Wednesday, July 24, 2013

What Did We Learn Today?

Last Thursday I had the kids do this layout exercise I came up with last year...

(Actually this is a little harder than last year because last year's group finished off the thing more quickly than I had anticipated.)

The idea is to get them to do some full scale layout using constructions that we're doing in the Drafting class at the same time.  In order to do this you need to do the following:
  • Construct a perpendicular bisector
  • Construct an ellipse
  • Construct a pentagon inscribed in a circle
Once you get through those, there's some other stuff, but that's the meat of the thing.  The ellipse construction is best accomplished with what I was taught as the "Card Method" and what seems to also sometimes be called the "Trammel Method"

One of the reasons the card method seems so right for this is that you can mark each of the three different ellipses at the same time just by making additional ticks.

Here is one group doing some layout:

Fast forward to today.  I'd planned on using today's class to talk about various approaches to full scale layout beyond geometric constructions: cartooning, projection, full scale plot, CNC...  But before getting to that I wanted to take some time and walk through the solution to the previous exercise since one of the two groups kinda imploded.

I talked a little bit about initial layout and then how to do a 3-4-5 triangle with tape measures instead of doing the bisector construction.  Then we discussed alternates on how to do the ellipse layout starting with the "String Method" which drove us off on a tangent about locating the foci of an ellipse.  So we watched a little bit of a video from Kahn Academy:

After rounding out discussion of the difficulties of implementing the string method and the two circle method we went back to a discussion of the card method.  And here I asked them a question I really didn't have an answer for.

"Are these ellipses concentric based on the center point or on something to do with the foci?"

I still don't know.

If you look at the drawing, it is clear that the offset distance at the compass points are true to the given dimensions:

But I found myself wondering if laying out the inner ellipses via the card method and additional ticks actually gives you the shape on the drawing.

The answer to that appears to be a no.

If you put additional ticks on the card when laying out the ellipses you get an inner ellipse that is always exactly the same distance away from the outer one - although at this point the conversation becomes difficult due to the use of "always" because you have to ask "where and in what direction?"  We looked at it rather exhaustively...

What we discover is that if you construct a circle with a radius of the offset distance anywhere along the perimeter of the ellipse except the compass points then that circle and the inner ellipse have no intersection.  Not only are the ellipses not concentric about the center point, but aside from the four compass points the distance is not the offset distance anywhere.

For most of the class this had reached brain freeze level a while ago - now the cranial numbness had started to get to me.

Then one of the kids had the bright idea of drawing the inner ellipse as an ellipse with known major and minor axes rather than by offsetting the first ellipse.  So I did that.  FWIW the ellipse that generates matches the offset generated ellipse only at the compass points and no place else.  Also, this ellipse intersects the circle with a radius of the offset distance not at a tangent, but at two points.

My faith in CAD at this point is starting to quake.  Most of the ellipse generated by OFFSET is too far away and most of the ellipse generated by ELLIPSE is too close.

While we're at this another student does a quick Google search and comes up with something akin to this:
"Normally if you offset an ellipse in AutoCAD, the resulting object is a spline. Kent's routine creates an ellipse whose quadrant points are exactly the desired distance away from the equivalent points on the original ellipse. Other points along the new ellipse entity are not necessarily a consistent distance away from the old one, and that is why AutoCAD creates a spline."
Which I guess is saying that when you use the offset command on an ellipse you get something that is more of a mathematical approximation as opposed to a true geometric construction.  That could I guess be another way of saying "concentric ellipses" may be a somewhat more complicated concept than is belied by simply using the OFFSET command.

So, now for the sake of the exercise we have another question:

"As the person replicating the design in full scale, do I need to know specifically how the drawing was constructed in order to replicate it?

Since we had discovered that an ellipse created by OFFSET would be different than one created with ELLIPSE, can I possibly create a high fidelity execution with only the drawing?  The answer to this would appear to be no; a dimensioned drawing would not be enough to mechanically recreate the shape correctly.  In order to be truly faithful one would have to either project, or plot full scale or CNC from the design drawing.

Except probably not.  Setting the CAD unit tolerance to 1/256" the difference between the intended and actual ellipses created by the OFFSET command was still showing as 0'-0" on a DIST query.  The distance between the intended and the actual ellipses created by using the ELLIPSE command for the inner figure was 25/256" - less than 1/8" over 20' or probably not something that would matter in regular theatre materials in a regular theatrical scale.

But if you find yourself doing any enormous ellipses for an incredibly anal designer you might want to be wary of any drawing or file but the designer's original.

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