I should clarify that I was testing with JTS 1.9; so if someone can tell me how to use Prepaired Geometry we can see what kind of improvement that makes?
The results are (for comparing 100 randomly generated little 2x2 squares arranged onto a 10x10 grid): a) 230 mills geometry.disjoint( geometry2 ) || geometry.touches( geometry2 )
b) 341 mills matrix.isDisjoint() || matrix.isTouches(2,2)
c) 441 mills geometry.relate( geometry2, "F********" )

My guess would be that the explicit relationship methods on the JTS geometry objects are optimized and do not compute the full matrix; all other options cost about the same as they are based on computing the complete matrix and then asking questions about the result. I was hoping the relate method would notice my pattern only cared about the intersection of the interior ;-)

Thanks for everyones time,
Jody
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