ST_Tesselate returns TIN geometry. But then I need to use other software to process geometry data and it only accept (multi-)linestrings and (multi-)polygons.
Is there way to convert TIN triangles to multipolygon?
TIN is 2-dimentional, no Z coordinate.
You can use ST_Dump to extract individual TRIANGLE elements from the TIN. Then, you can convert an individual TRIANGLE to a POLYGON using ST_ExteriorRing and ST_MakePolygon. If you then need to combine these polygons into a single MULTIPOLYGON, you could use ST_Collect. Putting that all together would look like this:
WITH test_geom AS (SELECT 'POLYGON (( 10 190, 10 70, 80 70, 80 130, 50 160, 120 160, 120 190, 10 190 ))'::geometry AS geom)
SELECT ST_Collect(geom) AS geom
FROM (
SELECT ST_MakePolygon(ST_ExteriorRing((ST_Dump(ST_Tesselate(geom))).geom)) AS geom
FROM test_geom) sq;
ST_DelaunayTrianglescollects all points and creates convex surface and trianglates it as shown on illustration on that page you provided link to. I don't need creating convex polygon, I just need trianglate existing multipolygons.