Mathematica is not really a reference in digital terrain models, and, there are very powerful software packages to deal with geographical information.
But... where would be the fun...
If the information in the files includes a digital terrain model (DTM), with the surface of the terrain defined by triangular faces (regular or not), then you can easily calculate the volume contained in the triangular projection down to a certain defined level.
Obviously, only CAD files have vector information (and the PDF format, but I wouldn't recomend it), and so, I believe that their option of JPG and TIFF is a no go, since it is probably just the Rasterize[CAD].
Since we are talking of such a small area, I believe there's no need for projection corrections (the fact that the earth is round kind of stuff).
To facilitate the algorithm, you first find the volume to a level below all levels of all the triangles, and then you add the box volume up to your desired level. This avoids mathematically dealing with triangles that cross the desired terrain level (that have a negative and positive filling).
Most of the trouble you will have is dealing with the information format.
If the triangles are defined just by individual lines, first you will need to join them together back into triangles:
lines = Import["dtm.dxf", "LineObjects"];
Something like:
triangleBuilder[lines_] :=
Module[{triangles, firstSelection, secondSelection, aux},
triangles = {};
Do[
(*first, for each line,
select the other ones that share the same vertice*)
firstSelection =
Select[lines, Length@Intersection[lines[[i]], #] == 1 &];
(*Then, from those,
we select the one that, for which, there's another line that links \
the vertices of it to the one of the originaly selected line*)
secondSelection =
Select[firstSelection, (aux =
Complement[Join[#, lines[[i]]], Intersection[#, lines[[i]]]];
MemberQ[firstSelection, aux] ||
MemberQ[firstSelection, Reverse@aux]) &];
(*clean duplicates, add to the triangle list*)
Do[
AppendTo[triangles,
DeleteDuplicates[Join[secondSelection[[j]], lines[[i]]]]],
{j, Length[secondSelection]}];
, {i, Length[lines]}];
(*clean duplicate triangles*)
DeleteDuplicates[
Map[Sort[#,
Function[{a, b},
If[a[[1]] != b[[1]], a[[1]] > b[[1]], a[[2]] > b[[2]]]]] &,
triangles]]
]
And you obtain this:
Once you have the list of triangles, you can easily calculate the volume contained below them.
(from its name, this information is probably directly available from the ArcView shapefile, if you can access it, but I'm no expert...)
But if the information you have are just points, or isolines (line having the same height), that is, if you don't have the triangles, things get a little more complicated to do it right.
points = Import["map.dxf", "VertexData"];
ListPointPlot3D[points, ColorFunction -> "Topographic",
PlotStyle -> PointSize[0.002]]
You can ask Mathematica for different representation:
ListPlot3D[points, ColorFunction -> "Topographic",
MeshFunctions -> {#3 &}, Filling -> Bottom, FillingStyle -> Brown]
ListPlot3D[points, ColorFunction -> "Topographic", Mesh -> All,
Filling -> Bottom, FillingStyle -> Brown]
And then you could use Mathematica's triangles to do the volume calculation (extracting them from the Graphics element).
Or I imagine you could build a 3D Interpolation function from the points, and work directly with it (probably, NIntegrate it to your desired level).
But I don't know if you can then explain how the mesh was calculated (since it belongs to Mathematica internals).
So, I would recommend picking up a secific algorithm, like a reciprocal distance algorithm (see: Computational Geosciences with Mathematica By William C. Haneberg; if you are lucky, Google Books shows you page 290; I will not copy the code here, since it probably breaks some copyrights), to obtain a rectangular point map.
With a rectangular grid, you can easily calculate the volume by the triangles...
Long time ago, GIS also used raster information as data source, but I don't think this is what they are talking about when they say JPG, TIFF, etc.
You can see that, as long as you have the scale information, you can calculate the volume from each pixel color/tone:
In what respects other elements of the GIS, well, things can get even fuzzier without more specifics...
After this introduction, take also a look at:
ArcGRID and GeoTIFF, and probably try to find examples (over the internet) of the formats they can supply, to see if you can work with them.
