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
Automotivedesigner