Performing Overlay of Two Triangulated Irregular Networks (TIN)

Question

I am referring to the paper here, section 2.6.1, on the adding and subtracting of two TINs:

The addition of two TINs can be determined exactly and stored into a new TIN, because the addition of piecewise linear functions again yields a piecewise linear function. The addition is done by performing an overlay of T1 and and T2, there are several algorithms for this. After this we obtain a subdivision where all faces have 3,4,5,6 edges. We now must fill in the height information for the vertices of the overlay..

Although I can understand every single word out of the passage, I don't know how to carry out the above procedure in practice to obtain the cut/fill of the two TINs.

More specifically, I would like to know how to perform the overlay of two TINs. There are references given at the end of the paper, but I can't have access to them because I'm not inside a university library. So any readily accessible online reference (or code samples) are greatly appreciated!

Answer 1

If you can overlay two (vector) polygon layers you can overlay two TINs. Some discussion of algorithms appears in many places,including

A Novel Algorithm for Union between Complex Polygons

Vector Overlay Processing - Specific Theory

A Design for Polygon Overlay Algorithm in the Simple Feature Model

Volumes from overlaying 3-D triangulations in parallel

(Unfortunately, most of these are abstracts, not the actual papers.) Basic algorithms will appear in any good textbook on computational geometry. Plane sweep algorithms are an attractive and oft-used choice. C++ source code is available.