CATIAa级曲面光顺原则介绍
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。
CATIA A级曲面基本设计
CATIA A级曲面基本设计示意图一、A级曲面基本设计意图：A级曲面通常是围绕造型师的设计意图，为了实现所需要的三维数字模型，来验证造型要求是否成立。
为了弥补手工模型制作缺陷，所以使用当今最先进的计算机辅助设计工具，进行数字化高精度处理，可直接定义所需的设计参数，可直接在计算机进行光顺品质检查。
所谓的A级曲面通常是指有规律性曲面，它可以定义单个曲面，也可以定义整体曲面的完整性，A级曲面严格定义就是完美表达形体，精度要求非常高。
二、A级曲面评价原则A级曲面: 所谓的A级曲面通常是指有规律性曲面，它可以定义单个曲面，也可以定义整体曲面的完整性，A级曲面严格定义就是完美表达形体，精度要求非常高。
对于单一A级曲面，其控制顶点排列必须有规律，最高阶数通常在5~6阶，最高一般不超过8阶。
曲面边界延伸后一般不会出现卷曲自交现象。
总之单一曲面要简单漂亮，曲率一般单凸，斑马纹一般均匀分布，并有规律性变化。
对于整体A级曲面，所有曲面控制顶点一般排列整齐，相关特征流动方向均匀一致，对于汽车高可见区零件及仪表板表面，门内饰板上部等，曲面的质量达到95%以上的大的特征面达到2阶曲率连续或2阶曲率以上连续, 5%的局部少可见区小面或过渡圆角达到1阶连续或1阶曲率以上连续. 特征面在分块线（分缝线）处在高可见区要2阶或以上曲率连续，少可见区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（如果是造型因素不连续也可以例外）。
特征性不连续属正常造型设计可以不连续，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2阶或2阶以上的连续，以使曲面质量达到较高水平。
三、A级曲面光顺基本要求外表面所有区域及内饰的高可见区表面都属于A级曲面。
A面中95%大面和明显区域特征面间拼接处位置偏差小于0.005mm, 角度偏差小于0.05度，且必须为单片面（v和u 方向均为单patch 面），阶数小于等于6阶，个别不超过8阶。
CATIA关于A面的讲座总结
10月4日，CATIA之家群关于A面的讲座总结,.讲座人-坐看云起时总结DREAMING GIRL一、A面的定义（1）平面曲线的光顺法则A．二阶几何连续B．不存在奇点和多余拐点C．曲率变化比较均匀D．应变比较小（2）空间曲线的光顺法则A．二阶连续性，即曲率连续B．不存在多余拐点C．曲率变化均匀D．不存在多余变绕点（饶率为0）E．饶率变化均匀注：曲线在一点的饶率等于副法失对弧长的转动率。
形象的讲就是空间曲线上每一点对应一个坐标系，这个点在沿着曲线运动，坐标系的转动就是曲线的饶率。
（3）A面的定义就是G2以上连续，就是高质量的自由曲面具有高审美和高质量的面叫A面。
（4）低次曲面的光顺规则：A．关键是曲线光顺（如飞机、船舶的骨架线）B．网格线无多余拐点及变饶点C．主曲率在节点处的跃度和足够小（3*3曲面，跃度和大概理解为3+3）D．高斯曲率变化均匀。
低次曲面的网格线，你稍微调下，对整张曲面的影响很大。
当你的曲面是高次曲面（8*8）时，就没有这么明显。
（5）高次曲面的光顺规则：同低次曲面，不包括C项。
（6）杂项：一般来说一个整车的点云，最终的结果和油泥模型在±5mm。
曲面质量好坏的评价标准：A．曲面光顺性B．捏合精度尽可能高。
二、G连续的有关定义：（1）概念：G0 点连续G1 切线连续G2 曲率连续G3 曲率变化率连续G4 曲率变化率的变化率连续。
（2）判定原则：A．G0 点连续在连接点处的法线方向不一致，判定为G0连续B. G1相切连续在连接点处的法线在一条直线上，但曲率不等。
相切连续必须满足邻近的N-1，M（N），M+1三点共线。
C. G2曲率连续N-1，M（N），M+1在重合点M（N）出的法线方向一致，曲率值相等N-2，N-1，M（N），M+1，M+2五点共面。
D．G3曲率的变化率连续除了具有G2连续外，而且从图上可以看出，曲率梳的边界线G1连续（即相切）。
（3）应用：一般汽车外覆盖件具有G2连续国外的豪华轿车一般为G3连续CATIA里以下几个模块都能做出A面：FSS，ACAFSS和CLASS A是同一类，追求的是内部参数，用的是NUPBS：非均匀有理样条。
catia曲线光顺命令
catia曲线光顺命令CATIA是一种强大的计算机辅助设计软件，广泛应用于工程设计和制造业。
它提供了一系列功能强大的工具，可以帮助工程师和设计师创建各种复杂的曲线和曲面模型。
其中，CATIA曲线光顺命令是一个非常有用的功能，可以用来改善和优化设计模型的外观和性能。
CATIA的曲线光顺命令主要用来处理和优化设计模型中的曲线和曲面。
它可以通过调整曲线的参数来改变其形状，使其更加平滑和连续。
曲线光顺命令可以应用于各种类型的曲线，包括直线、曲线、B样条曲线等。
在使用CATIA的曲线光顺命令之前，我们首先需要了解一些相关的概念和术语。
CATIA使用参数化模型来描述和控制曲线的形状和属性。
在CATIA中，曲线可以由一系列控制点和关键点来定义。
控制点用于指定曲线的形状，而关键点用于指定曲线上的特定位置。
CATIA还使用一些参数来控制曲线的平滑度和弯曲程度。
CATIA的曲线光顺命令可以通过两种方式应用于曲线。
第一种方式是通过选择控制点来调整曲线的形状和位置。
在这种方式下，我们可以通过拖动控制点来改变曲线的形状，并实时预览曲线的变化。
CATIA还提供了一些额外的工具和选项，可以帮助我们更好地编辑和控制曲线的形状。
另一种方式是通过调整曲线的参数来改变其形状。
在这种方式下，我们可以通过更改曲线的参数来调整其曲率和弯曲。
CATIA提供了一些参数化工具和表达式，可以帮助我们计算和调整曲线的参数。
通过调整这些参数，我们可以改善曲线的平滑度和连续性，并满足设计要求。
CATIA的曲线光顺命令还可以用来处理和优化曲面模型。
曲面通常由多个曲线组成，而曲线光顺命令可以帮助我们改进和优化曲线之间的过渡和连接。
通过调整曲线的形状和参数，我们可以使曲面更加平滑和连续，并满足设计要求。
除了曲线光顺命令，CATIA还提供了许多其他功能和工具，可以帮助我们更好地处理和优化曲线和曲面模型。
例如，CATIA的曲线修剪命令可以用来修剪和修复曲线的不连续部分，使其更加平滑和连续。
Catia_A级曲面设计
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.。
CATIA-a级曲面光顺原则介绍
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~R10 13．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。
A级面介绍：我们对A级曲面是这样理解的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。
CATIA CATIAA级曲面检查规范说明
重庆南方摩托车技术研发有限公司CATIA A 级曲面检查规范北京迅利创成科技有限公司日期：2011年12月7日目录1.规范描述............................... 错误!未定义书签。
级曲面介绍............................... 错误!未定义书签。
定义................................. 错误!未定义书签。
特征................................. 错误!未定义书签。
级曲面标准............................... 错误!未定义书签。
设置建模精度......................... 错误!未定义书签。
曲面间的间隙/重叠.................... 错误!未定义书签。
曲面间的连续性....................... 错误!未定义书签。
光顺性要求........................... 错误!未定义书签。
脱模................................. 错误!未定义书签。
配合间隙............................. 错误!未定义书签。
输出格式............................. 错误!未定义书签。
4规范内容 ............................... 错误!未定义书签。
高光连续性检查....................... 错误!未定义书签。
连续性检查.......................... 错误!未定义书签。
曲率梳连续性检查..................... 错误!未定义书签。
两零件搭接关系检查................... 错误!未定义书签。
A级曲面的间距离检查................. 错误!未定义书签。
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。
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。
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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~R10 13．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。
A级面介绍：我们对A级曲面是这样理解的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。
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7、是说关于拔模角度、对称性、间歇以及同相关曲面德关系等都要考虑。
这个要求我们在造型是对相关的项目问题也要予以足够的重视。
8、这是专门就曲率的变化来说的，光是曲率连续是不足以做出classa的曲面的。
还要求曲率的变化本身也是光顺的，实际上就是引出了G3的概念。
当然并不是说class a要求G3，但是比较接近G3的品质对曲面的品质肯定是有好处的关于A-classsurfaces，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“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）。
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。
他们按独立分类做出了同样的定义。
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向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。
A-surf 首先用于汽车，并在消费类产品中渐增<牙刷，Palm，手机，洗机机、卫生设备等）。
它也是美学的需要。
*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。
*切线连续<也称为G1连续）将生产一次完整的表面反射，反射线连续但呈扭曲状。
*曲率连续<也称为G2连续的，Alias可以做到G3！）将生产横过所有边界的完整的和光滑的反射线。
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日益提高，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。
曲面相接，视边界连接将会有以下G0、G1、G2三种情况：1．G0：曲线<面）上存在尖点<折断点），在它的两边的斜率和曲率都有跳跃，这种曲线<曲面）只是共同相接于同一边界；2．G1：曲线<面）上存在切点，在它的两边的斜率是相同的，但曲率有跳跃。
这种曲线<曲面）光滑！也就是一阶导数相同，这种曲面共同相切于同一边界，斜率为连续<曲率不一定连续）；3．G2：曲线<面）上的各个点的曲率都是连续变化的，在共同相接的边界曲率相同，也就是二阶导数相同；标注尺寸是为了传递设计意图，用通行的手段和表现方法<网格线基准是方便之一），以简单，准确，完备，条理来标注．知道设计意图，知道手段和方法，知道结果评价准则，就可以标注任何复杂的＂钣金件＂－－无非尺寸多些而记．表现手段多用几次吧．用这个思路看国标，是否一致？任何高标，理不过如此<同理有理可行天下嘛）．具体则需要设计者耐心辛苦点罢．见解相同，手段不一．故设计风格各异，花样百出．经验可借鉴，主要靠自己耶逆向项目在汽车覆盖件产品开发中的应用迅利科技有限公司刘文龙、卢金火摘要：本文介绍了汽车覆盖件产品逆向建模的开发流程，并对汽车覆盖件产品逆向建模的关键技术进行了讨论，最后以某车型的发动机罩外板为实例介绍逆向项目的应用方法。
关键词：覆盖件逆向项目曲面重构曲面品质评价1 前言目前，我国的汽车工业正以前所未有的速度发展，各汽车公司为了迅速占领汽车市场，不断地推出性能良好、价格适中、乘座舒适的汽车产品，以满足汽车用户的要求。
车身是汽车产品的外衣，它不仅影响着汽车的外观质量，而且也影响到汽车的乘座舒适性能。
因此，它是汽车产品的换型重点总成之一。
逆向建模是指利用测量设备测取实物模型的表面数据，在汽车车身产品开发过程中，许多时候汽车覆盖件并非由CAD模型描述，设计者面对的是实物样件。
为了适应先进技术的发展，需要通过一定的途径，将这些实物转化为CAD模型，使得能利用CAD/CAM、PDM等先进技术对其进行处理或管理。
这种从实物样件获取产品CAD模型的技术就是逆向项目(ReverseEngineering>。
广义的产品逆向项目包括形状(几何>反求、工艺反求和材料反求等诸多方面，是一个复杂的系统项目汽车覆盖件逆向建模开发流程当前，我国汽车覆盖件常用开发流程如下图所示本贴包含图片附件:首先，利用测量设备采集汽车覆盖件物理模型外表面的数据，生成三维点云数据；然后对点云进行处理，例如过滤处理，特征提取，三角化等；最后根据获得的点云，通过分析原模型的设计思想和曲面组成，利用CAD软件进行曲面重构，生成汽车覆盖件的CAD模型。
在生成CAD模型之后，就可以用现代先进的技术和管理方法对其进行各种处理和管理，例如，利用CAE技术对其进行各种分析；利用CAE技术对其进行虚拟制造或生成加工代码等，利用PDM技术对其进行数据管理及配置管理等。
汽车覆盖件，尤其是外覆盖件要求曲面质量高，建模误差小。
这就对测量点云的质量和重构曲面的品质和误差提出了很高的要求。
测量点云的质量主要取决于测量设备的精度，而重构曲面的品质客观上取决于所选用的造型软件的功能。
针对汽车覆盖件逆向开发的需求，我们提出了一种解决方法，并在我们进行项目服务过程中得到了应用和检验。
该解决方案选用德国Steinbichler公司的COMET光学测量系统作为测量设备，选用CATIA中的Digital Shape Editor和FreeStyle模块作为CAD软件。
下面将详细介绍在该解决方案中所采用的关键技术，并以发动机罩外板为例说明了利用该解决方案进行汽车覆盖件逆向开发的方法和流程二关键技术在汽车覆盖件的逆向开发过程中，采用了以下关键技术。
1. 测量利用测量方法从汽车覆盖件的外表面上提取数据是逆向项目的一个重要环节，其提取点云数据的精度和噪声直接影响后续的曲面重构。
当前有两种测量方法，一种是接触式测量，即用三坐标测量机在物理模型上打点，从而提取所打点的三维坐标信息。
利用这种方法提取的点云数据精度高，但效率低，所提取的点云点数少，不能反应自由曲面的特征，还有伤害物理模型外表面的危险，所以在汽车覆盖件逆向开发过程中很少取用。
第二种方法是非接触式测量，即用光学测量机或激光测量机从物理模型上提取表面数据。
利用这种方法提取的点数多，密度大，效率高，而且精度可以得到保证，所以在汽车覆盖件逆向开发过程中得到了越来越广泛地应用。
我们选用的是德国Steinbichler公司的COMET光学测量机。
它的测量原理是基于局部三角形测量法。
通过白光源将一束光栅投影到被测物体表面上，由一CCD镜头从所拍照片中获取投影光栅的信息，通过机械地连续改变光栅的形状，从而将被测物体表面划分成一个个很小的像素点，进而可以从目标镜头K1与K2之间的距离b及角α和β通过三角形法求得每个像素点的三维坐标值。
<如图2所示）。
本贴包含图片附件:我们之所以选择COMET作为该解决方案的测量设备，是因为它具有以下优点：它采用一个镜头，消除了因为一般光学测量机采用两个镜头所造成的阴影效应，从而提高了测量质量。
标定简单。
该测量系统一次标定，可长期使用，只有在更换镜头或长途运输之后，才需要重新标定。
它提供了特征拼合功能。
对于特征多的小尺寸对象，可以利用该功能提高测量效率，另外对于小尺寸对象，如果特征少，可以通过人为制造一些特征来利用该功能，从而减少测量过程中获取整体测量坐标这一环节，提高了测量效率。
测量精度高。
因为该测量机采用了光栅转换的专利技术，使像素点的分布即不同于平行网格，也不同于旋转网格，而是两者优点的综合，所以提高了测量精度。