[LSC] LDraw coplanarity check

[Philo]

> LDView's calculations for "non-flat" quads use the dot product of the 

> normalized surface normals of the two triangles in the quad (using every 

> combination of two triangles, actually).  If that's <= 0 for any of the 

> normal pairs, the quad is concave.  If it's <= 0.9 for any of the normal 

> pairs, LDView considers the quad to be non-flat.  Unless I did the math 

> wrong, that means LDView considers a quad to be flat as long as the two 

> triangles are within 25 degrees of being the same.  Ouch!  Maybe I 

> should go back and tighten that up.

> 

Ouch indeed! 25 degrees is a lot...


> Can a math person confirm that?  (I'm doing acos(0.9) = 25.8 degrees.  

> Is this the right calculation?  If so, then for 1-degree accuracy, I'd 

> need 0.9 to change to 0.9998.)  

I agree with your calculations. Note that the problem with cosine is 
that you get very low precision on angle when it is near 0. Computing 
sine like I did would be better for that.

 > Also, what should be considered
 > "acceptable" here.  Is 1 degree too tight?

I made a quick experiment with ldview. The visibility threshold seems to 
be around 0.4 degree. But that's for two side by side triangles. For a 
twisted quad, even with much higher non-coplanarity I see no shading 
variation (though looking at the quad from side show clearly it is not 
flat !!!). A practical value seems to be about 1 degree indeed.

Philo