[LSC] LDraw coplanarity check

[Michael Heidemann]

This answers my question why we need it.

It would be a good idea to have a value to change in LDView like in LDDP 
where I can adjust the accurance. After that we only have to specify a 
value for parts and primitives and 48'er primitives.

mikeheide

Travis Cobbs schrieb:

> I wasn't in on the beginning of this conversation, but based on what 

> I've seen, I'd like to thrown in my two cents.

>

> First of all, Philo is right when he points out that gaps are a 

> problem that isn't related to non-planar quads (other than the fact 

> that closing gaps often leads to non-planar quads).  It seems to me 

> that his sine calculation is the only thing that really matters.  The 

> reason that non-planar quads are bad is that there's no "right" way to 

> render them.  The quad is split into two triangles at render time, and 

> the split is arbitrary; which two triangles to choose?  If the two 

> triangles are at different angles, this will be visible.  If the quad 

> is planar, there's no problem.  The size of the quad has no impact on 

> the rendering error, though.

>

> 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.

>

> 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.)  Also, what should be considered 

> "acceptable" here.  Is 1 degree too tight?

>

> --Travis

>

> On Nov 14, 2007 12:56 PM, Philo <philohome at free.fr 

> <mailto:philohome at free.fr>> wrote:

>

>     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

>

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