Bedding planes, rose diagrams and bug fix

[John Halleck]

On Tue, 2 May 2000, Phil Underwood wrote:

> Date: Tue, 2 May 2000 02:11:03 +0100
> From: Phil Underwood <furbrain@furbrain.screaming.net>
> To: survex mailing list <survex@survex.com>
> Subject: Bedding planes, rose diagrams and bug fix
> 
> I'm thinking about making a couple of analysis tools for survex/chasm.
> One is a rose diagram - showing the comparative frequency of directions of
> legs. I've got a pretty basic one set up; are there any more features that
> people would appreciate? (eg weighting the relative contribution of legs by
> their length, excluding very short legs)

  Just off the top of my head:

  A rose diagram for dip.  (We have some caves here where there is a wide
  range of dips.)

  A note saying what angle the cave would have to be plotted at in order
  to minimise width, or total area.  (If I hunt for it, I can provide ForTran
  code that does this exactly using Little's observation.)

  "Side" views end on to the minimum width rectangle, and perpendicular to it.
  (In my experience, for dip controlled caves, this gives a good approximation
  to the dip.)

  A fit of the ceiling points to a plane to estimate dip.
  A plot of the cave after rotating that plane to level.

  A plot that shows error elipisoids (suitably scaled up, of course). 

  The convex hull of the survey points in the file...  (This allows a fast
  computation of the limits of the cave for other views, and allows a quick
  estimate of locations for label blocks.)
  
> Do people think that these kind of widgets are a good idea, or just
> pointless bells and whistles for what should be a lean mean cave-displaying
> machine?

  My personal opinionated opinion:  Anything that can show me information clearly
  that isn't obvious is of use in the end.   

> The other thing I'm currently thinking about is a gadget that will search
> through the legs in a survey, looking for any planes whcih seem to contain
> a lot of legs eg a phreatic level or a fault controlling the cave formation.

  Great idea.
 
> I've currently got to the stage where I can lots of slices through the cave
> and see if any have more legs in them than expected. What I would then need
> to do would be to take all these vectors and somehow take an average of
> these, turning it into a plane equation.

  There are good least squares plane fitting routines that can give you a good
  first estimate if you assume that all such planes have the same dip.

> The only thing I can come up with is taking the cross-product of two
> successive vectors, and summing all these cross-products together.
> Unfortunately, this would mean that the last leg of an odd number of legs
> should be ignored. Anyone got a better way of doing this? I don't really
> know much about linear algebra/ vector calculus /geometry so I would
> appreciate some input from anyone who knows this kind of stuff.

  I've not tried this, but:

  Get an estimate of the dip (as above).  Rotate the cave to make that plane
  level.  Now do histograms by depth.  This should give you the various bedding
  planes.
 
> BUG REPORT: [...]
> 
> I appear to have waffled on for far too long now, so I'll shut up.

  I, for one, would be interested in continuing that discussion.

> -- 
> Phil Underwood <furbrain@furbrain.screaming.net>
> Chasm's Homepage: http://members.xoom.com/bighairyone/chasm/
> "It's not what you've got, it's how you make it explode."
> 
> 
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