【转帖】Regarding A-class surfaces

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Regarding A-class surfaces,I think the two basic opinions are that class of surface either refers tolocation or quality (or maybe both)For example:   LOCATION  - all surfaces that a consumer normally seescan be considered class A surface.  The outside of a an automotive floor console would be class A, but the inside surfaces which normally include manufacturing flanges and attaching surfaces would be class B.QUALITY  - refers to surface topology.  Position, tangency, and curvatureacross surface boundries, and internal patch structure.  Some opinions arethat position continuity is class C, tangency continuity is class B, and curvaturecontinuity is class A.  But I think that these are more appropriately defined as C0, C1, and C2 condition refering to the B-spline curve equation and its 1st derivative (tangency=C1)and it's 2nd derivative (curvature=C2).So I think a class A surface can be discontinuous in curvature if that is the intention ofthe design (highlight reflection, or other reasons) and even discontiuous in tangencyif the intention is a crease or sharp edge( but usually molding or stamping requiresno sharp edges so Class A must be tangent continuous (C1)).-----------------------------------------------------------------------------------------------------------------------Second ThoughtHear is a further understanding of Class-A surfacing based on experiences with two automotive companies and whites goodsmanufacturers. They independently have the same definition for the classification. The physical meaning: Class A refers to those surfaces, which are CURVATURE continuous to each other at their respective boundaries. Curvaturecontinuity 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 touchingwithout directional (tangent) or curvature equivalence. In fact, tangent and point continuity is the entire basis most industries (aerospace, shipbuilding, BIW etc etc). For theseapplications, 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 classificationis primarily used in the automotive and increasingly in consumer goods (toothbrushes, PalmPC's, mobile phones, washingmachines, toilet lids etc etc etc). It is a requirement where aesthetics has a significant contribution. For this reason the exteriorof automobiles are deemed Class-A. BIW is NOT Class-A. The exterior of you sexy toothbrush is Class-A, the interior withribs and inserts etc is NOT Class-A. 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 continuitysurfaces 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 andre-appear at a location slightly different on the other surface. The same reflective phenomenon will show when there is a gapbetween 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 akink and continue. Unlike Point continuity the reflection (repeat REFLECTION) is continuos but has a tangent discontinuity init. 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 reflectionacross the boundary. Please do not believe me! This is the real physical world. Look at your cars rounded hood reflecting lines on the road or trees.Look at ripples of water that are not turbulent, reflection is everywhere but all blend into each other, as there is also curvaturecontinuity everywhere. Still not convinced - For an analytical approach, you may simply prove this point using any rendering package (eg. CATIA V4VST), Neon textures in 4D Navigator or DMU Navigator (V5), using the traditional CURVE1+REFLECT or /ANADIA in V4CATIA and of course the neon-tray dynamic reflect curve facility in V5. What about CATIA?? Traditionally CATIA has been used to create the "engineering" side of most designs, rather then the exterior "aesthetic" shell(ie Class-A). These traditional yet awesome tools (like SURF2) are geared for this kind of engineering work. The best examplebeing BIW in the automotive industry. Functions like SURF2 and FORMTOOL carve up even the most difficult inner panel structures into reality. This is why,historically, CATIA took an early strangle hold (amongst other reasons like a great capacity in all aspects of DMU andintegration across disciplines). CATIA comes from the aerospace industry. The exterior of aeroplanes (whose panels buckle between frames and expand withevery land-takeoff cycle) has very little "need" for curvature continuity and has 100% engineering factors driving its design(aerodynamics and structures). That is, there is zero styling in the design of an aircraft body. The fact that aeroplanes looks good and "smooth" is by virtue of itsoperation (streamlined as possible), their general cleanliness and most importantly the distance that one generally views them.If one was to look carefully down the fuselage of an aircraft on the ground, there is nothing smooth about it! Having the capability to cater for these industries in an engineering and process capacity with existing function and notrequiring the ability to create Class-A, has made CATIA the de-facto standard for the aerospace and automotive industries. As for Class-A, automotive manufacturers have utilised either or combinations of Alias and/or ICEM Surf (or others) toachieve these goals in a productive manner (remember the word productive). Alias has the ability cover the entire industrialdesign process from Sketches TO Surfaces on sketches TO Surface manipulation and build and further onto rendering andanimation. In retrospect, CATIA V4 can create Class-A surfaces with (1) compromise (eg. this deviation is OK, because it can be polishedby the toolmaker) and (2) an idiosyncratic approach by the CATIA operator - ie, it can be done but not as easily as with Aliasor ICEM Surf. Historically, its been "difficult" of Dassault to create software in V4 to easily create Class-A surfaces due to the use of Bezier(polynomial) based mathematics. There is nothing against Bezier based surfaces though. They are excellent for creating theengineering surfaces we have all come to love (BIW etc) utilising intelligent use of multi-patch surface methodology. In fact, Idoubt NURBS surfaces could do a better job. And without a doubt, V5, with its new architecture and use of Bezier and NURBS surfaces will go along way in being able toconfidently and more importantly competently producing these Class-A surfaces for an ever growing aesthetic minded world. And what about V4 CATIA?? CATIA V4 currently has the ability to create curvature continuous surfaces in two categories. Surfaces: a. Using SURF2 and SKIN (GSM) functions to sweep and loft as "long" a surface as possible. This will generally produce acurvature continuous surface with minimum deviation. b. Intelligent use of SPINES and LIMIT curves when using SURF2 and SKIN to closely match curvature across boundaries. c. Utilising conic surfaces and conic curve approximations to mimic curvature conditions. d. For parts with large variations within its shape cause techniques a and b to struggle. For this reason, we may take threeapproaches. d1. Create "unstressed" surfaces to the point of struggle and fill in the blank with blend surfaces and curvature continuity. This isvery much situation dependant. d2. Use ARC's and PATCHES's - ARC's and PATCHES have the peculiar yet great ability to * not go through all their constraints (good for the styling end of the design process) * the ability to deform a arc or patch to apoint * the ability to deform the boundary of a patch to an arc whilst maintaining the opposing continuity. * most importantly -the ability to reduce or increase degrees of arcs and patches to maximise or localise deformations. I have found these most useful. e. Utilise NURBSCRV and NURBSSRF when and arc or patch refuses to go close enough to the constraints of interest. Blends: These are a curious family of surfaces. One can utilise two functions within CATIA V4. The first is the ubiquitous BLENSURF functions, which allows a point/tangent/curvature continuos blend between any twocurves on any part of any plane, FSUR, RSUR, surface, face or skin. OR automatically creating bi-rail curves along twosurfaces at particular "radii" and placing a point/tangent/curvature continuous blend between them. Tensions and connectivitylocations are also adjustable. Although it is a great tool, one issue with Blensurf is its inability to blend around a large angle. For instance, if one constructstwo segment surfaces to each other at right angles with a gap between them and then placing a curvature continuos surface toconnect them. The result is very suprising. The surface comes off one with curvature continuity, takes the shortest route to theother and then blends with curvature again. It is not the expected shape in the blend, when comparing it to the curves createdusing CURVE2+CONNECT with curvature from the isoparametric curves of each surface. The reason for this is that Blensurf creates purely mathematical curvature. For the correct shape, mathematical andisoparametric curvature is required. Guess what my friends, Dassault are already on the ball, this is possible using GSM's SKINfunction blend and V5 GSD blends.

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