Preface

1. Sicicly is placed too far South and too much close to North Africa; this implies an unpleasant torrid summer, and in turn this poses severe limitations to agricoltural activities.
2. The Strait of Messina is exaggeratedly narrow, thus posing severe security risks to the navigation of capital ships and supertankers.
   Even worst, from time to time some crazy politician strongly advocates the very stupid idea to build an incredibly costly bridge crossing the Strait, completely overlooking the very high seismical risk of this district and purposely forgetting to remember that in 1908 both towns of Messina and Reggio Calabria were completely destroyed by an earthquake followed by a tsunami.
   More than 100,000 peoples lost their lives, and it was one of the most frightening natural disasters registered in Europe during modern times.

Step #1: translating Sicily into a more convenient position

CREATE TABLE sicilia_1 AS
SELECT cod_reg, 
   ATM_Transform(geometry,
      ATM_CreateTranslate(-150000, 150000)) AS geom
FROM sicilia_0;
SELECT RecoverGeometryColumn('sicilia_1', 'geom', 32632, 'MULTIPOLYGON', 'XY');

• all affine transformation related SQL function names start with an ATM_ prefix: this simply stands for Affine Transformation Matrix.
• ATM_Transform() is very similar to ST_Transform(); the most obvious difference is in that all transformation arguments are now expected to be passed under the form of an appropriate BLOB-serialized Affine Transformation Matrix.
• ATM_CreateTranslate() simply is an SQL function returning a BLOB-serialized Affine Transformation Matrix.
  The BLOB-Matrix will be initialized so to represent a simple 2D Translate accordingly to (tx, ty) arguments.
  You could eventually define a complete 3D Translate by passing (tx, ty, tz) arguments, but this isn't strictly required in our current example.

Step #2: rotating Sicily so to get a nice horizontal alignement

CREATE TABLE sicilia_2 AS
SELECT cod_reg, 
   ATM_Transform(geometry,
      ATM_Translate(-150000, 150000,
         ATM_Translate(cx, cy,
            ATM_Rotate(25,
               ATM_CreateTranslate(-cx, -cy))))) AS geom
FROM (SELECT cod_reg, ST_X(centroid) AS cx, ST_Y(centroid) AS cy, geometry
      FROM (SELECT cod_reg, ST_Centroid(geometry) AS centroid, geometry 
            FROM sicilia_0) AS g1
) AS g2;
SELECT RecoverGeometryColumn('sicilia_2', 'geom', 32632, 'MULTIPOLYGON', 'XY');

• correctly handling Rotation is rather complex. Any rotation will always imply a fixed center point, and by default this is exactly placed at the coordinates origin: (0, 0) (in the 2D case) or (0, 0, 0) (in the 3D case).
• so a very naive attempt to directly invoke ATM_Rotate(25) will simply relocate Sicily in Southern Spain, and this absolutely isn't our intention.
• what we really need is a more complex sequence of chained transformations:
  1. we'll start first by creating a new BLOB-Matix intended to relocate Sicily's centroid exactly on the coordinates origin: ATM_CreateTranslate(-cx, -cy)
  2. now we can safely chain the intended Rotation into the overall transformation stack: ATM_Rotate(25, atm-blob)
  3. after applying the Rotation we now have to relocate Sicily in its initial position: ATM_Translate(cx, cy, atm-blob)
  4. and finally we'll apply the Translation intended to reposition Sicily westwards and nothwards: ATM_Translate(-150000, 150000, atm-blob)
     we've used two separate translations simply for didactic clarity: we could easily merge both them into a single translation:
     ATM_Translate(cx - 150000, cy + 150000, atm-blob)
  5. this way ATM_Transform() will receive the final BLOB-Matrix resulting by chaining all the above transformation steps in the correct sequence.
• Very important notice: Affine Transformations are not commutative: the relative order of subsequent operations in a complex transformation chain should always be very carefully considered.
• all the FROM (SELECT ... FROM (SELECT ...) AS g1) AS g2 stuff simply is a rather trivial SQL trick based on two nested sub-queries.
  it's indented scope simply is avoiding to call too many times ST_Centroid(), ST_X() and ST_Y() in order to get the centroid coordinates.

Step #3: inflating and reshaping Sicily

CREATE TABLE sicilia_3 AS
SELECT cod_reg, 
   ATM_Transform(geometry,
      ATM_Translate(-150000, 150000,
         ATM_Translate(cx, cy,
            ATM_Scale(0.9, 1.3,
               ATM_Rotate(25,
                  ATM_CreateTranslate(-cx, -cy)))))) AS geom
FROM (SELECT cod_reg, ST_X(centroid) AS cx, ST_Y(centroid) AS cy, geometry
      FROM (SELECT cod_reg, ST_Centroid(geometry) AS centroid, geometry 
            FROM sicilia_0) AS g1
) AS g2;
SELECT RecoverGeometryColumn('sicilia_3', 'geom', 32632, 'MULTIPOLYGON', 'XY');

• there is nothing really new in this: we'll simply chain yet another transformation in the appropriate sequence order.
• ATM_Scale(sx, sy) is intended for the simpler 2D case.
• in the more general 3D case you can invoke ATM_Scale(sx, sy, sz)

Step #4: final touch: reflecting Sicily

CREATE TABLE sicilia_2 AS
CREATE TABLE sicilia_4 AS
SELECT cod_reg, 
   ATM_Transform(geometry,
      ATM_Translate(-150000, 150000,
         ATM_Translate(cx, cy,
            ATM_YRoll(180,
               ATM_Scale(0.9, 1.3,
                  ATM_Rotate(25,
                     ATM_CreateTranslate(-cx, -cy))))))) AS geom
FROM (SELECT cod_reg, ST_X(centroid) AS cx, ST_Y(centroid) AS cy, geometry
      FROM (SELECT cod_reg, ST_Centroid(geometry) AS centroid, geometry 
            FROM sicilia_0) AS g1
) AS g2;
SELECT RecoverGeometryColumn('sicilia_4', 'geom', 32632, 'MULTIPOLYGON', 'XY');

• there are several possible rotations supported by Affine Transformation:
  1. ATM_Rotate() always intends a 2D rotation, i.e. a rotation centered around the Z axis
  2. In the more general 3D case there are three possible rotations, one for each axis.
  3. the corresponding SQL functions are: ATM_XRoll(angle), ATM_YRoll(angle) and ATM_ZRoll(angle)
  4. Note: ATM_ZRoll() and ATM_Rotate() simply are two different alias-names for the same identical SQL function.

Final considerations

1. Agriculture: after its relocation Sicily will gain much more agricultural land and will enjoy a more favourable climate: still sunny and warm but much less arid.
   This will certainly start a noticeable development of many economic activities, both direct and indirectly derived.
2. Transportation systems: the suggested new layout for the Lower Tyrrhenian Sea strongly facilitates the development of maritime transports. Sicily could new become the central hub of a highly efficient network of high-speed and high-frequency ferry connections:
   • Palermo will now directly face Naples; Civitavecchia (Rome) seems to be a second obvious terminal for direct connections leading to Central Italy.
   • Messina will acquire a decisive strategic role, and will become the terminal for ferry connections leading to Civitavecchia, Leghorn and Genoa.
   • A less relevant (but anyway interesting) ferry link will join Trapani and Reggio Calabria.
   • Sardinia will strongly benefit from the new layout; Cagliari will be directly connected to Syracuse (or may be Augusta), and Olbia to Messina.
     This means definitely breaking the secular insulation of Sardinia, that will now start enjoying a stronger integration with all others regions of Southern Italy.
   • Last but not least: at a more strategic level it's absolutely obvious that now supertankers and big container ships can freely circumnavigate Sicily in any direction under uncompromised safety conditions.
     All Tyrrhenian harbors will now be directly conneted both to Eastern and Western Mediterranean, and this will surely induce a growth in the volumes of international traffics they could potentially attract.
3. Heavy industry: the new transportation system strongly centered around maritime communications will surely induce an active rebirth of shipyards, a fluorishing traditional excellence of many southern regions in past times but nowadays a perishing and declining industrial branch.
4. Tourism: the suggested new layout will certainly promote a strong development of international tourism.
   It's worth noting that the new layout will give birth to a wonderful island group extending between Sicily to Campania; several of these islands actually are active volcanoes, and this island chain will ideally join Mount Etna and Mount Vesuvius.
   This area could be considered the most impressive volcanic field of Europe and will certainly become a strong touristic attraction.
5. Internal commerce: we can easily forecast a strong growth in volume of internal exchanges thank to the better connectivity based on maritime transports..
   Just a single example: Sardinia should now be able to export its finest sheep-cheese on the Calabrian markets whilst Calabria could freely export its renown red hot chilly peppers to Sardinia, and both regions will widely befit from increased exchange volumes.
6. Practical realization: the present study clearly demonstrates that there are no Mathematics, Geometry or Geography adverse factors potentially forbidding the practical realization of the suggested idea.
   Unhappily the current state of the art in Geology poses many puzzling questions not yet fully resolved in a completely satisfying way.
   Anway we are hopefully expecting that future advancements in Tectonics (and more specifically a deeper comprehension of the micro-plaques mechanics) will surely allow to overcome any remaining issue.

SELECT ATM_Multiply(ATM_CreateRotate(15), 
                    ATM_Multiply(ATM_CreateScale(1.1, 1.2, 1.3), 
                                 ATM_CreateTranslate(10, 20, 30)));

SELECT ATM_Rotate(15, 
          ATM_Scale(1.1, 1.2, 1.3,
             ATM_CreateTranslate(10, 20, 30)));

SELECT ATM_Rotate(15, 
          ATM_Scale(1.1, 1.2, 1.3,
             ATM_Translate(10, 20, 30,
                ATM_Create())));