Description

Assume we are given a set S of points in 2D [...] and we would like to have something like "the shape formed by these points". This is quite a vague notion and there are probably many possible interpretations, the α-shape being one of them. Alpha shapes can be used for shape reconstruction from a dense unorganized set of data points. Indeed, an α-shape is demarcated by a frontier, which is a linear approximation of the original shape [1]. [1] F. Bernardini and C. Bajaj. Sampling and reconstructing manifolds using alpha-shapes. Technical Report CSD-TR-97-013, Dept. Comput. Sci., Purdue Univ., West Lafayette, IN, 1997. Source: CGAL ALpha Shapes This function compute the concave hull of a set of geometry, but using CGAL and a different algorithm than ST_ConcaveHull performed by the GEOS module. See : Concave Hulls in JTS

Availability: 3.3.0 - requires SFCGAL >= 1.4.1.

This method needs SFCGAL backend.

Examples

Concave Hull of a MultiPoint (same example As ST_OptimalAlphaShape)

SELECT ST_AsText(ST_AlphaShape('MULTIPOINT((63 84),(76 88),(68 73),(53 18),(91 50),(81 70),
                (88 29),(24 82),(32 51),(37 23),(27 54),(84 19),(75 87),(44 42),(77 67),(90 30),(36 61),(32 65),
                (81 47),(88 58),(68 73),(49 95),(81 60),(87 50),
                (78 16),(79 21),(30 22),(78 43),(26 85),(48 34),(35 35),(36 40),(31 79),(83 29),(27 84),(52 98),(72 95),(85 71),
                (75 84),(75 77),(81 29),(77 73),(41 42),(83 72),(23 36),(89 53),(27 57),(57 97),(27 77),(39 88),(60 81),
                (80 72),(54 32),(55 26),(62 22),(70 20),(76 27),(84 35),(87 42),(82 54),(83 64),(69 86),(60 90),(50 86),(43 80),(36 73),
                (36 68),(40 75),(24 67),(23 60),(26 44),(28 33),(40 32),(43 19),(65 16),(73 16),(38 46),(31 59),(34 86),(45 90),(64 97))'::geometry,80.2));

POLYGON((89 53,91 50,87 42,90 30,88 29,84 19,78 16,73 16,65 16,53 18,43 19,37 23,30 22,28 33,23 36,26 44,27 54,23 60,24 67,
          27 77,24 82,26 85,34 86,39 88,45 90,49 95,52 98,57 97,64 97,72 95,76 88,75 84,83 72,85 71,88 58,89 53))

Concave Hull of a MultiPoint, allowing holes (same example as ST_OptimalAlphaShape)

SELECT ST_AsText(ST_AlphaShape('MULTIPOINT((63 84),(76 88),(68 73),(53 18),(91 50),(81 70),(88 29),(24 82),(32 51),(37 23),(27 54),(84 19),(75 87),(44 42),(77 67),(90 30),(36 61),(32 65),(81 47),(88 58),(68 73),(49 95),(81 60),(87 50),
                (78 16),(79 21),(30 22),(78 43),(26 85),(48 34),(35 35),(36 40),(31 79),(83 29),(27 84),(52 98),(72 95),(85 71),
                (75 84),(75 77),(81 29),(77 73),(41 42),(83 72),(23 36),(89 53),(27 57),(57 97),(27 77),(39 88),(60 81),
                (80 72),(54 32),(55 26),(62 22),(70 20),(76 27),(84 35),(87 42),(82 54),(83 64),(69 86),(60 90),(50 86),(43 80),(36 73),
                (36 68),(40 75),(24 67),(23 60),(26 44),(28 33),(40 32),(43 19),(65 16),(73 16),(38 46),(31 59),(34 86),(45 90),(64 97))'::geometry, 100.1,true))

POLYGON((89 53,91 50,87 42,90 30,88 29,84 19,78 16,73 16,65 16,53 18,43 19,37 23,30 22,28 33,23 36,26 44,27 54,23 60,24 67,27 77,24 82,26 85,34 86,39 88,45 90,49 95,52 98,57 97,64 97,72 95,76 88,75 84,83 72,85 71,88 58,89 53),
              (36 61,36 68,40 75,43 80,50 86,60 81,68 73,77 67,81 60,82 54,81 47,78 43,76 27,62 22,54 32,48 34,44 42,38 46,36 61))

Concave Hull of a MultiPoint, allowing holes (same example as ST_ConcaveHull)

SELECT ST_AlphaShape(
            'MULTIPOINT ((132 64), (114 64), (99 64), (81 64), (63 64), (57 49), (52 36), (46 20), (37 20), (26 20), (32 36), (39 55), (43 69), (50 84), (57 100), (63 118), (68 133), (74 149), (81 164), (88 180), (101 180), (112 180), (119 164), (126 149), (132 131), (139 113), (143 100), (150 84), (157 69), (163 51), (168 36), (174 20), (163 20), (150 20), (143 36), (139 49), (132 64), (99 151), (92 138), (88 124), (81 109), (74 93), (70 82), (83 82), (99 82), (112 82), (126 82), (121 96), (114 109), (110 122), (103 138), (99 151), (34 27), (43 31), (48 44), (46 58), (52 73), (63 73), (61 84), (72 71), (90 69), (101 76), (123 71), (141 62), (166 27), (150 33), (159 36), (146 44), (154 53), (152 62), (146 73), (134 76), (143 82), (141 91), (130 98), (126 104), (132 113), (128 127), (117 122), (112 133), (119 144), (108 147), (119 153), (110 171), (103 164), (92 171), (86 160), (88 142), (79 140), (72 124), (83 131), (79 118), (68 113), (63 102), (68 93), (35 45))'::geometry,102.2, true);

POLYGON((134 80,136 75,130 63,135 45,132 44,126 28,117 24,110 24,98 24,80 27,82 39,72 51,60 48,56 34,52 52,42 50,
                34 54,39 66,40 81,34 90,36 100,40 116,36 123,39 128,51 129,58 132,68 135,74 142,78 147,86 146,96 146,
                108 142,114 132,112 126,112 116,116 110,120 108,125 108,128 106,125 96,132 87,134 80))

See Also

ST_ConcaveHull, ST_OptimalAlphaShape