处理知道相互影响的曲面操作而年切断的点和弯曲曲线。 约束在这些控制的利用下，曲面形态不是被那些描述的奇特行为所左右，而是被一种或多种简单直接的标准所决定，就不如说曲面应该越光滑越好，与原型形状越一致越紧密越好，如此等等。 我们这种陈述的选择是被为了提供给用户一种简单的独立描述的外观所激发的；但是，维持这种外观确实非常困难的。正式地说，我们的方 法是使曲面的详述承担对约束的变化性和最优化问题的解释，换言之，是在极端完整的条件下进行约束的曲面。为了认识到我们不仅要尽快形成和解决满足相互影响的目的，也要足够精确地准备有用的曲面造型，我们必须要做到以下关键问题： nts我们需要的一个曲面是简明的，是有能力在对曲面复杂性没有固有限制的情况下决定详细程度的改变；是有能力描述 nC 的曲面（在练习中，我们经常满足 2C 连续）和提供我们所希望的有效率的约束最优化问题的解决方法。从 另外的方面来说，在描述被向用户隐藏之前，我们不需要曲面负责一种直观的或自然的方法去控制点的操作。 我们必须能够精确的，高效的利用和维持约束在曲面上的变化，包括那些需要曲面包含一条曲线，或者需要两个曲面用一条被详细说明的整齐的曲线所连接。这样的约束产生了特殊的问题，因为这种约束平均含有一个必须极端化的整体。依照这种约束下，我们必须能够极端化任何一种曲面整体的变化，去产生清楚的曲面，使与详细的安置形状之间的偏差最小化，如此等等。 产生没有制定描述显示完全界限而能反映变化的解决方法的曲面，曲面描述的决定必须被自动 化控制。理想地来说，细分应该被一种应归于曲面近似值错误的测量驱动的。随着约束的增加，额外的自由度必须被准备去容许所有约束在没有错误的调节下同时被满足。不像点约束那样需要被精确的满足，整体的约束需要对带给它们有详细公差在内的近似值误差。额外的细分部分应该被误差的估计所驱动的，而这些误差是那种约束变化最小化是被近似的误差。 在这篇文章中，我们报道了我们在追踪那些需要详细说明的实质研究事项上的进步。根据工作的背景和联系的讨论，我们将在每个产生的外形上标明地址。首先，简洁的描述能任意详述曲面的要求使我们去思考局部精 细描述的方案。经管很多方面已经得到发展，但是不nts能满足我们描述的所有要求。我们描述一个曲面是基于 B型活动曲线规在不同的详述水平上的制造张量的总计上。其次，我们考虑约束本身的最优化问题。我们给出一些客观的方程式函数，讨论为了控制在曲面上的任意点和曲线而做的线性约束。然后我们就把问题转到自动化曲面磨光基于两种近似值误差上：客观函数误差和约束误差。最后，我们描绘初步的实施方法和提供结果。 控制相互作用的网孔局限性的操作在以前就已经很著名了。对它们的解说， Fowler和 Bartel提出允许用户熟练操作任意线性曲线和曲面上的点的方法： 曲线 /表面被强迫窜改被抓取的点。当点被相互作用地移动，控制点的修改是使限制的修改服从最小化。参数的导数也为直接的处理被呈现给使用者 ,用点去控制曲面的方位和曲率。通过超越点的约束， Celnike 和 Welch 提出了一种冻结内含式曲线形状的技术。尽管有关曲面沿着一条沿着控制曲线移动的论点还没有被提出来。 我们的一项主要需求是在能被决定的细节上没用先验的限制表现平滑的表面能力。虽然一些不均匀细化方案已经被发展了，但是还没有一种现有的符合我们的全部需要的方案。它们中的大多数不能提供我们所需要的 2C 连续性。在计算机图形方面，贝塞尔曲线片已经广泛地用来做不均匀细化。但是一般来说，如果在细分之后被操作，贝塞尔曲线碎片之间的高次序连续性是不被保护的，虽然用 1G 连续性阐明贝塞尔曲线碎片的细化。虽然支持拓扑无规律网孔的三角形片被广泛地应用于有限元分析，但是已经被限制在第一次序的连续性上。nts最经发展的指向三角形 B型 活动曲线规碎片作为一种构造一个横跨三角形网孔的高次序连续性曲面的方法，尽管对于一个如此表现还没有出现一个有 效率计算细分的方案。 Forsey提出一种用一种矩形层的 B型 活动曲线规覆盖来创建 2C 曲面精确方案。覆盖能手动对曲面增加细节，已经大规模和小规模改变曲面形状能通过操作不同高度控制点来实现。虽然分层抵消也许能适当指导使用者控制点的操作，但是这并不能满足我们对于一种用于约束变化最优化的精制基础的要求。一种常规张量积曲面的基本优势是线性的：曲面的点和派生物是控制点的一次函数。因为单位法线用于计算抵消，所以在 Forsey的线性公式形成下被丢失。我们在较后的区域倚重线性； 主要抵消表示法的使用有可能对性能有破坏性的影响。 约束变化最优化对所谓的自然样条的阐述起着非常重要的作用，把篡改控制点的立方的 2C 平面曲线分段。自然样条把第二派生的正方形的整体最小化的试验使之遭遇频繁地添加约束作为一个变化的微积分示范问题。 首要是变化为基础的曲面造型已经广泛的用于计算机现象去解决曲面重建问题，在一个曲面上适合立体地测量，日期的嘈杂定位，表面定方向，投影等等。类似的阐述已经被物理地基于可变表面的造型的计算机图像所使用。 这些全部以有规则的，有限的，有规则的确定解释的格子为基础。 基于第二派生物规则的约束最优化已经被用于平的 B行活动曲线规的曲面。 当在寻找弯的或直的横截面线时， Moreton把发生在表面nts是曲线网格的曲面上的曲率变化最小化。虽然这样的方法会造成非常失败的曲面，但是他们的平顺性的非线性阻止它们被用于交互式曲面设计。 Celniker提议一种为了交互式自由形态的曲面设计，以身体为基础的造型，那种表面用一种三角形片的 1C 网孔， 而且位置和常态可能沿着片边界被控制。相互影响是 可能的，因为曲面平整问题被阐述成一个二次函数最小化服从线性约束。我们的方法是近似地讲述这方面的相互关系。 我们需要一种平滑可变曲面的表示方法，使之在可以决定的细节上没有先前的限制。更进一步，我们需要这样一个曲面上的点是形状控制参数的线性函数，屈从一个更容易的控制问题。 B型活动曲线规的张量积方便地表示 nC 分段多项式曲面作为控制点集合非线性形状功能的总数， 而且他们形成我们表示方案的基础。不幸的是，标准的张紧积结构不允许细节通过局部改进被不均匀地添加添加在曲面上。我们替换如局部改进的区域作为曲面的总和，更加细微化地参数化曲面。不同水平的表面片被评价和总计去计算曲面值的不均匀。虽然这是涉及到对 B型活动曲线规的 Forsey的覆盖方案，但是 因为为覆盖没有分层抵销的观念，形成非常简单。不均匀表面是简单的稀疏的，统一的分层堆积总和，可能以任意方式重叠。更近一步来说，产生的曲面形状保持着一个控制点的一次函数，引导一个易于控制的曲面控制问题。 nts 附录 B1 外文文献 Variational Surface modeling We present a new approach to interactive modeling of free-from surfaces. Instead of a fixed mesh of control points, the model presented to the user is that of an infinitely malleable surface, with no fixed controls. The user is free to apply control points and curves which are then available as handles for direct manipulation. The complexity of the surfaces shape may be increased by adding more control points and curves, without apparent limit. Within the constraints imposed by the controls, the shape of the surface is fully determined by one or more simple criteria, such as smoothness. Our method for solving the resulting constrained variational optimization problem rests on surface representation scheme allowing nonuniform subdivision of B-spline surfaces. Automatic subdivision is used to ensure that constraints are met, and to enforce error bounds. Efficient numerical solutions are obtained by exploiting linearities in the problem formulation and the representation. The most basic goal for interactive free-form surface design is to make it easy for the user to control the shape of the surface. Traditionally, the pursuit of this goal has taken the form of a search for the “right” surface representation, one whose degrees of freedom suffice as controls for direct manipulation by the user. The dominant approach to surface modeling, using a control mesh to manipulate a B-spline or other tensor product surface, clearly reflects this outlook. The control mesh approach is appealing in large measure because the surfaces response to control point displacements is intuitive: pulling or pushing a control point makes a local bump or dent whose shape is quite easily controlled by fine interactive positioning. Unfortunately, local bumps and dents are not the only features one wants to create. For example, almost anyone who has used a control mesh interface has had ntsthe frustrating experience of trying to make a conceptually simple change, but being forced in the end to precisely reposition manyeven allthe control points to achieve the desired effect. This sort of problem is bound to arise whenever the controls provided to the user are closely tied to the representations degrees of freedom, since no fixed set of controls can be expected to anticipate all of the users needs. The work we will describe in this paper represents an effort to escape this kind of inflexibility by severing the tie between the controls and the representation. The model we envision presenting to the user is that of an infinitely malleable piecewise smooth surface, with no fixed controls or structure of its own, and with no prior limit on its complexity or ability to resolve detail. To this surface, the user may freely attach a variety of features, such as points and flexible curves, which then serve as handles for direct interactive manipulation of the surface. Within the constrains imposed by these controls, surface behavior is governed not by the vagaries of the representation, but by one or more simply expressed criteriathat the surface should be as smooth as possible, should conform as closely as possible to a prototype shape, etc. Our choice of this formulation is motivated by the desire to present a simple representation-independent faade to the user, however, maintaining the faade is anything but simple. Formally, our approach entails the specification of surface as solutions to constrained variational optimization problems, i.e. surfaces that extremize integrals subject to constraints. To realize our goal of forming and solving these problems quickly enough to achieve interactivity, yet accurately enough to provide useful surface models, we must address these key issues: We require a surface representation that is concise, yet capable of resolving varying degrees of detail with no inherent limit to surface complexity; that is capable of representing nC surfaces (in practice we are usually content with 1C continuity) and that supports efficient solution of the constrained optimization problems we wish to solve. On the other hand, since the representation is to be hidden from the user, we do not require the surface to respond in an intuitive or natural way to direct control-point manipulation. We must be able to accurately and efficiently impose and maintain a variety of constraints on the surface, including those requiring the ntssurface to contain a curve, or requiring two surfaces to join along a specified trim curve. Such constrains raise special problems because the constraint equation involves an integral which must be extremized. Subject to the constraints, we must be able to extremize any of a variety of surface integralsto create fair surfaces, minimize deviation from a specified rest shape, etc. To create surfaces that reflect the variational solution, without letting the limitations of the representation show through, the resolution of the surface representation must be automatically controlled. Ideally, subdivision should be driven by a measure of the error due to the surface approximation. As constraints are added, additional degrees of freedom must be provided to allow all constraints to be satisfied simultaneously without ill conditioning. Unlike point constraints, which can be met exactly, integral constraints require subdivision to bring their approximation error within a specified tolerance. Additional subdivision should be driven by estimates of the error with which the constrained variational minimum is approximated. In this paper we report on our progress to date in pursuing the substantial research agenda that these requirements define. Following a discussion of background and related work, we will address each of the issues outlined above. First, the need to compactly represent arbitrarily detailed surfaces leads us to consider schemes for locally refinable representations. Although many have been developed, none meets all of our requirements. We describe a surface representation based on sums of tensor-product B-splines at varying levels of detail. Next we consider the constrained optimization problem itself. We give formulations for several quadratic objective functions, and discuss linear constraints for controlling arbitrary points and curves on the surface. We then turn to the problem of automatic surface refinement based on two kinds of approximation error: objective function error, and constraint error. Finally, we describe a preliminary implementation and present results. The limitations of control meshes as interactive handles have been noted before. To address them, Fowler and Bartels present techniques that allow the user to directly manipulate arbitrary points on linear blend curves and surfaces: the curve/surface is constrained to interpolate the grabbed point. As the point is moved interactively, the change to control points is minimized subject to the interpolation constraint. Parametric derivatives are also presented to the user for direct manipulation, to control surface orientation and curvature at a point. Moving beyond point constraints, Celniker and Welch presented a technique for freezing ntsthe shape along an embedded curve, although the issues involved in having the surface track a moving control-curve were not addressed. One of our key requirement is the ability to represent smooth surfaces with no a priori limit on the detail that can be resolved. Although a number of nonuniform refinement schemes have been developed, no existing one meets all of our needs. Most of these fail to provide 2C continuity we require. In computer graphics, Bezier patches have been widely used for nonuniform refinement. In general, however, higher-order continuity between Bezier patches is not preserved if they are manipulated after subdivision, though formulates adaptive Bezier patch refinement with 1G continuity. Triangular patch, which support topologically irregular meshes, are widely used in finite element analysis, but have been restricted to first-order continuity. Recent developments point to triangular B-spline patches as a way of constructing a surface with high-order continuity across a triangular mesh, although a computationally efficient refinement scheme for such a representation has not yet been presented. Forsey presents a refinement scheme that uses a hierarchy of rectangular B-spline overlays to produce 2C surfaces. Overlays can be added manually to add detail to the surface, and large- or small-scale changes to the surface shape can be made by manipulating control points at different levels. The hierarchic offset scheme may be well-suited to direct user manipulation of the control points, but it does not meet our need for a refinable substrate for constrained variational optimization. One of the fundamental advantages of conventional tensor product surface is linearity: surface points and derivatives are linear functions of the control points. Under Forseys formulation linearity is lost because unit normals are used to compute offsets. We depend heavily on linearity in later sections; use of the hierarchic offset representation would have a devastating impact on performance. Variational constrained optimization plays a central role in the formulation of so-called natural splines, piecewise cubic 2C plane curves that interpolate their control points. The proof that natural splines minimize the integral of second derivative squared subject to the interpolation constraints frequently appears as a demonstration problem in the calculus of variations. Surface models based on variational principals have been widely used in computer vision to solve surface reconstruction problem, in which a surface is fit to stereo measurements, noisy position date, surface orientations, shading information etc. Similar formulations have ntsbeen employed in computer graphics for physically based modeling of deformable surfaces. All of these are based on regular finite difference grids of fixed resolution. Constrained optimization based on second-derivative norms has been used in fairing B-spline surfaces. Moreton minimizes variation of curvature to generate surfaces which skin networks of curves while seeking circular or straight-line cross-sections. Such schemes can give rise to very fail surfaces, but the nonlinearity of their fairness metrics prevents them from being used for interactive surface design. Celniker proposed a physically-based model for interactive free-form surface design, in which the surface is modeled using a 1C mesh of triangular patches, and position and normal may be controlled along patch bounda
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