Class A曲面的定义

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catiaClass-A知识解读

开瑞汽车工程研究院 KAERI
A-class 包括多方面评测标准 , 比如说反射是不是好看、顺眼等等。当然，G2可以说是一个基本要求,因为 g2以上才有光顺的反射效果。但是, 即使 G3 了，也未必是 a-class, 也就是说有时虽然连续，但是面之间出现褶皱，此时就不是 a-class 通俗一点说，class-A就必须是G2以上连接。 G3 连续的面不一定是 CLASS-A 曲面。汽车业界对于 a class要求也有不同的标准， GM 要求比 TOYOTA ， BMW 等等要低一些，也就是说 gap 和 angle 要求要松一些。关于 A-class surfaces ，涉及曲面的类型的二个基本观点是位置和质量。位置——所有消费者可见的表面按 A-Surface 考虑。汽车的 console （副仪表台）属于 A-surf ，内部结构件则是B-surf。
开瑞汽车工程研究院 KAERI
曲线连续
开瑞汽车工程研究院 KAERI
曲面连续
开瑞汽车工程研究院 KAERI
高光表现
开瑞汽车工程研究院 KAERI
前风挡玻璃，曲率连续（对称面要求）
开瑞汽车工程研究院 KAERI
开瑞汽车工程研究院 KAERI
开瑞汽车工程研究院 KAERI
B、切向连续
开瑞汽车工程研究院 KAERI
1、根据造型特征拆分曲面，分块要合理，曲面在UV方向都保证曲率的连续性及变化趋势的合理。面的分块应该将主模型作为一个整体来考虑，整体的思想可保证整个面的和谐统一 2、建议采用尽可能少的面片，曲面使用单段面和低阶面，一般少于6阶。 3、基本曲面应该建立到或超过理论的相交区域，这提供了更大的自由度，用来对过渡面变化调整和高光线控制。曲面应该产生预期的延伸，延伸没有任何不正常结果（例如猴尾巴和螺旋），这允许下游的建模者产生延伸用来满足实体建模、工艺补充面、钻模和夹具需要。 4、曲面应该修剪到内部边界并且能够缝合，要提供生成修剪实体的理想数据。

CLASS-A级曲面要求与检查方法-如吾意-2020-9-3

CLASS-A级曲面要求与检查方法1 范围本标准规定了CLASS-A级曲面建构要求与检查的方法。

本标准适用于乘用车外表面及内饰面的A 级曲面建构（以下简称“A 面”）。

汽车其他可见面也可参照使用。

2 规范性引用文件下列文件对于本标准的应用是必不可少的。

凡是标注日期的引用文件，仅限标注日期的版本适用于本标准。

凡是不注日期的引用文件，其最新版本（包括所有的修改单）适用于本标准。

GB 11552-2009 乘用车内部凸出物GB 11522-2009 乘用车外部凸出物3 术语和定义下列术语和定义适用于本标准。

3.1A面A面是指有着严格表面质量要求的曲面或曲面组，此概念由 DASSAULT 最早在CATIA V4中提出，用以定性并定量约束单个曲面或曲面组整体的质量。

3.2B样条曲面任意空间曲面都可以看作是无数点的集合。

如下图所示，在 V 方向任意截面上选择M+1 个点为特征顶点，用最小二乘积逼近方法可生成一条曲线，该曲线即为 B 样条曲线。

同样，在 V 方向的不同截面上可生成一组(N+1)条 B 样条曲线。

用同样的方法在 U 方向的不同截面也生成一组(M+1)条 B 样条曲线。

两组 B 样条曲线的直积可求得 B 样条曲面。

该曲面即为我们要描述的任意复杂空间曲面。

图14 分类按覆盖面积和造型优先级，造型表面元素可分为基础面和特征细节两类。

示例1：车门玻璃面、顶盖和挡风等为基础面；示例2：如棱线和倒角等为特征细节。

5 A面常规要求5.1 基础面要求5.1.1 对于基础面，采用非四边域的形式构建。

其U/V段数必须为 1，如果是贝塞尔曲面，其阶数不超过7；如果是B样条曲面，其阶数不超过6。

构建初始，必须先分析确定曲面是否有对称性，以及U/V是否正交。

5.1.2大部分的造型基础面是单凸曲面，这类曲面可分为球形面（高斯曲率为正）和鞍形面（高斯曲率为负）两种。

如果基础面非单凸（S形，多为过渡面），必须在造型一开始就加以明确。

车身ClassA评价标准和方法.pdf

车身Class A评价标准和方法Prepared byCLASS A的概念一、一、CLASS1、连续性的几种方式曲面曲线的连续性有以下几种方式，并做相应的几何表达：POINT连续Tangent连续Curvature连续高质量连续C0C1C2G0G1G2G3上述四种连续性关系只是构造Class A的基础，在应用这些概念时必须综合进行考虑。

对于精度的要求可根据对象的不同要求来确定。

2、CLASS A的评估方法对于汽车外形来讲，最重要的是曲线、曲面的评估方法。

在传统的手工处理时。

曲线质量是由设计人员从各个方向观察画在图板上的大比例曲线来进行检查。

车型设计人员通过观察可以指出哪一段是好的，哪一段有鼓包等等。

为了解释相应的现象，在被检查曲线上画出相应曲率半径的的对数值，设计人员可指出有问题的区域相应于曲线上的不光顺区域，这种方法被称为轮廓检验或曲率半径分布。

一个CAD系统不仅必须提供各种曲面定义方法，还必须提供曲面质量评估技术。

一种检查曲面设计质量的方法是模拟曲面的高光。

对应于手工制作的油泥高光检查方法如下：把模型置于在墙上和天花板上安装了许多平行白炽灯的房中，观察这些平行光在曲面上的图象，并检查出不和谐的地方。

高光对曲面上点的法矢方向的变化十分敏感。

轮廓图的杂乱无章表明曲面上相应区域内曲率分布不均。

在C1连续的边界处，高光轮廓图有断点，对C0连接则不连续。

另一种评估形状的方法是观察曲面上曲线或截面线的曲率轮廓图。

不规则的轮廓图表明曲面上相应区域质量不好（不光顺）。

曲率半径检查比高光检查容易，因此在设计阶段常采用这种方法。

但是，仅用曲率轮廓图检查对于评估曲面质量是不够的。

因为有时曲率轮廓图看起来很好，但是高光分布图有波动，必须对曲面进行修改。

有时也用彩色光照图评价曲面质量。

但是通常彩色光照图显示并不十分有效，因为光照图显示的目的是得到高质量的图像，并不能完全显示出产品的曲面质量。

但是，随着近来计算机硬件和软件性能的提高，计算汽车在各种金属材质上的反光性质以便进行光线的跟踪计算。

A面严格定义

1 范围本标准规范了CLASS A SURFACE设计的基本要求，及检查标准。

2 CLASS A SURFACE定义CLASS A SURFACE（文中后继简称“A面”）指有着严格表面质量要求的曲面或曲面组，此概念由DASSAULT最早在CATIA V4中提出，用以定性并定量约束单个曲面或曲面组整体的质量。

3 CLASS A SURFACE常规要求按覆盖面积和造型优先级，造型表面元素可分为基础面和特征细节两类。

基础面，如：车门玻璃面、顶盖和挡风等。

特征细节，如：棱线和倒角等。

基础面对于基础面，严禁采用非四边域的形式构建。

其U/V 段数必须为1，如果是BEIZER曲面，其阶数不超过7；如果是B-SPLINE，其阶数不超过6。

构建初始，必须先分析确定曲面是否有对称性，以及U/V是否正交。

大部分的造型基础面是单凸曲面，这类曲面可分为球形面（高斯曲率为正）和鞍形面（高斯曲率为负）两种。

如果基础面非单凸（S形，多为过渡面），必须在造型伊始就加以明确。

以曲线为基础构造基础面时，曲线在保证高质量的同时务必要简洁。

建模前先确定参数化方式，避免建立曲面时产生交叉节点或增加数据量。

按建模顺序，基础面可分为基础大面和过渡大面。

基础大面，如：风窗表面和车门外板表面等。

过渡大面，如：前、后保险杠的包角面等。

基础大面的四个曲面边界均不应小于实际选用区域，边界按曲率延伸时，不应出现层叠或扭曲等质量缺陷。

过渡大面的过渡对应曲面边界须严格锁定在理论过渡边界，其控制点分布应与两侧曲面控制点相对应。

过渡大面时切忌因为提高连续性而降低曲面自身的质量注：为保证曲面内部的G3和G4连续性，减少控制点数目，避免产生工程建模和投图过程中不必要的辅助线，自身对称的曲面（如顶盖大面）应尽量一次构建。

会签2004-7-15 实施CHWS-009特征细节特征棱线特征棱线的位置和消失区域须与造型设计完全一致。

倒角倒角的半径最小值通常在弦长中心垂直对应点，控制点排列宽度必须与R大小相对应；R尽量取整数。

对于A级曲面的理解（一）

对于A级曲面的理解（一）做冲压的伙伴，也经常需要去应对零件的表面缺陷问题。

所谓知己知彼百战不殆，如果我们能够深刻的理解A级曲面的定义，了解质量对冲压件表面的管控的原因，则可以更好的应对问题，更好的解决问题，更好的为企业服务。

A级曲面概念适用于汽车开发领域，在整个汽车开发的流程中，有一称为Class-A Engineering的工程阶段，该阶段的重点工作是：确定汽车曲面的品质可以符合A级曲面的要求。

设计阶段做到A级曲面的要求，制造过程中则需要将这些图纸的定义转化为现实的零件，且仍能够满足设计定义。

A级曲面，虽然更多的是一种美学的要求，但是为了能够更好的管控和评价，在设计阶段，从数学和几何上要求如下：相邻曲面间间隙G0在 0.005mm 以下，切率改变G1在0.16度以下，曲率改变G2在0.005 度以下，符合这样的标准才能确保钣金件的环境反射中大概率不会出问题。

若不能满足A级曲面，则用户会感受到汽车的表面的光影不顺，特别是在某些特定的光线下，能够明显的感觉到车子外观存在缺陷，从而对车子的品质产生质疑。

A级曲面包括多方面评测标准，比如说反射是不是好看、顺眼等等。

当然，G2可以说是一个基本要求，因为G2以上才有光顺的反射效果。

但是，即使G3了，也未必是A级曲面，也就是说有时虽然连续，但是面之间出现褶皱，此时就不是A级曲面。

进一步讲：A级曲面必须是G2以上连接，但G3连续的面不一定是A级曲面。

A级曲面有可能是曲率不连续的，如果那是设计的意图，甚至有可能切线不连续,如果设计意图是一处折痕或锐边（而通常注塑或冲压不能有锐边，因此A级曲面一定是切线连续的）。

汽车业也有这种简单的分类法：A级曲面指的是车身外表面及白车身；B面指的是不重要表面，比如内饰表面等；C面指的是不可见表面。

但是现在随着现代美学的发展及舒适性要求的日益提高，对汽车内饰件也提到了A级曲面的要求。

不同汽车厂商对于A级曲面的要求也不尽相同。

随着美学和舒适性的要求日益提高，对汽车内饰件也提到了A级曲面的要求。

何谓A级曲面的评定标准

何謂A級曲面的評定標準汽車外形設計對曲面的評定標準分為A、B、C3級。

A級要求最高，反射評定不可以出現變異，對於車身來說，一般指車身外表可見件及內飾可見件，如頂蓋，發動機罩外板，葉子板、保險桿及內飾儀錶板等部件。

B級是指地板等大型不可見件。

C級主要是結構撐件，如支架等。

關於A-class surfaces，涉及曲面的類型的二個基本觀點是位置和質量。

．位置—所有消費者可見的表面按A-Surface考慮。

汽車的console（副儀錶台）屬於A-surf，內部結構件則是B-surf。

．質量—涉及曲面拓撲關係、位置、切線、曲面邊界處的曲率和曲面內部的patch 結構。

有一些意見認為“點連續”是C類，切線連續是B類，曲率連續是A類。

而我想更加適當地定義為C0、C1和C2，對應於B樣條曲線方程和它的1階導數（相切=C1）和它2階導數（曲率=C2）。

因此一個A-surf有可能是曲率不連續的，如果那是設計的意圖，甚至有可能切線不連續,如果設計意圖是一處折痕或銳邊,（而通常射出或沖壓不能有銳邊，因此A-surf一定是切線連續(C1)的)。

第二種思維以汽車公司和白車身製造方面的經驗為基礎，做出對A-surf更深刻的理解。

他們按獨立分類做出了同樣的定義。

1.物理定義：A-surf是那些在各自的邊界上保持曲率連續的曲面。

曲率連續意味著在任何曲面上的任一"點"中沿著邊界有同樣的曲率半徑。

曲面是挺難做到這一點的，切線連續僅是方向的連續而沒有半徑連續，比如說倒角。

點連續僅僅保證沒有縫隙，完全接觸。

事實上，切線連續的點連續能滿足大部分基礎工業（航空和航太、造船業、BIW等）。

基於這些應用，通常並無曲率連續的需要。

2.根據定義：A-surf是那些在產品中可見的有特定物理意義的曲面。

A-surf首先用於汽車，並在消費類產品中漸增（牙刷，PDA，手機，洗衣機......等）。

同時它也是美學的需要，在真實世界裡，曲率連續是無處不在的，是主旋律．點連續（也稱為G0連續）在每個表面上生產一次反射，反射線成間斷分佈。

曲率变化率的化率连续逆向造型的A级曲面详解

在整个汽车开发的流程中，有一工程段称为 Class A Engineering，重点是在确定曲面的质量可以符合A级曲面的要求。

所谓A级曲面的定义，是必须满足相邻曲面间之间隙在 0.005mm 以下（有些汽车厂甚至要求到 0.001mm），切率改变 ( tangency Change )在0.16度以下，曲率改变 (curvature change) 在0.005 度以下，符合这样的标准才能确保钣件的环境反射不会有问题。

a-class包括多方面评测标准,比如说反射是不是好看、顺眼等等。

当然，G2可以说是一个基本要求,因为g2以上才有光顺的反射效果。

但是,即使G3了，也未必是a-class,也就是说有时虽然连续，但是面之间出现褶皱，此时就不是a-class通俗一点说，class-A就必须是G2以上连接。

G3连续的面不一定是CLASS-A曲面。

汽车业界对于a class要求也有不同的标准，GM要求比TOYOTA ，BMW等等要低一些，也就是说gap和angle要求要松一些。

关于A-class surfaces，涉及曲面的类型的二个基本观点是位置和质量。

位置——所有消费者可见的表面按A-Surface考虑。

汽车的console（副仪表台）属于A-surf，内部结构件则是B-surf。

质量——涉及曲面拓扑关系、位置、切线、曲面边界处的曲率和曲面内部的patch结构。

有一些意见认为“点连续”是C类，切线连续是B类，曲率连续是A类。

而我想更加适当地定义为C0、C1和C2，对应于B样条曲线方程和它的1阶导数（相切=C1）和它2阶导数（曲率=C2）。

因此一个A-surf有可能是曲率不连续的，如果那是设计的意图，甚至有可能切线不连续,如果设计意图是一处折痕或锐边,（而通常注塑或冲压不能有锐边，因此A-suuf一定是切线连续(C1)的）。

第二种思想以汽车公司和白车身制造方面的经验为基础，做出对A-surf更深刻的理解。

Class A曲面数模的质量定义和检测

Ａ级曲面就是通常所讲的Ｃａ，ｌｓｌｓＣｓＡ一词ｓＡａ最初是由法国ＤｓａｈＳｓｍ公司在开发大型ａｓｕｙｔｅ
ＣＤＣＭ软件包ＣＴＡ时提出并付诸应用的，Ａ／ＡＡＩ常译作Ａ级曲面，专指车身模型中对曲面质量有较高要求或特殊要求的一类曲面，外形曲面、表板如仪和内饰件表面等。ＣＴＡＶ从ＡＩ５版本开始，件中新软增加了ＡＡ（ｕｏｏｖｌｓ）模块，专门用于ＣＡｔｍｔｅＣａｉｓＡ
低生产成本等）又精确表达造型意图的光顺曲面。
关键词：ｌｓＡ曲面Ｃａｓ数模
１前言
在当今汽车车身设计中广泛使用的数字模型对提升整车开发效率有着巨大的作用，根据设计目的的不同，曲面数模大体上有以下几种用途：达造型表意图的ＣＳＡ（计算机辅助造型）视觉评审使用的ｖ，Ｒ数模，加工快速样件／泥的ｍｏｋｐ数模，产使油ｃｕ生
轻型汽车技术
２１（）２３００９总５
技术纵横
３３
Ｃａｓ曲面数模的质量定义和检测ｌｓＡ
孙大鹏程鹏罗伟
（上汽商用车技术中心车身开发部）
摘要
Ｃａ曲面是既满足结构工程上的条件（满足结构件的布置、ｌｓｓＡ包括满足成型工艺、降
般而言，质量等级其实并没有一个非常确切

A级曲面

CLASS ‘A’ SURFACING‘A'Class surfacing and its importance:A class surfaces are those aesthetic/free form surfaces,which are visible to us(interior/exterior),having an optimalaesthetic shape and high surface quality.Mathematically class A surface are those surfaces which arecurvature continuous while providing the simplest mathematical representation needed for the desiredshape/form and does not have any undesirable waviness.Curvature continuity:It is the continuity between thesurfaces sharing the same boundary.Curvature continuitymeans that at each point of each surface along the commonboundary has the same radius of curvature.Why Class A is needed:We all understand that today products are not only designed considering the functionality but special consideration aregiven to its form/aesthetics which can bring a desire in onesmind to own that product.Which is only possible with high-class finish and good forms.This is the reason why in designindustries Class A surface are given more importance.UNDERSTANDINGUnderstanding for Class A surfaces:1. The fillets -Generally for Class A, the requirement is curvature continuous and Uniform flow of flow lines from fillet to parent surface value of 0.005 or better (Position 0.001mm and tangency to about 0.016 degrees).2. The flow of the highlight lines -The lines should form a uniform family of lines. Gradually widening or narrowing but in general never pinching in and out.3. The control points should form a very ordered structure -again varying in Angle from one Row to the next in a gradual manner (this will yield the good Highlights required).4. For a Class A model the fillet boundary should be edited and moved to form a Gentle line -and then re-matched into the base surface.5. Matched iso-params in U & V direction are also a good representation of class A.6. The degree (order) of the Bezier fillets should generally be about 6 (also for arc Radius direction) sometimes you may have to go higher.7. Also you have to take care of Draft angle, symmetry, gaps and matching of surfaces Created with parent or reference surfaces.8. Curvature cross-section needles across the part -we make sure the rate of Change of curvature (or the flow of the capping line across the top of the part) is Very gentle and well behaved.The physical meaning:Class A refers to those surfaces, which are CURVATURE continuous to each other at their respective boundaries. Curvature continuity means that at each "point" of each surface along the common boundary has the same radius of curvature.This is different to surfaces having;Tangent continuity -which is directional continuity without radius continuity -like fillets.Point continuity -only touching without directional (tangent) or curvature equivalence.In fact, tangent and point continuity is the entire basis most industries (aerospace, shipbuilding, BIW etc ). For these applications, there is generally no need for curvature.By definition:Class A surface refers to those surfaces which are VISIBLE and abide to the physical meaning, in a product. This classification is primarily used in the automotive and increasingly in consumer goods (toothbrushes, PalmPC's, mobile phones, washing machines, toilet lids etc). It is a requirement where aesthetics has a significant contribution. For this reason the exterior of automobiles are deemed Class-A. BIW is NOT Class-A. The exterior of you sexy toothbrush is Class-A, the interior with ribs and inserts etc is NOT Class-A. QUESTION:What is Body_in_white?What is class A surface?Are the interior trim (A,B,C pillar, dash board, center console, handles) of a car using class A surface? Anybody using the basic design bundle of UG for class A surfacing? UG\Shape Studio?How does it compare with Catia?Ans:1A class A surface is anything that you the customer sees. i.e. exterior panels and interior surfaces.A ClassB surface is something that is not always visible i.e. the underside of a fascia that you would have to bend down to see.A Class C surface is the back side of a part of a surface that is permanently covered by another part.BIW is stuff like the body side etc..Ans:2Actually 'body in white' is the term used to describe the whole vehicle body after it has been welded/bolted together before it is painted or any parts are attached on the fit up line.Ans:3We also use it to mean after it has been painted -I always assumed that the white bit refers to primer. Next step is to fit the windscreen and backlight, when it becomes the glazed body in white, or BIW+G.ANS: 4BIW -Some surfaces are Class A, i.e. body side, roof, sill appliqué.I heard some time ago from a old designer that the term BIW comes from when cars were built from wood, they were painted white as it gives the frame a uniform color so imperfections were easily visible.Ans:5BIW meaning Body In White is so called due to its appearance after the application of the primer to the entirely Body panel assembled vehicle just before going into the painting process.Usually the primer is white or silver grey which gives the so called name.ANS: 6Catia is mostly used for BIW design (Ford switching to catia, and Toyota). Is this because itcould easily create quintic surfaces? With UG with Design bundle only, most of the surfaces created are cubic.-------------------------------------------------------------------ANS: 7A class surface means -it is not just seen surface and unseen surface In normal no technical words,A class surface meansIt is smooth looking reflective surface with no distortion of light highlights, which moves in a smooth uniform designer intended formations.when you create -car body panel, due to their complex shapes it not possible to create the surface with one single face /patch so you make multiple face/patch ( surface is a group of face/patch added together.)when these things are added, at the boundary of joining you need to have connectivity and continuation of minimum order two.for exampleIn case one, at the connecting boundary of two patches you have common boundary but it is sharp corner. this does not qualify as A class surface.In case two -at the connecting boundary of two patches have common boundary and no sharp corner -but you have tangent continuity, this also does not qualify as A class surface.In case two -at the connecting boundary of two patches have common boundary and no sharp corner -you have tangent continuity and curvature continuity this does qualify as A class surface. ( sine curve is good example for curvature continuity. but you can not call it a A class surface )reason is very simple the real requirement of aesthetic and good looking and designer intended shape is not there.ANS:8For obtaining Class-A surfaces,CATIA is more commonly used due to its inherent ability to model very high quality surfaces in general.But,any engineering software(CATIA,UG,IDEAS,Pro-E,etc)cannot develop a Class-A surface.This being due to engineering calculations involved in any surface generated by such softwares.For pure Class-A surfaces you would need styling softwares like Alias,Studio,etc.The use of any software would depend on the level of expectations placed on you.If your projects need only the modeling of the trim,generic engg softwares will do,but if you intend to go down right from styling,you would need Studio,etc.-------------------------------------------------------------------ANS:9IHO,Catia V4has added a tool called Blend surf that is able to obtain virtual curvature continuity.Previously, even styling was comfortable with models-and hence tools-defining fillets with conics,and many OEMs still accept this for Class-A surfaces.Catia V5has GUI interfaces to impose curvature continuity the same way that Alias-Wave front Studio Tools(Auto Studio)does.They are both based on piece-wise polynomial equations,for what its worth.While a conic fillet is not technically curvature continuous,there are many vehicles,including luxury models,that have utilized them for Class-A surfaces and downstream-parts.Considering the tolerances in creating molds and dies and then producing parts from them....a sheet metal panel is not a math model.-------------------------------------------------------------------ANS:10It is true that it is tough to make good curvature continuous surface in UG,but not impossible.Remember one thing A-class doesn't mean just curvature continuity.and smooth reflections on CAD surface.it is lot more than that.Imagine.what happens to your A class surface in case pressed sheet metal body panel. and molded plastic components.They have to retain there intended smoothness and other characteristics to remain A class.to achieve this lot of other things has to be taken care while designing A class surfaces.For example:1-Line features on body side external panel and feature on hood panel which is very common,are to be designed to avoid skidding while they are pressed.like wise2-Flange width and other things are to be taken care while designing fenders wheel arch area for avoiding bulging effect and skidding effect.3-Fuel lid opening area,plunged flange for bulge effect.4-Panel stretching needs to be taken care.Lot many other things go in designing A class sheet metal panels for door,roof etc.5-In case of plastic,sink marks and other things.ANS:11In Europe a'A'class surface is generally taken to be the visible side of any component/assembly-a'B' class surface generally relates to the opposite(or inside)face of an'A'surface-i.e.the surface which defines the thickness of the part,and is where the mounting and reinforcing detail tends to be located.'B' class surfaces can also be referred to as'engineering surfaces.I have not personally heard of any surface being referred to as a'C'type.Catia,while it is ok for surfacing tends to be more used for generating engineering surface detail and solid models-software packages like ICEMSURF tend to be more used for generating visual quality surfaces.-------------------------------------------------------------------ANS:12True A-class surfacing-especially on vehicle exteriors goes further than G2or"curvature"continuity.G3is often sought on the more major block surfaces.G3deals with curvature"acceleration",i.e.the rate of change of curvature across a boundary.G2means as has been described before that the curvature value is the same across a boundary.G3means that the surface curvature leading to the boundary is changing shape at the same rate.Its like driving a car round a bend,you start off straight then gently add steering lock to the point where you need no more,then you gently wind off the steering until you're straight again.If you look at the curve your car made,this would be G3.A-Class and B-class would refer to surface quality required for the component which is different to A-side and B-side which refers to which is the visible/non visible part of a component.ICEM surf is considered the best tool for speedy A-class surfacing due to the sophistication of its real-time diagnostics.The consequence:The consequence of these surfaces apart from visually and physically aesthetic shapes is the way they reflect the real world. What would one expect to see across the boundary of pairs of point continuity, tangent continuity and curvature continuity surfaces when reflecting a straight and dry tree stump in the desert????Point Continuity (also known as G0 continuity) -will produce a reflection on one surface, then at the boundary disappear and re-appear at a location slightly different on the other surface. The same reflective phenomenon will show when there is a gap between the surfaces (the line markers on a road reflecting across the gap between the doors of a car).Tangent Continuity (also known as G1 continuity) -will produce a reflection on one surface, then at the boundary have a kink and continue. Unlike Point continuity the reflection (repeat REFLECTION) is continuous but has a tangent discontinuity in it. In analogy, it is "like" a greater than symbol.Curvature Continuity (also known as G2 continuity, Alias can do G3!) -this will produce the unbroken and smooth reflection across the boundary.To achieve the same Class 'A' surfaces that automotive manufacturers demand, consumer product manufacturers have availed themselves of the same advanced surface modeling tools. What is a Class 'A' surface? The simple answer is that it is a perfectly smooth surface with no anomalies, in which all adjoining surfaces have curvature continuity. This means that where two surfaces meet, the graduation of one into the other is achieved without discernible abrupt transitions. The techniques used to create Class 'A' surfaces typically reside in top level surface modeling software developed for the motor industry, rather than mid-range mechanical CAD packages that have evolved from 3D solid modeling for mechanical assemblies.Analyzing A Class SurfaceHighlight plot :Highlight is the behavior of the form orShape of a surface when a light ornature reflects on it. This reflection oflight or nature gives you anunderstanding about the quality ofsurface. This reflection required shouldbe natural, streamline and withuniformityDesigner Fillets:If you take two adjoining2D lines,or a couple of tangential surfaces,the intersection between them can be turned into an arc(2D)or a fillet(3D),each of which is inserted with a constant radius.However the transition from each line or surface can often be too abrupt for the design.According to Mike Lang,Technical Director of VX,fillets should look simple-you shouldn't see a fillet line in a model.They should also be simple to create."Achieving tangent and curvature continuity in complex shapes on other systems is hard work.A reduction in the weight of a curve will allow it to retain its tangency,but sharpen the change in curvature. This can be seen most effectively by reducing the weight almost to zero.Fairings-the shape of the curve-can be influenced by energy,variation,jerk,bend or tension-each of which will produce a subtle difference in the mathematical fit through the curve.Echo Attributes:Part of the process of obtaining Class'A'surfaces is being able to see what's happening to the curve or the surface as it is being developed.Increasing the scale of the iso lines allows designers to pick up smaller imperfections in surfaces.Where blue iso lines lose their curve they change to white.The shifting colors of Gaussian shading are also particularly adept at detecting subtle blemishes.Echo Attributes also has numerous other modifiable elements,including the ability to apply colors to lines and surfaces,and to alter the transparency of the surface.Curvature plots on non-designer fillets show regular arcs,unlike designer fillets that show the weighting of the curve at each point."good design work relies on good wire frame technology.If you don't have basic curve geometry,you won't be able to produce a good surface”.Designers must always go through the routine of checking curves,especially if the design has come in from an outside source-perhaps containing older style Bezier curves with lots of points.The following describes the mathematics for the so called Bezier curve.It is attributed and named after a French engineer ,Pierre Bezier ,who used them for the body design of the Renault car in the 1970's.They have since obtained dominance in the typesetting industry.Consider N+1control points pk (k=0to N)in 3space.The Bezier parametric curve function is of the form.B (u)is a continuous function in 3space defining the curve with N discrete control points P k .u=0at the first control point (k=0)and u=1at the last control point (k=N).Notes:•The curve in general does not pass through any of the control points except the first and last. From the formula B (0) = P 0and B (1) = P N .•The curve is always contained within the convex hull of the control points, it never oscillates wildly away from the control points.•If there is only one control point P 0, i.e.: N=0 then B (u) = P 0for all u.•If there are only two control points P 0and P 1, i.e.: N=1 then the formula reduces to a line segment between the two control points.•the term shown below is called a blending function since it blends the control points to form the Bezier curve.Bezier Curves•The blending function is always a polynomial one degree less than the number of control points. Thus 3 control points results in a parabola, 4 control points a cubic curve etc.•Closed curves can be generated by making the last control point the same as the first control point. First order continuity can be achieved by ensuring the tangent between the first two points and the last two points are the same.•Adding multiple control points at a single position in space will add more weight to that point "pulling" the Bezier curve towards it.•As the number of control points increases it is necessary to have higher order polynomials and possibly higher factorials. It is common therefore to piece together small sections of Bezier curves to form a longer curve. This also helps control local conditions, normally changing the position of one control point will affect the whole curve. Of course since the curve starts and ends at the first and last control point it is easy to physically match the sections. It is also possible to match the first derivative since the tangent at the ends is along the line between the two points at the end.Second order continuity is generally not possible.•Except for the redundant cases of 2 control points (straight line), it is generally not possible to derive a Bezier curve that is parallel to another Bezier curve.A circle cannot be exactly represented with a Bezier curve.It isn't possible to create a Bezier curve that is parallel to another,except in the trivial cases of coincident parallel curves or straight line Bezier curves.Bezier curves have wide applications because they are easy to compute and very stable. There are similar formulations which are alsocalled Bezier curves which behave differently, in particular it ispossible to create a similar curve except that it passes through the control points. See also Spline curves.Examples: The pink lines show the control point polygon, the grey lines the Bezier curve.1.The degree of the curve is one less than the number of controlpoints, so it is a quadratic for 3 control points. It will always besymmetric for a symmetric control point arrangement.2.The curve always passes through the end points and is tangent tothe line between the last two and first two control points. Thispermits ready piecing of multiple Bezier curves together with first order continuity.3.The curve always lies within the convex hull of the control points.Thus the curve is always "well behaved" and does not oscillatingerratically.4.Closed curves are generated by specifying the first point the sameas the last point. If the tangents at the first and last points match then the curve will be closed with first order continuity.. Inaddition, the curve may be pulled towards a control point byspecifying it multiple times. 1 2 3 4The Bezier surface is formed as the Cartesian product of the blending functions of two orthogonal Bezier curves.Where P i,j is the i,jth control point. There are N i+1and N j+1control points in the i and j directions respectively. The corresponding properties of the Bezier curve apply to the Bezier surface. -The surface does not in general pass through the control points except for the corners of the control point grid. -The surface is contained within the convex hull of the control points. Along the edges of the grid patch the Bezier surface matches that of a Bezier curve through the control points along that edge.Closed surfaces can be formed by setting the last control point equal to the first. If the tangents also match between the first two and last two control points then the closed surface will have first order continuity. While a cylinder/cone can be formed from a Beziersurface, it is not possible to form a sphere.BEZIER SURFACEA little history of Surface Modeling A little historySurface modeling was developed in the automotive and aerospace industries in the late1970s to design and manufacture complex shapes.Nurbs--nonuniform rational B-splines--and cubic-surface formats appeared early and remain the primary spline and surface formatsused throughout the CAD industry.Nurbs and cubics are supported byIGES(Initial Graphics Exchange Specification),a neutral file format for exchanging data between CAD systems.Nurbs and cubic formats are represented in a computer by polynomial equations generated by a CAD system,and onscreen through thelocation and shape of curves and surfaces.For example,the equationof a line,a first-degree polynomial,has this formY=ax+bThe equation for a parabola,a second-degree polynomial,has the formY=ax2+bx+cAnd the equation of a cubic spline,a third-degree polynomial,looks likeY=ax3+bx2+cx+dThe more terms in the polynomial equation,the more"shape"thecurve or surface has.The data structure of a Nurbs curve or surface is comprised of points, weights,and parameter values that define a control net which istangent to the curve or surface.The control net on a Nurbs surface is a rectangular grid of connected straight-line elements which define thetangency of the surface at positions along the control net.The points inthe database which describe the control net are not actually on the surface,they are at the vertices of the control net.Weights in theNurbs data structure determine the amount of surface deflectiontoward or away from its control point.Cubic data structures use third-degree polynomials that describe pointsactually on the curve or surface.Therefore,the Nurbs control net is an abstraction of the underlying surface,whereas the cubic equation is the surface.Nurbs and cubic formats each have advantages and disadvantages.Nurbs equations model more complex shapes by increasing the degree of the exponents in the polynomial,thus increasing the memory required to store and evaluate the equation.Cubic equations,on the other hand,require less storage and can capture complex shapes by adding more cubic segments to the spline or surface.Nurbs and cubic equations are said to be"piecewise"and"parametric,"which means the curve or surface is a sequence of connected segments that use parametric u and v values ranging from0to1or0to n(number of segments)to calculate points along the curve or surface.Nurbs and cubic formats each have advantages and disadvantages.Nurbs equations model more complex shapes by increasing the degree of the exponents in the polynomial,thus increasing the memory required to store and evaluate the equation.Cubic equations,on the other hand,require less storage and can capture complex shapes by adding more cubic segments to the spline or surface.Nurbs and cubic equations are said to be"piecewise"and"parametric,"which means the curve or surface is a sequence of connected segments that use parametric u and v values ranging from0to1or0to n(number of segments)to calculate points along the curve or surface.Ultimately,a good CAD system shields users from having to know too much about the mathematics that represent the underlying surfaces.In addition,surface modelers should:Provide enough tools to completely define any feature on the part using surfaces.Have many functions for defining the different shapes of surfaces including ruled,revolved,lofted,extruded, swept,offset,filleted,blended,planar boundary,and drafted.Each of these functions have further variations. For example,offset surfaces should allow for constant or tapered offsets.Draft-surface functions should let users input curves to define the draft surface,or allow using curves on a surface whereby the draft angle is referenced off a surface-normal vector at points along the curve.The lofted surface should allow for the input of cross-section curves or for the input of curves both along and across the surface.Support functions such as surface trimming,extending,intersecting,projecting,polygon tessellation,IGES translation,coordinate-system transformations,and editing.Allow extracting surface data such as flow curves,vectors,and planes,among other functions.Have a set of tools for defining points,planes,vectors,and splines used with surface modeling.Most surface creation functions need user inputs to define surfaces.Two useful surface-modeling functions are the controlled sweep and the draft surface.A controlled sweep forces a profile curve to remain perpendicular to the sweep path by using a control surface.Without a control surface in the construction of a swept surface,the profile curve typically wants to lay down or spin around the sweep path.A properly defined control surface solves the problem.A draft surface is similar to a controlled sweep in that it uses curves lying on one surface to create another.The resultant draft surface passes through the input curve and is composed of straight-line elements radiating from the reference surface at an angle to the surface normal vectors taken at points along the input curve.A draft-surface function can build one surface perpendicular to another,along a curve.A Comparison Between Solid-Surface Modeling:While surface modelers excel at defining complex shapes,solid modeling is good at quickly building primitive geometry.Primitive geometry consists of basic surfaces such as planes,cylinders,cones, spheres,and tori.Surface modeling is not as fast at creating simple part geometry,but if your solid modeler can't easily model a feature,such as a fillet,surface modeling can almost always finish the part. And for every solid-modeling function there is a counterpart in surface modeling.Nurbs surfaces can be incorporated into an existing solid model by"stitching"the Nurbs surface to the solid model.Some parts can be completely defined by a solid modeler as a collection of primitive surfaces,while other parts require Nurbs surfaces to fully define the geometry.Most parts manufactured with tooling require some kind of Nurbs surface to support production.Reverse engineering is heavily dependent on Nurbs surfaces to capture digitized points into surfaces.In addition,Nurbs-surface files generated over the last20years are circulating in IGES format between vendors and subcontractors.These files support the design of parts in one system and manufacturing in another.Solid modeling will not replace Nurbs-surface modeling because the two work hand in hand to complete part geometry.TYPES OF CONTINUTYContinuity is a measure of how well two curves or surfaces "flow" into each other.•POSITION (G0)This type of continuity between curves implies that the endpoints of the curves have the same X,Y, and Z position in the world space. This is the minimum requirement for obtaining G0.•TANGENT (G1)This type of continuity between curves implies that the tangent CVs must be on one line.•CURVATURE (G2)This continuity type impacts the third CV of the curve. All three CVs have to be considered in order to maintain a smooth curvature comb.If a curvature comb does not have a smooth transitional line. In order to improve the curvature comb, manually modify the position of the three CVs that constitute the G2continuity.。

A级曲面1

汽车A级曲面-A级曲面设计软件比较-ICEM Surf/Alias/UG/Imageware/CA TIA 在整个汽车开发的流程中，有一工程阶段称为Class-A Engineering：重点是在确定曲面的品质可以符合A级曲面的要求。

所谓A级曲面的定义：是必须满足相邻曲面间间隙(Gap)在0.005mm 以下（有些汽车厂甚至要求到0.001mm），切率改变( Tangency Change ) 在0.16度以下，曲率改变(Curvature change) 在0.005 度以下，符合这样的标准才能确保钣金件的环境反射不会有问题。

Class-A包括多方面评测标准，比如说反射是不是好看、顺眼等等。

当然，G2可以说是一个基本要求，因为G2以上才有光顺的反射效果。

但是，即使G3了，也未必是Class-A，也就是说有时虽然连续，但是面之间出现褶皱，此时就不是Class-A，通俗一点说：Class-A 必须是G2以上连接，但G3连续的面不一定是Class-A曲面。

汽车业也有这种简单的分类法：A面指的是车身外表面及白车身；B面指的是不重要表面，比如内饰表面等；C面指的是不可见表面。

但是现在随着现代美学的发展及舒适性要求的日益提高，对汽车内饰件也提到了Class-A的要求。

不同汽车厂商对于Class-A的要求也不尽相同，GM要求比TOYOTA、BMW等要求低一些，也就是说Gap和Angle 要求要松一些。

目前国内的A级曲面的生成软件中，比较流行的有Alias、ICEM Surf、UG、Imageware/Surfacer、CA TIA V5 等。

同时每个软件有配套的数据展示软件,即虚拟现实展示软件(渲染)。

1)Alias：大多数设计公司和整车企业采用Autodesk Alias软件作为A级曲面生成工具。

它主要的优点是生成曲面的速度快，在软件中可以根据造型的意图进行快速修改，进行曲面的检测和验收，还能提供很漂亮的造型展示。

A级曲面全面介绍

产品设计：A级曲面全面介绍2012-07-23 在整个汽车开发的流程中，有一工程段称为 Class A Engineering，重点是在确定曲面的品质可以符合A级曲面的要求。

所谓A级曲面的定义，是必须满足相邻曲面间之间隙在 0.005mm 以下(有些汽车厂甚至要求到 0.001mm)，切率改变 ( tangency Change ) 在0.16度以下，曲率改变 (curvature change) 在0.005 度以下，符合这样的标准才能确保钣件的环境反射不会有问题。

a-class包括多方面评测标准,比如说反射是不是好看、顺眼等等。

当然，G2可以说是一个基本要求,因为g2以上才有光顺的反射效果。

但是,即使G3了，也未必是a-class,也就是说有时虽然连续，但是面之间出现褶皱，此时就不是a-class 通俗一点说，class-A就必须是G2以上连接。

G3连续的面不一定是CLASS-A曲面。

汽车业界对于a class要求也有不同的标准，GM要求比TOYOTA ，BMW等等要低一些，也就是说gap和angle要求要松一些。

关于A-class surfaces，涉及曲面的类型的二个基本观点是位置和质量。

位置--所有消费者可见的表面按A-Surface考虑。

汽车的console(副仪表台)属于A-surf，内部结构件则是B-surf。

质量--涉及曲面拓扑关系、位置、切线、曲面边界处的曲率和曲面内部的patch结构。

有一些意见认为“点连续”是C类，切线连续是B类，曲率连续是A类。

而我想更加适当地定义为C0、C1和C2，对应于B样条曲线方程和它的1阶导数(相切=C1)和它2阶导数(曲率=C2)。

因此一个A-surf有可能是曲率不连续的，如果那是设计的意图，甚至有可能切线不连续,如果设计意图是一处折痕或锐边,(而通常注塑或冲压不能有锐边，因此A-suuf一定是切线连续(C1)的)。

第二种思想以汽车公司和白车身制造方面的经验为基础，做出对A-surf更深刻的理解。

CATIA中A级曲面应用全面介绍精华篇

A级曲面没有十分严格的数学描述也没有十分严格的概念定义。

在汽车行业，所谓A级曲面的定义，是必须满足相邻曲面间的间隙在 0.005mm 以下（有些汽车厂甚至要求到 0.001mm），切率改变 ( Tangency Change ) 在0.16度以下，曲率改变 (Curvature Change) 在0.005 度以下，符合这样的标准才能确保钣件的环境反射不会有问题。

CLASS-A包括多方面评测标准，比如说反射是不是好看、顺眼等等。

当然，G2可以说是一个基本要求，因为G2以上才有光顺的反射效果。

但是，即使G3了，也未必是A级曲面，也就是说有时虽然连续，但是面之间出现褶皱，此时就不是A级曲面了。

通俗一点说，CLASS-A就必须是G2以上连接。

汽车业界对于A级曲面要求也有不同的标准，GM要求比TOYOTA ，BMW等要低一些，也就是说Gap和Angle要求要松一些。

关于A级曲面，涉及曲面类型的二个基本观点是位置和质量。

位置，所有消费者可见的表面按A-Surf考虑，汽车的Console（副仪表台）属于A-Surf，内部结构件则是B-surf；质量，涉及曲面拓扑关系、位置、切线、曲面边界处的曲率和曲面内部的Patch结构。

在老的汽车业有这样一种分类法：A面，车身外表面，白车身；B面，不重要表面，比如内饰表面；C面，不可见表面。

这其实就是A级曲面的基础。

但是现在随着美学和舒适性的要求曰益提高，对汽车内饰件也提到了A-CLASS的要求。

因而分类随之简化，A面，可见（甚至是可触摸）表面；B面，不可见表面。

关于曲面质量的连续理论，有一些意见认为“点连续”是C类，切线连续是B类，曲率连续是A类。

而我想更加适当地定义为C0、C1和C2，对应于B样条曲线方程和它的1阶导数（相切=C1）和它2阶导数（曲率=C2）。

因此一个A-surf有可能是曲率不连续的，如果那是设计的意图，甚至有可能切线不连续，例如设计意图是一处折痕或锐边。

01__CLASSA简介及曲面质量分析

但是这种连续级别将比G3计算起来更复杂，而且在视觉效果上与G3连续基本一致，故很少使用。
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CLASS – A表面的质量分析——斑马线 1/3
斑马线介绍（也叫做高光测试）：
斑马线实际上是模拟一组平行的光源照射到索要检测的表面上所观察到的反光效果。 • G0的斑马线在连接处毫不相关，各走各的，线和线之间不连续，通常是错开的。 • G1的斑马线虽然在相接处是相连的，但是从一个表面到另一个表面就会发生很大的
大多数设计公司和整车企业采用Autodesk Alias软件作为A级曲面生成工具。它主要的优点是生成曲面的速度快，在软件中可以根据造型的意图进行快速修改，进行曲面的检测和验收，还能提供很漂亮的造型展示。
Alias 数据演示给人的感觉往往造型很眩，但在软件中展示的效果与实际车辆展示效果相差太远，样件不能真实地表达汽车的造型。另外由于数学算法的局限，它的表面质量不能达到一流水平，满足不了世界上一流汽车公司对于产品表面的质量要求。
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CLASS-A的总结

汽车CLASS-A曲面设计

龙源期刊网汽车CLASS-A曲面设计作者：来源：《汽车观察》2011年第10期CLASS－A曲面設计是汽车整车开发的关键技术之一，是贯穿造型创意和工程設计的纽带，在造型設计工程化的过程中，需要有效地控制特征品质和造型细节。

同捷公司拥有百余名富有经验的汽车造型创意开发队伍，通过几百个车型的开发，不断探索，总结了一些行之有效的方法，以下将详细介绍。

CLASS－A曲面包含造型工程品质和CLASS－A内在品质两层含义：造型工程品质：造型品质的衡量则是仁者见仁，智者见智，很难形成统一的评判标准。

同捷的要求是主要特征必须有参考依据，整车造型风格必须协调统一；确保工程品质，外观品质基准书，断差表现出产品的雕塑感和品质感，提高制造和設计的一致性。

CLASS－A内在品质：CLASS－A曲面的特征制作、控制方法，各部件之间配合规律，曲面检查、评价方法等。

CLASS－A曲面的过渡或圆角区域满足曲率或以上连续，特征线、边界线光顺；反射线、斑马纹分布均匀且粗细均匀变化；控制顶点分布规则，各行控制顶点间角度变化均匀。

求特征线合理拆面：对于复杂的汽车车身曲面来说，用一张曲面表达不到位，必须用多张曲面拼接而成，要求面与面拼接后各个参数没有明显的畸变。

在拼接过程中经常要处理曲面与曲面之间的过渡曲面或圆角等，在构造过渡圆角曲面的过程中，影响过渡圆角曲面的因数很多，但最重要的是两曲面的理论交线。

一般来说，希望要构建过渡圆角曲面的2个(组)基本曲面应该建立到或超过理论交线。

这为基面调整带来方便，也为模具和工装設计提供工艺补充面，同时还可以利用交线来控制主面的质量。

四边构面合理变形：CLASS－A曲面的要领是用正向的思路来做点云拟合创建数学模型，我们用四边面的方式来制作曲面，单个曲线要光顺，对应边的曲线趋势要一致，如果造型特征不一致，中间必须增加线串控制。

特征线、曲面的边界线、线与线之间的对比关系，线条之间的关系处理好了，就能得到一张好面。

车身CLASS A评价标准和方法

车身Class A评价标准和方法一、CLASS A的概念1、连续性的几种方式曲面曲线的连续性有以下几种方式，并做相应的几何表达：上述四种连续性关系只是构造Class A的基础，在应用这些概念时必须综合进行考虑。

对于精度的要求可根据对象2、CLASS A的评估方法对于汽车外形来讲，最重要的是曲线、曲面的评估方法。

在传统的手工处理时。

曲线质量是由设计人员从各个方向观察画在图板上的大比例曲线来进行检查。

车型设计人员通过观察可以指出哪一段是好的，哪一段有鼓包等等。

一个CAD系统不仅必须提供各种曲面定义方法，还必须提供曲面质量评估技术。

一种检查曲面设计质量的方法是模拟曲面的高光。

高光对曲面上点的法矢方向的变化十分敏感。

轮廓图的杂乱无章表明曲面上相应区域内曲率分布不均。

在C1连续的边界处，高光轮廓图有断点，对C0连接则不连续。

另一种评估形状的方法是观察曲面上曲线或截面线的曲率轮廓图。

不规则的轮廓图表明曲面上相应区域质量不好（不光顺）。

曲率半径检查比高光检查容易，因此在设计阶段常采用这种方法。

但是，仅用曲率轮廓图检查对于评估曲面质量是不够的。

因为有时曲率轮廓图看起来很好，但是高光分布图有波动，必须对曲面进行修改。

有时也用彩色光照图评价曲面质量。

但是通常彩色光照图显示并不十分有效，因为光照图显示的目的是得到高质量的图像，并不能完全显示出产品的曲面质量。

但是，随着近来计算机硬件和软件性能的提高，计算汽车在各种金属材质上的反光性质以便进行光线的跟踪计算。

这样就可以在实际生产之前较为真实地评估汽车的外形及色彩。

二、Class A评价标准1、曲面及曲面之间的过渡面曲率连续2、曲面的控制多边形较为均匀整齐、法矢指向一致3、采用低阶曲面。

曲面的评定标准

曲面的评定标准汽车外形设计对曲面的评定标准分为A、B、C3级。

A级要求最高，反射评定不可以出现变异，对于车身来说，一般指车身外表可见件及内饰可见件，如顶盖，发动机罩外板，叶子板、保险杆及内饰仪表板等部件。

B级是指地板等大型不可见件。

C级主要是结构撑件，如支架等。

关于A-class surfaces，涉及曲面的类型的二个基本观点是位置和质量。

．位置—所有消费者可见的表面按A-Surface考虑。

汽车的console（副仪表台）属于A-surf，内部结构件则是B-surf。

．质量—涉及曲面拓扑关系、位置、切线、曲面边界处的曲率和曲面内部的pat ch结构。

有一些意见认为“点连续”是C类，切线连续是B类，曲率连续是A类。

而我想更加适当地定义为C0、C1和C2，对应于B样条曲线方程和它的1阶导数（相切=C 1）和它2阶导数（曲率=C2）。

因此一个A-surf有可能是曲率不连续的，如果那是设计的意图，甚至有可能切线不连续,如果设计意图是一处折痕或锐边,（而通常射出或冲压不能有锐边，因此A-surf一定是切线连续(C1)的)。

第二种思维以汽车公司和白车身制造方面的经验为基础，做出对A-surf更深刻的理解。

他们按独立分类做出了同样的定义。

1.物理定义：A-surf是那些在各自的边界上保持曲率连续的曲面。

曲率连续意味着在任何曲面上的任一"点"中沿着边界有同样的曲率半径。

曲面是挺难做到这一点的，切线连续仅是方向的连续而没有半径连续，比如说倒角。

点连续仅仅保证没有缝隙，完全接触。

事实上，切线连续的点连续能满足大部分基础工业（航空和航天、造船业、BIW等）。

基于这些应用，通常并无曲率连续的需要。

2.根据定义：A-surf是那些在产品中可见的有特定物理意义的曲面。

A-surf首先用于汽车，并在消费类产品中渐增（牙刷，PDA，手机，洗衣机......等）。

同时它也是美学的需要，在真实世界里，曲率连续是无处不在的，是主旋律．点连续（也称为G0连续）在每个表面上生产一次反射，反射线成间断分布。

Class A曲面的定义

Class A曲面的定义Class A一词最初是由法国Dassault System公司在开发大型CAD/CAM 软件包CATIA 时提出并付诸应用的，常译作A级曲面，专指车身模型中对曲面质量有较高要求或特殊要求的一类曲面，如外形曲面、仪表板和内饰件的表面等。

从CATIA V5版本开始，软件中新增加了ACA(Automotive Class A)模块，专门用于Class A曲面的设计。

Class A曲面与通常所说的光顺曲面有相似之处，只不过Class A特指汽车车身上的一部分曲面。

依次类推，对于车身内覆盖件，如内板件，其曲面称为Class B、Class C等。

Class A曲面是既满足几何光滑要求，又满足审美需求的曲面。

对于光滑曲面已经有很多的研究结论，参照施法中和朱心雄的定义可归纳如下：1)曲面片满足G2连续；2)没有多余的拐点；3)曲率分布均匀；4)应变能最小。

光顺则包含光滑和顺眼两层含义，上面归纳的定义是对光滑的数学描述，而对顺眼的衡量则是仁者见仁，智者见智，没有统一的评判标准。

曲面模型设计从始至今已有了四十多年的历史，取得了很大的进展，尤其体现在大型CAD应用软件包上，出现了很多曲面建模系统，如基于NURBS的、基于Bezier的、基于B样条的以及混合建模系统等，不一而足。

而由Dassault System提出的Class A曲面，为业界所承认并得到了广泛应用，主要是因为其简洁明了。

通过参阅一些资料，并且做了大量曲面和零件的设计工作，对Class A曲面的要求总结如下：(1)曲面片由B样条方法(包括NURBS和Bezier方法)描述，节点向量采用累加弦长参数化法；(2)曲面在u，v方向上次数在三次(四阶)至七次(八阶)之间，最高不要大于九次(十阶)；(3)相邻曲面片满足G2连续（曲率过渡均匀，至少满足G1，特殊要求满足G3）；(4)大的曲面片为全凸的(法方向指向曲面同侧)。

自由形状描述理论在许多文献中都有详细论述，现在总结的对车身曲面模型的更高要求，就是建立在这些理论的基础上。