Can you explain SDO_RELATE and SDO_GEOM.RELATE differences?

Question

Ok, so I'm doing some spatial queries identifying geometries that interact with each other, and everything's groovy until the customer says, ok, get rid of the ones that just touch, which means that a call to SDO_RELATE with an ANYINTERACT mask no longer does the trick. First we tried setting a multiple mask and those queries ran like 9 hours. I figured that since we're burning that much time, we might as well build a table that stores the interaction as identified by DO_GEOM.RELATE with a DETERMINE mask.
Then I noticed an odd thing happening on the way to the forum. For some geometries I get SDO_RELATE with ANYINTERACT returning TRUE and then SDO_GEOM.RELATE returns DISJOINT with the same tolerance that is coded in the metadata (0.5). When tolerance is bumped up to 27, I get TOUCH back. The funny thing is that there are 3 geometries involved here, the reference geom, one that yields TOUCH, and the one that yields DISJOINT.
Stepping back from this behavior, doing some head-scratching and chin-stroking, I ran accross this statement in the Oracle® Spatial User's Guide and Reference 10g Release 2 (10.2) [here.|http://download.oracle.com/docs/html/B14255_01/sdo_operat.htm#i78531]
Unlike with the SDO_GEOM.RELATE function, DISJOINT and DETERMINE masks are not allowed in the relationship mask with the SDO_RELATE operator. This is because SDO_RELATE uses the spatial index to find candidates that may interact, and the information to satisfy DISJOINT or DETERMINE is not present in the index.
Now, how can a function that cannot determine DISJOINT relationships be reliable in determining ANYINTERACT relationships? Actually in this case, the answer we needed is given by SDO_RELATE, as we were looking for a touch relationship for all 3 geometries, except we got the DISJOINT with the SDO_GEOM.RELATE until we cranked up the tolerance.
These are the geometries involved:
Base geom:
SDO_GEOMETRY(2003, 8265, NULL), SDO_ELEM_INFO_ARRAY( 1, 1003, 1), SDO_ORDINATE_ARRAY( -81.9497222222222, 32.0836111111111, -82.2163888888889, 31.7502777777778, -81.9997222222222, 31.4002777777778, -81.9997222222222, 31.8502777777778, -81.9497222222222, 32.0836111111111))
Geom that yields ANYINTERACT and TOUCH:
SDO_GEOMETRY(2003, 8265, NULL), SDO_ELEM_INFO_ARRAY( 1, 1003, 1), SDO_ORDINATE_ARRAY( -81.77888889, 31.3330555608386, -81.59972222, 31.4252777808399, -81.99972222, 31.7997222208455, -81.99972222, 31.4002777808396, -81.88777778, 31.3330555608386, -81.77888889, 31.3330555608386))
Geom that yields ANYINTERACT and DISJOINT:
SDO_GEOMETRY(2003, 8265, NULL), SDO_ELEM_INFO_ARRAY( 1, 1003, 1), SDO_ORDINATE_ARRAY( -81.39166667, 31.6836111108438, -81.34972222, 31.8502777808462, -81.99972222, 31.8500000008462, -81.99972222, 31.7997222208455, -81.59972222, 31.4252777808399, -81.52472222, 31.4377777808401, -81.45805556, 31.5419444408417, -81.47055556, 31.6252777808429, -81.39166667, 31.6836111108438))
Both should touch the base geom along the -81.99972222 or at least both should be disjoint at a tolerance of 0.5 but one is and the other isn't.
So how do I know when to trust SDO_RELATE? How do I know what tolerance will give me consistency?
Oh, yeah, we have the query down to about 45 mins, by using SDO_GEOM.RELATE with DETERMINE and SDO_FILTER in the where clause. (comparing each geometry to each geometry in a table of about 10K rows)

Answer 1

ConSolTed,
It looks to me like the geometries in question are disjoint by 0.000247 meters.
Check my math:
-81.9997222222222 - -81.99972222 = -0.0000000022222 degrees
111,000 meters/degree @equator * -0.0000000022222 * cos(31.4) = -0.000247
So I would expect sdo_geom.relate to return TOUCH for both geometries, and sdo_anyinteract to return TRUE for both, when the tolerance is around .0005 and up. But I've never been good at this math stuff.
Anyone know why ConSolTed's query below, now with a tolerance of 26 meters, returns Disjoint?
SQL> select version from v$instance;
VERSION
10.2.0.4.0
SQL> SELECT
2 SDO_GEOM.RELATE(
3 SDO_GEOMETRY(2003, 8265, NULL, SDO_ELEM_INFO_ARRAY( 1, 1003, 1), SDO_ORDINATE_ARRAY( -81.9497
222222222, 32.0836111111111, -82.2163888888889, 31.7502777777778, -81.9997222222222, 31.400277777777
8, -81.9997222222222, 31.8502777777778, -81.9497222222222, 32.0836111111111))
4 , 'determine',
5 SDO_GEOMETRY(2003, 8265, NULL, SDO_ELEM_INFO_ARRAY( 1, 1003, 1), SDO_ORDINATE_ARRAY( -81.391666
67, 31.6836111108438, -81.34972222, 31.8502777808462, -81.99972222, 31.8500000008462, -81.99972222,
31.7997222208455, -81.59972222, 31.4252777808399, -81.52472222, 31.4377777808401, -81.45805556, 31.5
419444408417, -81.47055556, 31.6252777808429, -81.39166667, 31.6836111108438))
6 , 26) relationship
7 FROM dual;
RELATIONSHIP
DISJOINT