What is definition of class A surface?

The distance between each point of the edges of two neighboring patches must comply with the following limits:
• For class A: no more than 0.01 mm.
• For class B: no more than 0.02 mm.
• For class C: no more than 0.05 mm.
Tangents continuity
The angle between the tangents to the surface on the edges of two neighboring patches must comply with the following limits:
• For class A: no more than 6’ (0.1◦).
• For class B: no more than 12’ (0.2◦).
• For class C: no more than 30’ (0.5◦).
Curvature continuity
The control parameter is the patch curvature along its contour.
• Class A surfaces must have coincident curvature at least every 100 mm of
contour of two neighboring patches.
• Class B and C have no applicable rule.
Points of maximum curvature or inflection are only allowed along patch contours of Class A surfaces.
Completion surfaces
As we have seen, they do not belong to the aesthetic surface (even if part of them is visible and influences the aesthetic evaluation of the body), but are added to represent the part as it can be produced.
• For class C surfaces: completion surfaces are not required; gaps are represented by double lines drafted onto the aesthetic surface.
• For class B surfaces: only rounded contours are represented on the surface
that is always fixed to the body.
• For class A surfaces: completion surfaces must be designed in all detail.
Shape tolerance
The shape tolerances are measured by comparison of a surface patch with the
counterpart on the aesthetic surface.
• For class A surfaces: no more than ±0.5 mm on body shell surfaces (or large
surfaces) and no more than ±0.2 mmfor interior trimming (or small surfaces).
• For class B surfaces: no more than ±1.0 mm on body shell surfaces (or large
surfaces) and no more than ±0.5 mm for interior trimming (or small surfaces).
• For class C surfaces: shape tolerance is not applied.

Class A surfaces is a term used in most in automotive design to describe a set of freeform surfaces of high efficiency and quality. Actually it is nothing more than saying the surfaces have curvature and tangency alignment. It is smooth looking reflective surface with no distortion of light highlites, which moves in a smooth uniform designer intended formations.

I’m by no means an expert, far from it in fact so someone correct me if I’m wrong.
The last sentence in Indrek’s answer is (I think) about as good a description as you can have.
A Class A surface will show no distortion of light reflected from it, specifically in areas that the surface changes direction, like around the fender of a car or the engine cowling on an airplane .
As for recognizing it in CAD, Solidworks, and I’m sure other software, has analysis tools to check on this. Zebra Stripes is one, it projects a series of stripes on the surfaces, if the stripes flow smoothly over the surface, it indicates that the surfaces should reflect light without distortion.
Check out Matt Perez’s Predator Drone tutorial (link below), he gives some advice on this topic.
http://www.solidworkslessons.info/#!__predator-drone-online-tut

ok, that is wiki definition, but for argument only, how would you describe class A surface, or recognize one on CAD platform?

All answers are right.. We do the face analysis to identify the curvature continuty..must be curvature continuty for a-class surface. There r one zebra analysis availible in solidwork to identyfy that mast be non brakeble zebra reflaction on that face

Found this on wiki. I've always understood it this way. Class A is usually closest to Curvature continuity. (G2)

Positional continuity (G0)
holds whenever the end positions of two curves or surfaces are coincidental. The curves or surfaces may still meet at an angle, giving rise to a sharp corner or edge and causing broken highlights.
Tangential continuity (G1)
requires the end vectors of the curves or surfaces to be parallel, ruling out sharp edges. Because highlights falling on a tangentially continuous edge are always continuous and thus look natural, this level of continuity can often be sufficient.
Curvature continuity (G2)
further requires the end vectors to be of the same length and rate of length change. Highlights falling on a curvature-continuous edge do not display any change, causing the two surfaces to appear as one. This can be visually recognized as “perfectly smooth”. This level of continuity is very useful in the creation of models that require many bi-cubic patches composing one continuous surface.

-James-

Class A surfaces is a term used in automotive design to describe a set of freeform surfaces of high efficiency and quality. Although, strictly, it is nothing more than saying the surfaces have curvature and tangency alignment - to ideal aesthetical reflection quality, many people interpret class A surfaces to have G2 (or even G3) curvature continuity to one another (see freeform surface modelling).
Class A surfacing is done using computer-aided industrial design applications. Class A surface modellers are also called "digital sculptors" in the industry. Industrial Designers develop their design styling through the A surface, the physical surface the end user can feel, touch, see etc.
A common method of working is to start with a prototype model and produce smooth mathematical Class A surfaces to describe the product's outer body. From this the production of tools and inspection of finished parts can be carried out. Class A surfacing complements the prototype modelling stage by reducing time and increasing control over design iterations.
A class A surface can be defined as any surface that has styling intent.