A级曲面定义及标准2014.12.10

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车身曲面光顺与a级曲面评价标准

车身曲面光顺与A/B/C三级曲面评价标准1基本概念（1）A/B/C级曲面阐述A级曲面: 对于高可见区零件（外表面及仪表板上及前表面，门内饰板等），曲面的质量要达到大的特征面要达到如下所述的3阶曲率连续或3阶曲率以上连续,局部少可见区达到2阶曲率连续或2阶曲率以上连续. 特征面的连接和联结处或零件分块线处在高可见区要2阶曲率及2阶曲率以上曲率连续，少可见区特征联结处或不特别重要的零件分块线（缝隙处）区可小区域1阶曲率连续。

对于大曲面特征最好采用单一特征曲面，个别不能用一个面而必须用两个特征面拼接的高可见区大面，要努力争取三阶及三阶以上的连续，以使曲面质量达到较高水平。

在光顺A级曲面时，建议CAD软件中，Preference中精度误差Tolerance值设置小于等于0.001（一般用0.0001），角度误差小于0.1度(一般用0.01度)。

软件中默认值0.0254和0.5度只适合C级曲面。

B级曲面: 曲面的质量要达到少可见区域如下所述的2阶连续或2阶以上连续,局部极少可见区达到1阶连续或1阶以上连续. 或达不到A级要求的较好曲面。

软件中默认值改为0.01和0.1度适合B级。

C级曲面: 曲面的质量要达到小的极少可见区域如下所述的1阶连续或1阶以上连续,局部极少可见区达到0阶连续或0阶以上连续. 软件中默认值0.0254和0.5度适合C级曲面。

当然不重要的较小易成型零件可以考虑精度误差Tolerance值设置成0.05及1度，以便减少建模时间。

所有种类曲面，都要满足如下一些要求: 设计部门从美学角度通过的造型形状面数模要符合所有已知的结构工程、制造工程和人机工程标准及人类能力因素（Human Factors Criteria），并且要满足所有的模具制造工程和工装夹具的要求。

但在不改变造型风格基础上或造型能忍受的情况下，要尽力放宽曲面与测量点云之间的变化范围，以获得较好的曲面质量。

即光顺的罚值（Threhold）可以适当放大。

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。

汽车A面解释

G0连续1.一条曲线的一个端点与另一条曲线的一端点相接触,我们可认为：两曲线在这一点的连接处于G0连续状态。

2.一个曲面的一边界与另一曲面的一边界重合,我们可认为：两曲面在这一边界的连接处于G0连续状态。

3.如果两者间的连续性达不到G0我们称之为误差,这个误差是个绝对误差,是以毫米或英寸为测量单位的一距离值。

G1连续1.曲线与曲线在某一点处于G0连续状态，且两曲线在某一点的法线相同，在这一点的切线的夹角为零度时，我们就称两条曲线处于G1连续。

2.如果曲面与曲面在曲线的某一处于G0连续状态，曲面a在曲线b的任意点的法线方向和曲面b在曲线b的同一点的法线方向相同，我们就称两个曲面处于G1连续。

3.如果两者间的连续性达不到G1我们称之为G1误差,这个误差是个绝对误差,是以deg 或rad为测量单位的一角度值。

G2连续1.曲线与曲线在某一点处于G1连续状态，两条曲线在在这一点的曲率的向量，如果两条曲线向量(方向和绝对值) 相同，我们就说这两条曲线处于G2连续。

2.当曲面与曲面在曲线A处于G1连续状态，曲面A在曲线A的任意点的法方量和曲面B在曲线B的同一点的法方量相同，我们就说这两个曲面处于G2连续。

3.如果两者间的连续性达不到G2我们称之为G2误差，这个误差是个相对误差汽车A级曲面汽车A级曲面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。

A级曲面设计规范

XXXXX有限公司A级曲面设计规范编制:日期:校对:日期:审核:日期:批准:日期:20发布 20--实施XXXXX有限公司发布一、A级曲面光顺原则1．所有特征都必须具有可扩展性和可编辑性。

2．所有特征都必须分解成单凸或单凹特征。

3．所有特征面的光顺保证2阶导数以上连续。

4．所有特征线（面）函数必须小于6阶。

5．所有特征间的连接要2阶导数以上连续（曲率连续）6．所有特征间的连接偏差小于0.0001。

7．一块大面上多特征拼接的，建模默认误差小于0.0001，角度误差小于0.01度。

8．单一特征面的建模默认误差小于0.00001，角度误差小于0.001度9．造型决定的不同特征形状可不要求曲率连续或相切连续。

10．在不能保证大特征面如上质量情况下，宁可牺牲边界线或缝线或特征连接，特征的连续保证相切连续（角度误差小于0.1度）。

11．不明显的局部特征过渡区（如A柱下端与翼子板过渡区），允许曲率不连续，但要保证相切连续。

12．外观特征筋线倒角R2~R5 仪表板边界相交倒角 R5~R1013．顶盖、发动机盖、行李箱盖，与侧围做大面相交，然后以交线为中心，依据点云特征，进行曲率或相切连续。

14．大于R10的倒角，要考虑搭桥，保证曲率连续。

15．为获得A级曲面、允许与点云误差±5mm。

16．零件边界线必须光顺。

17．一块大面如果在两头曲率变化太大（相差2倍以上）必须分开特征，然后与主曲面拼接，拼接精度偏差小于0.0001，角度偏差小于0.01度）。

18．不可以用多个特征断面，用扫面（sweep）的方法，但可用单特征面（曲率变化不超过2倍）多个断面扫面。

19．不可用多个边界约束的小面拼接零件。

二、A级面介绍1.轮廓曲面--通常都是A级曲面，这样的曲面通常都要求曲率连续，沿着曲面和相邻的曲面有几乎相同的曲率半径（相差0.05或更小，位置偏差0.001mm 或角度相差0.016度。

）2、A级曲面用高光等高线检测时显亮的曲线--这些曲线应该有一个共同的曲率特征，等高线连续且过度均匀、逐渐的发散或收缩，而不是一下子汇集消失到一点3、A级曲面上的控制点也应该按一定的规律分布，一行控制点与另一行相邻的控制点的角度变化应该有一定的规律可循，这是画高质量的曲线所必需的4、A级曲面模型的曲面的边界线又该可以被编辑、移动以生成另外一个曲线，同时这个新生成的曲线可以重新加入曲面来控制区面。

犀牛A级曲面全面介绍

3、A 级曲面上的控制点也应该按一定的规律分布，一行控制点与另一行相邻的控制点的角度变化应该有一定的规律可循，这是画高质量的曲线所必需的
4、A 级曲面模型的曲面的边界线又该可以被编辑、移动以生成另外一个曲线，同时这个新生成的曲线可以重新加入曲面来控制区面。
6、贝塞尔曲面的阶次和控制点数目一般应该是六，有时候可能会更高
有一些意见认为“位置续”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 G0、 G1 和 G2，对应于 B 样条曲线方程和它的 1 阶导数（相切=G1）和它 2 阶导数（曲率=G2）。
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(G1)的）。
G0 由于使模型产生了锐利的边缘，所以平时都极力避免，甚至想尽办法摆脱这种效果。不常用 G1 由于制作简单，成功率高，而且在某些地方及其实用，比如手机的两个面的相交处就用这种连续级别。比较常用 G2 由于视觉效果非常好，是大家追求的目标，但是这种连续级别的表面并不容易制作（ VFX 的这些高手们出的题目基本上就是和这种连续级别表面的制作方法拼命的），所以需要大家多多用心练习，这也是 Nurbs 建模中的一个难点。这种连续性的表面主要用于制作模型的主面和主要的过渡面。 G3,G4 这两种连续级别通常不使用，因为他们的视觉效果和 G2 几乎相差无几，而且消耗更多的计算资源。这两种连续级别的优点只有在制作像汽车车体这种大面积、为了得到完美的反光效果而要求表面曲率变化非常平滑的时候才会体现出来。检测工具---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变形，通常会在相接的地方产生尖锐的拐角。 G2 的斑马线则是相连，且在连接处也有一个过渡，通常不会产生尖锐的拐角，也不会错位。 G3,G4 的斑马线很难和 G2 的区分开。但是要注意，有时候显示的误差也会产生错位或者尖锐的拐角。注意鉴别哦。可以调整一下显示精度之后再看。

汽车车身A级曲面的表示与次数选择

汽车车身A级曲面的表示与次数选择作为一种新颖的设计展示形式，汽车车身曲面已经在汽车设计领域中具有了重要的地位。

其中，A级曲面是一种被广泛使用的汽车设计曲面之一。

本文将介绍A级曲面的表示方法以及相应的次数选择问题。

A级曲面是一种最基础的汽车设计曲面，通常用于车身表面的主要曲线、连续曲面联通和型式线的设计。

A级曲面的特点在于其表面的连续性和光滑度，设计人员需要通过合理的曲面构建和优化来达到这一点。

表示A级曲面的方法和次数选择会影响到车身设计的效果和质量。

曲面表示方法目前，常见汽车车身曲面的表示方法包括：1. Bézier曲线Bézier曲线是基于多项式函数的一种数学方法，它能够通过少量控制点来构建连续光滑的曲线。

它被广泛应用于汽车车身曲面设计中，可以通过调整控制点的位置来实现曲线的精细调整和优化。

2. NURBS曲线NURBS曲线是非均匀有理B样条曲线的缩写，是一种比Bézier曲线更高级的曲线构造方法。

同样可以通过少量控制点来构建光滑的曲线，但相比于Bézier曲线，NURBS曲线更具有精确性和自由度，能够更好地实现曲面的优化和参数化管理。

3. 曲面拟合曲面拟合是通过对一组离散点进行曲面近似求解的方式，可以通过调整离散点的位置和权重来实现曲面的优化和精细调整。

曲面拟合的优势在于可以快速处理不规则曲面和复杂形式的汽车设计。

曲面表示次数选择表示A级曲面的次数通常会影响到车身曲面的精细度和流畅感。

通常的选择方法有以下几种：1. 3次曲面3次曲面是指由三次多项式函数组成的曲面，通常用于大致的曲面布局和分块设计。

具有计算速度快和精度较低的特点，但不适用于精细和低误差的曲面设计。

2. 4次曲面4次曲面由四次多项式函数组成的曲面，可以更好地达到曲面的精细度和光滑性，适用于大多数的汽车车身设计。

3. 高次曲面高次曲面拥有更高的曲面精度和更流畅的曲线特点，通常可以满足更为精细的曲面设计需求。

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。

曲面设计

A级曲面的评价标准1， A级曲面的定义设计中心从审美角度通过的数模要尊重所有已知的工程、制造和人类因素标准(Human Factors Criteria) ，并且要满足所有模具工程和刀具加工的要求。

2，A级曲面的要求:A级曲面数模输出是作为数模要素的的最高要求。

一些部分虽然满足了所有曲面质量方针的要求，但是违反了主要制造或人类因素标准(HumanFactorsCriteria)的要求，这样也不能满足曲面数模审核的要求，二者都要满足。

输出的数模应该满足下列所有主要的要求:1 )数模精度误差及设计中心的可交付要求2 )曲面内在质量3 )曲面连续过度与质量4 )过度曲面的流动路径5)曲面或局部协调性和对局部特征分界面需考虑的项目6 )工程制造标准需符合的要求.7 )模具拔模的工程制造需符合的要求3，数模精度误差使用建模尺寸误差0.01mm和角度误差0.5度将有助于满足. 相邻曲面的输出要求。

使用更严格的误差是允许的，但对满足以下的输出标准可能不是必须的。

对特殊要求的零件可提高数量级。

所有外部数模满足尺寸误差0.025mm，相切误差0.50度(例外见以下的注释)。

所有的内部数模满足尺寸误差0.025mm，相切误差1.0度(例外见以下的注释)。

由于考虑到满足指定的误差需要的时间，放宽以上相连曲面的要求在很小的圆角半径区域是允许的。

从美学的质量考虑，这种努力没有附加价值。

假若以下的例外没有禁止实体模型的产生和确认，可以被作为最后一着，而不是通用规则。

1)外部.3mm- -5mm 半径圆角---相连曲面相切误差1度。

3mm或以下半径圆---相连曲面相切误差2度。

2)内部3mm--mmn半径圆---相连曲面相切误差2度。

3mm或以下半径圆---相连曲面相切误差3度。

达到或超过以上误差方针应该是所有数模输出的目标。

4，于构造实体的曲面数据要求1 )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度面变化调整和高光线控制。

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。

汽车A级曲面评估标准

汽车A级曲面评估标准1 范围本标准规定了车身外形曲面Class A的一些基本的质量和检验要求。

本标准适用于汽车A级曲面的评估。

2 规范性引用文件下列文件中的条款通过本标准的引用而成为本标准的条款。

凡是注日期的引用文件，其随后所有的修改单（不包括勘误的内容）或修订版均不适用于本标准，然而，鼓励根据本标准达成协议的各方研究是否可使用这些文件的最新版本。

凡是不注日期的引用文件，其最新版本适用于本标准。

3 术语3.1 A Class 曲面：达到G2, G3连续，即2阶或3阶连续。

面与面之间曲率连续。

（见图一）3.2 B Class 曲面：达到G1连续，即1阶连续。

面与面之间相切连续；曲率不连续；点连续；（见图二）3.3 C Class 曲面：达到G0连续，即0阶连续。

面与面之间点连续；曲率不连续，相切不连续。

4 职责本标准规定的车身外形曲面Class A的一些基本的质量和检验要求，由其设计部门负责。

5 内容5.1技术要求：面的质量要求最终是精细的光学质量要求，以达到良好的视觉效果。

用户可以在丰富的灯光条件下获得好的外表效果，这就说明这个数据模型是高质量的。

为了达到这个目的通常使用一些灯光来检查面的连续性和表面的张力。

在CATIA软件中有一些检测的方法如：斑马线，反射线等都可以作为数据检测的方法。

5.2数据质量要求：5.2.1 面的分块：a 面应该具有一定的造型效果。

b 面的分块应该将主模型作为一个整体来考虑，而不是由一些小块组合起来变成整体。

被分块的面以面的边界为边界，整体的思想可保证整个面的和谐统一。

建议采用尽可能少的面片，面片采用贝塞尔（BEZIER）曲面（见图三），曲面使用单段面和低阶面。

不要采用非均匀有理样条（NURBS）曲面（见图四）。

5.2.2 为了指导正确的完成数据，要避免下面的情况：a 在属于模型的元素之间不合理的分块b 出现重面；c 存在一些不属于模型的元素，不能被剪切；d 存在三角面和单独的面(见图五)；e 过多的使用了延伸面或是超出边界过多；f 偶然出现面的参数不能调整；g 面的边界线对应面的轮廓线5.2.3 半径和过渡面：1用数字化方法创建过渡面时，尽可能避免在一些过渡面上使用出现呆板的曲率变化或是定曲率的方式，这些呆板的面仅限于在一些不重要的或是不显眼的地方。

汽车A面解释

G0连续1.一条曲线的一个端点与另一条曲线的一端点相接触,我们可认为：两曲线在这一点的连接处于G0连续状态。

2.一个曲面的一边界与另一曲面的一边界重合,我们可认为：两曲面在这一边界的连接处于G0连续状态。

3.如果两者间的连续性达不到G0我们称之为误差,这个误差是个绝对误差,是以毫米或英寸为测量单位的一距离值。

G1连续1.曲线与曲线在某一点处于G0连续状态，且两曲线在某一点的法线相同，在这一点的切线的夹角为零度时，我们就称两条曲线处于G1连续。

3.如果两者间的连续性达不到G1我们称之为G1误差,这个误差是个绝对误差,是以deg 或rad为测量单位的一角度值。

2.当曲面与曲面在曲线A处于G1连续状态，曲面A在曲线A的任意点的法方量和曲面B在曲线B的同一点的法方量相同，我们就说这两个曲面处于G2连续。

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。

曲率变化率的变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 Engineerin，g 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（curvaturechange）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con sole（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（相切二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 —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。

汽车A级曲面

A级曲面全面介绍2007-3-7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。

曲面标准

曲面数模输出标准1综述1.1 A级曲面阐述设计中心从审美角度通过的数模要尊重所有已知的工程、制造和人类因素标准（Human Factors Criteria），并且要满足所有模具工程和刀具加工的要求。

1.2 文件内容本文努力去量化数模的误差和精度以确保输出数模满足要求的标准。

同时本文也提供了一些推荐性经验，这些经验说明了在数模从设计中心输出之前如何满足设计质量审核的目标。

A级曲面数模输出是作为数模要素的许多基本部分的最高要求。

一些部分虽然满足了所有曲面质量方针的要求，但是违反了主要制造或人类因素标准（Human Factors Criteria）的要求，这样也不能满足曲面数模审核的要求，二者都要满足。

输出的数模应该满足下列所有主要的要求：１）数模精度误差及设计中心的可交付要求２）曲面内在质量３）曲面连续过度与质量４）过度曲面的流动路径５）曲面或局部协调性和对局部特征分界面需考虑的项目６）工程制造标准需符合的要求７）模具拔模的工程制造需符合的要求８）设计、质量和验证审核９）标准检查列表2.1符合标准的格式要求2.1.1 建模误差使用建模尺寸误差0.01mm和角度误差0.5度将有助于满足相邻曲面的输出要求。

使用更严格的误差是允许的，但对满足以下的输出标准可能不是必须的。

对特殊要求的零件可提高数量级。

2.1.2 数模输出标准（UDR and VDR）所有数模输出以UG、CATIA、ProE，Ideas等文件提供数模可以用实体或曲面模型提供所有外部数模满足尺寸误差0.025mm，相切误差0.50度（例外见以下的注释）。

所有的内部数模满足尺寸误差0.025mm，相切误差1.0度（例外见以下的注释）。

参考NOA#52中检验几何的方针用来进行曲面和实体的确认.注释：由于考虑到满足指定的误差需要的时间，放宽以上相连曲面的要求在很小的圆角半径区域是允许的。

从美学的质量考虑，这种努力没有附加价值。

假若以下的例外没有禁止实体模型的产生和确认，可以被作为最后一着，而不是通用规则。

A级曲面

逆向工程的最高品质─A级曲面在目前的汽车制造相关行业中，造型设计A级曲面的意义及其应用，始终是众人关注的焦点。

另外，也有越来越多消费性产品，随着美学与舒适性的要求日益提高，亦逐渐的为其产品外观造型品质，提升为A级曲面的水准。

因此，我们可以明确的了解到A级曲面的设计工艺，在未来仍然是热门的显学。

一、A级曲面的由来A级曲面一词，最初是由法国达梭公司［Dassault］在开发CATIA这套设计软体时所提出并开始使用的，此一名词所指的是对于较高品质的曲面设计或是有特殊目的要求的曲面设计，口语化与简化的称呼。

因此在一开始提出这样的词汇同时，亦有B级曲面与C级曲面。

将曲面品质所表示的定义套用在最早导入与应用的汽车制造业中，分别表示：车身外观要求A级曲面水准；内部部件为B级曲面水准。

但随着现代设计越来越重视美学，在内部部件中汽车内装件也将越来越多要求A级曲面品质。

二、A级曲面的设计规范1.A级曲面的定义A级曲面所表示的是最高品质的曲面，没有十分严谨的数学描述也没有十分严谨的观念定义，而这样的名称对于设计人员而言显得笼统没有依据，因此业界发展出一套可以接受的规范数据来定义A级曲面。

就相邻曲面边界定义的条件是必须达到间隙距离在0.005公厘以下、切线角度改变在0.16度以下、曲率数值改变在0.005度以下的标准，符合这样标准的曲面才能确保环境光影的反射没有问题。

再对曲面内部品质进行评估时，光影反射线的呈现应连续且过渡均匀，并且逐渐变化的扩展或收缩，没有曲率特征的表现效果应与光影反射线的描述等同。

我们从美学的观点来看，所谓的A级曲面，就是光线表现出平顺光滑流畅的视觉感受，避免凸起或凹陷的情形出现在不正常的位置上。

这样的物理定义称之为G2连续。

2.A级曲面的建立在建构高品质曲面时，应该要以完整的形体来思维建构，先屏除各部份的零件分块，将整个产品外观造型视为由一组互相连续的曲面够成的外壳，在确保各曲面的状态达到A级曲面的条件下，再去思考产品的特征细节。