How do we define the footprint of a cave?

[gypcaver]

What is the footprint of a cave? Or another way of wording it is, "what area does a cave lie under?" Can we determine the "footprint" by using the plan view of a cave map? I have an idea of what I mean by the footprint, but I'm interested in hearing how others would define the footprint.

[BryantG]

Good question. In my opinion there isn't an exact answer to that question. You could define it strictly as the plan view of a cave with a topo overlay as you alluded to, or a number of other ways. A more hydrologic way of thinking on the matter would be to consider the immediate drainage basin of the cave and the area that encompasses. I realize it is highly difficult to discern an exact recharge area for a karst feature but it is still a 'footprint of a cave' more or less.

--Bryant

[rjack]

What is the footprint of a cave? Or another way of wording it is, "what area does a cave lie under?" Can we determine the "footprint" by using the plan view of a cave map? I have an idea of what I mean by the footprint, but I'm interested in hearing how others would define the footprint.

Same way you would a house. Look at the outline in plan view and the limits of that outline are the footprint. Multiple levels don't count if they are directly on top of one another. "Overhangs" where one level is slightly lateral from another expand the footprint. Imagine, "how big of a shoe would I need to step on all of this feature's area but no more?"

foot·print
/ˈfo͝otˌprint/Noun
1.The impression left by a foot or shoe on the ground or a surface.
2.The area covered by something, in particular.

[Extremeophile]

What is the footprint of a cave? Or another way of wording it is, "what area does a cave lie under?" Can we determine the "footprint" by using the plan view of a cave map? I have an idea of what I mean by the footprint, but I'm interested in hearing how others would define the footprint.

Sounds like you're looking for an objective quantitative value to use for comparing cave systems (e.g. Fort Stanton v Mammoth). I don't think a standard convention exists. It seems like the way to do it is to draw some sort of polygon around the known extents of the cave and then integrate the area of that polygon. The most simple approach would be to make that polygon a rectangle with the extents being the furthest north-south and east-west. Of course in this scenario two nearly identical cave systems might have very different calculated footprints if they happen to be very linear but one is oriented NE-SW and the other is oriented directly E-W. Of course Compass already does this in "Cave Statistics" and quantifies surface length, surface width, and surface area.

[tncaver]

Would it not be logical for the footprint of a cave to be in relation to the surface area, that can be displayed by the plan of the cave map as overlaid and represented on a topographic map? Therefore the footprint would equal the surface area in square feet on the map. The area might be subject
to interpretation rather than an exact number.

[gypcaver]

Yes, I'm looking for an objective way to define the footprint of a cave. The definition should be easily understood and should not be dependent upon the orientation of the cave. I propose that the footprint should be defined as the smallest convex polygon that encloses the horizontal extent of the cave. One can visualize this as a rubber band or string stretched around the plan map. The vertices, or corners, of the polygon would be at the ends of the remote passages of the cave. This definition is easy to understand. The area of a complex polygon is fairly easy to compute, if one knows the coordinates of the vertices, and it seems to fit what one would mean by the footprint.

Others have talked about the cave field being an irregular concave polygon that "reasonably closely embraces the plan array of the cave." This could be visualized as if one chose a small segment length (toothpick) and placed the segments around the edge of the plan map so that the ends or edges of the segments were up against the sides of the cave passages on the map. As one chooses smaller and smaller segments, the area of this irregular polygon comes closer and closer to matching the outer edges of the cave passages. One could argue that this is the footprint of the cave.

I don't like this latter definition because it is somewhat subjective (how small do you make the segments?) and not easily computed.

Comments?

[Extremeophile]

I propose that the footprint should be defined as the smallest convex polygon that encloses the horizontal extent of the cave. One can visualize this as a rubber band or string stretched around the plan map. The vertices, or corners, of the polygon would be at the ends of the remote passages of the cave. This definition is easy to understand. The area of a complex polygon is fairly easy to compute, if one knows the coordinates of the vertices, and it seems to fit what one would mean by the footprint.

I'd support this definition. Maybe you could send an email to Larry Fish and see if he could incorporate this calculation into Compass. This might also make an interesting Convention discussion topic.

The only practical concern I have is where to find rubber bands big enough.

[Marlatt]

I propose that the footprint should be defined as the smallest convex polygon that encloses the horizontal extent of the cave. One can visualize this as a rubber band or string stretched around the plan map. The vertices, or corners, of the polygon would be at the ends of the remote passages of the cave. This definition is easy to understand. The area of a complex polygon is fairly easy to compute, if one knows the coordinates of the vertices, and it seems to fit what one would mean by the footprint.

I'd support this definition. Maybe you could send an email to Larry Fish and see if he could incorporate this calculation into Compass. This might also make an interesting Convention discussion topic.

The only practical concern I have is where to find rubber bands big enough.

I've actually done this some time ago, using the .sta file which Compass can generate from survey data. At one point, I was trying to compare areal densities (total survey length / footprint area) for various caves in my database. Like most of my projects, however, this has been neglected due to competing priorities. I might be able to find my code somewhere...

Stuart

[lleblanc]

I propose that the footprint should be defined as the smallest convex polygon that encloses the horizontal extent of the cave. One can visualize this as a rubber band or string stretched around the plan map. The vertices, or corners, of the polygon would be at the ends of the remote passages of the cave. This definition is easy to understand. The area of a complex polygon is fairly easy to compute, if one knows the coordinates of the vertices, and it seems to fit what one would mean by the footprint.

I'd support this definition. Maybe you could send an email to Larry Fish and see if he could incorporate this calculation into Compass. This might also make an interesting Convention discussion topic.

The only practical concern I have is where to find rubber bands big enough.

I've actually done this some time ago, using the .sta file which Compass can generate from survey data. At one point, I was trying to compare areal densities (total survey length / footprint area) for various caves in my database. Like most of my projects, however, this has been neglected due to competing priorities. I might be able to find my code somewhere...

Stuart

I recall coding that very algorithm with 20 lines of APL in my Artificial Intelligence class almost 30 years ago. I still have the code but I doubt I can still read APL. I do remember the principle, though and I may add that to the Auriga Statistics in a future version.

[Bob Thrun]

I propose that the footprint should be defined as the smallest convex polygon that encloses the horizontal extent of the cave.

This is the Convex Hull Problem. I have two books on Computational Geometry. They each devote a whole chapter to the Convex Hull, showing different ways to solve the problem. The convex hull can be used to find the rotation that gives the smallest piece of paper for the map.

[Aaron Addison]

I would like to propose that cave footprints are a voxel problem, not polygonal.

If the goal is to establish a standard that all caves can be measured against, simply pick a voxel size and stick to it, say 10m. Bigger passages will require more voxels.

The math is much more straightforward. Cover all cave passages with voxels, and count them up.

Aaron

[rjack]

Why would the footprint, which has been defined in cartography as a 2 dimensional shape for eons, suddenly become defined by 3 dimensional shapes (cubes)?

[Aaron Addison]

ok, then just lay a standard grid over any cave and count the squares.

[Chris Chenier]

Using the convex hull is likely the way to go as it is straightforward to define yet does not rely on setting an arbitrary grid size or an arbitrary segment (toothpick) length.

I don't see much point in using footprint by itself (as an L-shaped cave would have a large footprint compared with a linear cave, yet be very similar in morphology), but density computations could be interesting to quantify the "maziness" if various caves. Computing the density of cave passages would be done by dividing the total length of all cave passages by the footprint area.

Note that a 3D convex hull could be just as easily constructed, giving a volume to the cave, and by extension, a 3D density.

Regardless of the system used, one will want to use a computer to automate the process. Constructing convex hulls is not as complex as one might think, and depending on which algorithm is used, can be performed just as fast, or even faster than a simple sort of all stations. Algorithms to construct a convex hull from a set of points in 2D or 3D (the coordinates of all survey stations) are available on the web, and anyone who has written code to handle geometry problems should be able to do this without problems. As a comparison, this is much simpler than closing survey loops.