[LSC] LDraw coplanarity check

[Philo]

I got further on this one and made some experiments...

First I tested -dist and -det from LDDP with a slightly non planar quad 
at different scales. Here are the results:
4 16 0 0 10 1000 0 0 1000 1000 0 0 1000 0
0 // -dist = 10    -det = 10000000    -sine = 0.014
4 16 0 0 1 100 0 0 100 100 0 0 100 0
0 // -dist = 1     -det = 10000       -sine = 0.014
4 16 0 0 0.1 10 0 0 10 10 0 0 10 0
0 // -dist = 0.1   -det = 10          -sine = 0.014
4 16 0 0 0.01 1 0 0 1 1 0 0 1 0
0 // -dist = 0.01  -det = 0.01        -sine = 0.014

As you can see, -dist returns a value proportional to the size of the 
quad, while -det provides a value proportional to the cube of the size!!!

I then crufted an Excel sheet 
(http://www.brickshelf.com/gallery/Philo/Misc/coplanarity2.xls) with the 
angular criteria I proposed, which properly provides a nice constant 
figure (-sine in the results above). I also tested the same quad in 
different position and orientation with the same result (within 
calculation precision)

Tested with real life value (see bottom of excel sheet), I also get very 
consistent values,  all below 10^-3 (that's a 0.06 degree angle!)


> My mathematics are not so good that I fully understand what you are 

> writing. But if we measure an angle, what is about huge parts? Same 

> angle (that is good for us) but big gap in the part.


I don't think this is a problem. I mean - gaps should not happen of 
course, but generally we adjust quad apexes to match neighbour surfaces 
(precisely to close gaps) and in the process get a non-planar surface. 
While gaps can be easily spotted with the eyes while reviewing parts, 
planarity needs a measurement tool.

Orion, would it be difficult to implement that within LDDP? I'd like to 
be able to test the sine criteria on a larger scale with real parts.

Philo