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Mathematic criterial of CAD Class-A surfaces

Mathematic criterial of CAD Class-A surfaces

Mathematic criterial of CAD Class-A surfaces


I'm searching for the mathematical criterials of a CAD Class-A surface?

Tx Ralf
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RE: Mathematic criterial of CAD Class-A surfaces


This topic was addressed with no resolution in Thread87-21426.

Best regards,

Matthew Ian Loew

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RE: Mathematic criterial of CAD Class-A surfaces

There is a differance between a CAD class A and a manufacturing class A.
For example on a fascia the exterior surface is all class A (owned by the studio). But in production that same surface will be broken into Class A,B and C surfaces for the supplier and OEM quality.
The reason being that a CAD class A determines the shape / reflex  of a surface. A manufacturing A,B or  C surface determines what defects are allowed on that surface in production.

RE: Mathematic criterial of CAD Class-A surfaces

Heres the the best mathematical analysis I can give you.
Generally in automotive, Class A surface must be continous, tangent continous and then curvature continous to a certain designated tolerance given by a department. Continous means a two surface edges must mate within a certain tolerance. Tangent continous means that the angles at the mating area must be less than a given tolerance. Curvature continous means the radius of curvature for each mating patches must be within a certain radius tolerance. (follow the 1st derivative, 2nd derivative, 3rd derivative thought pattern here)

Class A/Class 1 must follow all three requirements. If you are missing curvature continuity, the reflection lines between patches or even adjacent body panels, will be visually off, and non continous, yes, the average person can see this.

There are only a few software packages that can actually hold, modify and check curvature continuity (easily). These include ICEM SURF (industry standard) Alias, Imageware/Freeform, PDGS and the CATIA 5 add on ACA module. (there may be more)
Standard CAD packages like I-DEAS, UG, CATIA, PRO-E,
 SOLIDWORKS and RHINO cannot do this. Before people start to object to my last statement, Every CAD system can model a car body, just not to curvature continous industry tolerances. These are defined in the program, and are not as subjective as everybody seems to think.

hope this clears in up a little bit


RE: Mathematic criterial of CAD Class-A surfaces


Do you have any references to publicly avalable numbers for those tolerances?

What do you think of the talk of controling the 4th derivative (curvature flow)?

RE: Mathematic criterial of CAD Class-A surfaces

I don't have public tolerances to post. At the end of the day, the tolerances will have to be tight enough not to show up on milled tool steel.

The 4th derivative, rate of curvature change, is only supported on Catia ACA package as far as I know. It may be
eventually used as a diagnosis tool, but it is unproven value as of now. It is pretty tricky sometimes just to get up to curvature continuity in a patch corner. You can chase yourself around a corner for days, until it is right. I can't imagine adding another degree onto it, unless new methods were developed (but I haven't used it personally)

Hope this helps,


RE: Mathematic criterial of CAD Class-A surfaces

I've heard that Alias has it and I know Imageware 10 has it but I've used it either.

Corners are allways a problem. Imageware doesn't even allow a 3 sided surface for a corner.

RE: Mathematic criterial of CAD Class-A surfaces

    StudioTools, from Alias|Wavefront has Up to G4 Continuity.
G0:Position, G1:Tangency, G2:Curvature, G3:Constant change of rate of curvature, G4:Constant rate of change of the rate of change of the curvature. Simple Huh!

    In my experience as an Industrial Designer, G3 is enough and hard enough, as it has taken me up to 20 hours to create transition surfaces for a chair that took less than five hours of primary surfacing! The problem is similar to solving a set of simultaneous equations by discovering algebra on your own. I have found very little (Alias manuals only) written material on transition surfaces and trial and error is very slow.

    Anybody knows any good surfacing books?

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