# WL#7221: Geometry Set Operations

Status: Complete

Implement MySQL GIS relation check functions using boost geometry. Gis features are more and more powerful, important and pervasive in RDBMS products, and MySQL GIS needs extensive improvements in terms of functionality, reliablity and performance. We want to achive this by replacing the home grown gis computation core with boost geometry, just like PostGIS is using GEOS, so that we have all features boost geometry can provide. Boost geometry is more powerful and robust and keeps growing, we will grow with it.

F-0: All functions in this WL are *new* to end users, because the documentation says they don't exist before. However, they are tested in mysql public and private test suites. Thus we need to cover usage of these functions in MySQL documentation. F-1: Usage or input data format shall not change, existing SQL query code shall need no change at all. F-2: Some type combinations which were not supported before will be supported, specifically the following are supported now: intersection(point, point), intersection(point, multipoint), intersection(point, linestring), intersection(point, multilinestring), intersection(point, polygon), intersection(point, multipolygon), intersection(multipoint, point), intersection(multipoint, multipoint), intersection(multipoint, linestring), intersection(multipoint, multilinestring), intersection(multipoint, polygon), intersection(multipoint, multipolygon), intersection(linestring, point), intersection(linestring, multipoint), intersection(polygon, point), intersection(polygon, multipoint), intersection(multilinestring, point), intersection(multilinestring, multipoint), intersection(multipolygon, point), intersection(multipolygon, multipoint) union(point, point), union(point, multipoint), union(point, linestring), union(point, multilinestring), union(point, polygon), union(point, multipolygon), union(multipoint, point), union(multipoint, multipoint), union(multipoint, linestring), union(multipoint, multilinestring), union(multipoint, polygon), union(multipoint, multipolygon), union(linestring, point), union(linestring, multipoint), union(polygon, point), union(polygon, multipoint), union(multilinestring, point), union(multilinestring, multipoint), union(multipolygon, point), union(multipolygon, multipoint) difference(point, point), difference(point, multipoint), difference(point, linestring), difference(point, multilinestring), difference(point, polygon), difference(point, multipolygon), difference(multipoint, point), difference(multipoint, multipoint), difference(multipoint, linestring), difference(multipoint, multilinestring), difference(multipoint, polygon), difference(multipoint, multipolygon), difference(linestring, point), difference(linestring, multipoint), difference(polygon, point), difference(polygon, multipoint), difference(polygon, linestring), difference(polygon, multilinestring), difference(multilinestring, point), difference(multilinestring, multipoint), difference(multipolygon, point), difference(multipolygon, multipoint), difference(multipolygon, linestring), difference(multipolygon, multilinestring) F-3: Calling a set operation with an unsupported type combination will return an error ER_GIS_UNSUPPORTED_ARGUMENT to client, so that the entire query doesn't produce any result, even if only one row in the table has unsupported geometry. Unsupported geometries: none. F-4: Geometry set operation calls of two geometries of different srids is always not supported, and client will get error ER_GIS_DIFFERENT_SRIDS, and the error will cause the entire query to fail without producing any result even if only one row has this error. F-5: Max SRID number is 4294967295 (0xFFFFFFFF), if given srid larger than this, the value's lower 4 bytes are used as the srid value (4 bytes unsigned integer).

I-1: No new files Here it's supposed that #WL7220 will be completed first, so we won't list the need for boost library, it's the same as that of #WL7220. I-2: No new syntax Here it's supposed that #WL7220 will be completed first, so we won't list the changes to srid, it's the same as that of #WL7220. I-3: No new commands I-4: No new tools. I-5: No impact on existing functionality. I-6: Result representation change: The set operations' result geometry's WKT/WKB may change, but the content in essence doesn't change. For example, in previous versions we may return a geometry collection having two polygons, now we return a geometry collection containing a multipolygon, which contains the same two polygons. And also, we will always return polygons with its rings' points in anti-clockwise order. Both are due to how boost geometry works.

It's not straight forward to use boost geometry in mysql gis, because 1) it doesn't support geometry collection(OGC defined), 2) Not all 4 standard check functions(intersection, union, difference, symdifference) are fully supported. 3) All the geometry types are separate and independent class templates, no inheritance or polymorphism, and all the algorithm functions are function templates requring geometry type parameters. 4) Boost geometry set operations return result in a unique way, we have to do some further computation to get correct results. What we can and will do in this worklog is to reimplement the gis set operation functions by using existing boost geometry features as much as we can, and fall back to old gis implementation if we can't implement a feature using boost geometry directly or indirectly. And in the future when boost geometry start to support more type combinations we can easily use it instead, we won't wait for boost geometry enhancement/improvement in this work log. All gis set operation functions have two parameters, given a pair of argument g1 and g2, for a set operation function, if the type combination is directly supported by boost geometry, simply call the corresponding boost geometry function template instantiated with g1's and g2's geometry types; This is static dispatching --- we have to enumerate all the possible type combinations of g1 and g2, which are supported by each boost geometry set operation function template, and instantiate the function template with the types, and construct the boost geometry objects bg1 and bg2 from g1 and g2, and then call the function with the arguments bg1 and bg2. For the unsupported type combinations, try to indirectly use supported geometry types of boost geometry to do further computing to get the result. Some type combinations can be computed using the supported type combinations of the same set operation, or by calling relation check functions to test relationship of g1 and g2, e.g. multipoint INTERSECTION polygon isn't supported by boost::geometry::intersection, but we can check whether each point of the multipoint is in the polygon, and collect the ones that are not to form another multipoint, which is the result. Another unique complication of boost geometry set operations is that they need a 3rd template type --- the geometry type to take out set operation result, and valid options are multipoint, multilinestring and multipolygon. For any set operation, and for each pair of type combination, there are often more than one supported result parameter types, we need to make sure whether we need to call the function multiple times with each supported type of result parameter, and if so, we need to do the multiple calls and assemble the results into a correrct final result. In order to work with existing gis code, we need to keep and use the existing Geometry class and its children classes in existing mysql gis, and use these classes in new implementation, and keep the geometry internal format unchanged, also keep the sql functions GeomFromText/GeomFromWkb's internal result format unchanged. Construct boost geometry objects and call boost geometry algo functions in Item_func_spatial_operation::val_str, reimplement this function using above methods. Following is a complete list of type combinations for each set operation function that are implemented using boost geometry directly or indirectly via further computation: 1. Implemented via direct boost geometry set operation calls: Note that the 3rd geometry type of the rows below is the supported result type, for example, we have intersection linestring multipolygon multipoint intersection linestring multipolygon multilinestring this means we can call boost::geometry::intersection with a linestring and multipolygon geometry objects as input argument and use a multipoint or multilinestring as result argument, to take back the intersection points or linestrings. In this case it's possible for both results to appear, so we will need to combine the two results and avoid repetitive points(remove those that are already on the result line strings from the multipoint result). For other cases such as difference linestring polygon multipoint difference linestring polygon multilinestring it's impossible for there to be a multipoint result, then we will ignore it and simply fetch result with a multilinestring object in the call. And consequently although BG supports many type combinations for symdifference, the real useful ones are can be directly called are only four (polygon combinations), the rest are useless and have to be indirectly computed: symdifference polygon polygon multipolygon symdifference polygon multipolygon multipolygon symdifference multipolygon polygon multipolygon symdifference multipolygon multipolygon multipolygon All type combinations directly supported by BG: union_ polygon polygon multipolygon union_ polygon multipolygon multipolygon union_ multipolygon polygon multipolygon union_ multipolygon multipolygon multipolygon intersection linestring linestring multipoint intersection linestring polygon multipoint intersection linestring polygon multilinestring intersection linestring multilinestring multipoint intersection linestring multipolygon multipoint intersection linestring multipolygon multilinestring intersection polygon linestring multipoint intersection polygon linestring multilinestring intersection polygon polygon multipoint intersection polygon polygon multipolygon intersection polygon multilinestring multilinestring intersection polygon multipolygon multipoint intersection polygon multipolygon multipolygon intersection multilinestring linestring multipoint intersection multilinestring polygon multilinestring intersection multilinestring multilinestring multipoint intersection multilinestring multipolygon multilinestring intersection multipolygon linestring multipoint intersection multipolygon linestring multilinestring intersection multipolygon polygon multipoint intersection multipolygon polygon multipolygon intersection multipolygon multilinestring multilinestring intersection multipolygon multipolygon multipoint intersection multipolygon multipolygon multipolygon difference linestring linestring multipoint difference linestring polygon multipoint difference linestring polygon multilinestring difference linestring multilinestring multipoint difference linestring multipolygon multipoint difference linestring multipolygon multilinestring difference polygon linestring multipoint difference polygon polygon multipoint difference polygon polygon multipolygon difference polygon multilinestring multilinestring difference polygon multipolygon multipoint difference polygon multipolygon multipolygon difference multilinestring polygon multilinestring difference multilinestring multilinestring multipoint difference multilinestring multipolygon multilinestring difference multipolygon linestring multipoint difference multipolygon polygon multipoint difference multipolygon polygon multipolygon difference multipolygon multipolygon multipoint difference multipolygon multipolygon multipolygon sym_difference linestring linestring multipoint sym_difference linestring polygon multipoint sym_difference linestring multipolygon multipoint sym_difference polygon linestring multipoint sym_difference polygon polygon multipoint sym_difference polygon polygon multipolygon sym_difference polygon multilinestring multilinestring sym_difference polygon multipolygon multipoint sym_difference polygon multipolygon multipolygon sym_difference multilinestring polygon multilinestring sym_difference multilinestring multilinestring multipoint sym_difference multipolygon linestring multipoint sym_difference multipolygon polygon multipoint sym_difference multipolygon polygon multipolygon sym_difference multipolygon multipolygon multipoint sym_difference multipolygon multipolygon multipolygon 2. Computed type combinations Following is a list of computed type combinations for each set operation, which are NOT directly supported by boost geometry, but can be computed using the type combinations that boost geometry directly supports. For the symetric functions(intersection, union, symdifference), code is written without redundancy --- simply switch the two parameters and call the function again. In the implementation we often need to do geometry relation checks, we do so by calling the Item_func_spatial_rel's core function(a static one). 2.1 intersection intersection(point, point), intersection(point, multipoint), intersection(point, linestring), intersection(point, multilinestring), intersection(point, polygon), intersection(point, multipolygon), intersection(multipoint, point), intersection(multipoint, multipoint), intersection(multipoint, linestring), intersection(multipoint, multilinestring), intersection(multipoint, polygon), intersection(multipoint, multipolygon), intersection(linestring, point), intersection(linestring, multipoint), intersection(polygon, point), intersection(polygon, multipoint), intersection(multilinestring, point), intersection(multilinestring, multipoint), intersection(multipolygon, point), intersection(multipolygon, multipoint) 2.2 union union(point, point), union(point, multipoint), union(point, linestring), union(point, multilinestring), union(point, polygon), union(point, multipolygon), union(multipoint, point), union(multipoint, multipoint), union(multipoint, linestring), union(multipoint, multilinestring), union(multipoint, polygon), union(multipoint, multipolygon), union(linestring, point), union(linestring, multipoint), union(polygon, point), union(polygon, multipoint), union(multilinestring, point), union(multilinestring, multipoint), union(multipolygon, point), union(multipolygon, multipoint) 2.3 difference difference(point, point), difference(point, multipoint), difference(point, linestring), difference(point, multilinestring), difference(point, polygon), difference(point, multipolygon), difference(multipoint, point), difference(multipoint, multipoint), difference(multipoint, linestring), difference(multipoint, multilinestring), difference(multipoint, polygon), difference(multipoint, multipolygon), difference(linestring, point), difference(linestring, multipoint), difference(polygon, point), difference(polygon, multipoint), difference(polygon, linestring), difference(polygon, multilinestring), difference(multilinestring, point), difference(multilinestring, multipoint), difference(multipolygon, point), difference(multipolygon, multipoint), difference(multipolygon, linestring), difference(multipolygon, multilinestring) 2.4 symdifference All the type combinations other than the 4 directly supported polygon/multipolygon combinations. They are implemented using the definition of symdifference: g1 symdifference g2 := (g1 union g2) difference (g1 intersection g2)

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