smart guessing optional
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abelvm
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## Pole of inaccessibility (PIA)
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Function to find the [PIA](https://en.wikipedia.org/wiki/Pole_of_inaccessibility) from a given polygon and tolerance, following the quadtree approach by [Vladimir Agafonkin](https://github.com/mourner) described [here](https://github.com/mapbox/polylabel)
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### CDB_PIA (polygon geometry, tolerance numeric DEFAULT 1.0)
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#### Arguments
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| Name | Type | Description |
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|------|------|-------------|
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| polygon | geometry | Target polygon |
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| tolerance | numeric | Threshold to decide to take a cell into account |
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### Returns
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| Column Name | Type | Description |
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|-------------|------|-------------|
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| point | geometry| Pole of inaccessibility |
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#### Example Usage
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```sql
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with a as(
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select st_geomfromtext('POLYGON((-432540.453078056 4949775.20452642,-432329.947920966 4951361.232584,-431245.028163694 4952223.31516671,-429131.071033529 4951768.00415574,-424622.07505895 4952843.13503987,-423688.327170174 4953499.20752423,-424086.294349759 4954968.38274191,-423068.388925945 4954378.63345336,-423387.653225542 4953355.67417084,-420594.869840519 4953781.00230592,-416026.095299382 4951484.06849063,-412483.018546414 4951024.5410983,-410490.399661215 4954502.24032205,-408186.197521284 4956398.91417441,-407627.262358013 4959300.94633864,-406948.770061627 4959874.85407739,-404949.583326472 4959047.74518163,-402570.908447199 4953743.46829807,-400971.358683991 4952193.11680804,-403533.488084088 4949649.89857885,-406335.177028373 4950193.19571096,-407790.456731515 4952391.46015616,-412060.672398345 4950381.2389307,-410716.93482498 4949156.7509561,-408464.162289794 4943912.8940387,-409350.599394983 4942819.84896006,-408087.791091424 4942451.6711778,-407274.045613725 4940572.4807777,-404446.196589102 4939976.71501489,-402422.964843936 4940450.3670813,-401010.654464241 4939054.8061663,-397647.247369412 4940679.80737878,-395658.413346901 4940528.84765185,-395536.852462953 4938829.79565997,-394268.923462818 4938003.7277717,-393388.720249116 4934757.80596815,-392393.301362444 4934326.71675815,-392573.527618037 4932323.40974412,-393464.640141837 4931903.10653605,-393085.597275686 4931094.7353605,-398426.261165985 4929156.87541607,-398261.174361137 4926238.00816416,-394045.059966834 4925765.18668498,-392982.960705174 4926391.81893628,-393090.272694301 4927176.84692181,-391648.240010564 4924626.06386961,-391889.914625075 4923086.14787613,-394345.177314013 4923235.086036,-395550.878718795 4917812.79243978,-399009.463978251 4912927.7157945,-398948.794855767 4911941.91010796,-398092.636652078 4911806.57392519,-401991.601817112 4911722.9204501,-406225.972607907 4914505.47286319,-411104.994569885 4912569.26941163,-412925.513522316 4913030.3608866,-414630.148884835 4914436.69169949,-414207.691417276 4919205.78028405,-418306.141109809 4917994.9580478,-424184.700779621 4918938.12432889,-426816.961458921 4923664.37379373,-420956.324227126 4923381.98014807,-420186.661267781 4924286.48693378,-420943.411166194 4926812.76394433,-419779.45457046 4928527.43466337,-419768.767899344 4930681.94459216,-421911.668097113 4930432.40620397,-423482.386112205 4933451.28047252,-427272.814773717 4934151.56473242,-427144.908678797 4939731.77191996,-428982.125554848 4940522.84445172,-428986.133056516 4942437.17281266,-431237.792396792 4947309.68284815,-432476.889648814 4947791.74800037,-432540.453078056 4949775.20452642))', 3857) as g
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),
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b as (
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select ST_Transform(g, 4326) as g from a
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)
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SELECT st_astext(CDB_PIA(g)) from b;
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```
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## Densify function
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Iterative densification of a set of scattered points using Delaunay triangulation. The new points are located at the centroids of the grid cells and have as assigned value the barycentric average value of the cell's vertex.
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### CDB_Densify(geomin geometry[], colin numeric[], iterations integer)
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#### Arguments
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| Name | Type | Description |
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|------|------|-------------|
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| geomin | geometry[] | Array of points geometries |
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| colin | numeric[] | Array of points' values |
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| iterations | integer | Number of iterations |
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### Returns
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Returns a table object
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| Name | Type | Description |
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|------|------|-------------|
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| geomout | geometry | Geometries of new dataset of points|
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| colout | numeric | Values of points|
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#### Example Usage
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```sql
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with data as (
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select
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ARRAY[7.0,8.0,1.0,2.0,3.0,5.0,6.0,4.0] as colin,
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ARRAY[ST_GeomFromText('POINT(2.1744 41.4036)'),ST_GeomFromText('POINT(2.1228 41.3809)'),ST_GeomFromText('POINT(2.1511 41.3742)'),ST_GeomFromText('POINT(2.1528 41.4136)'),ST_GeomFromText('POINT(2.165 41.3917)'),ST_GeomFromText('POINT(2.1498 41.3713)'),ST_GeomFromText('POINT(2.1533 41.3683)'),ST_GeomFromText('POINT(2.131386 41.413998)')] as geomin
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)
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select CDB_Densify(geomin, colin, 2) from data;
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```
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## TINMAP function
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Generates a fake contour map, in the form of a TIN map, from a set of scattered points.Depends on **CDB_Densify**.
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Its iterative nature lets the user smooth the final result as much as desired, but with a exponential time cost increase.
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### CDB_TINmap(geomin geometry[], colin numeric[], iterations integer)
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#### Arguments
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| Name | Type | Description |
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|------|------|-------------|
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| geomin | geometry[] | Array of points geometries |
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| colin | numeric[] | Array of points' values |
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| iterations | integer | Number of iterations |
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### Returns
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Returns a table object
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| Name | Type | Description |
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|------|------|-------------|
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| geomout | geometry | Geometries of new dataset of polygons|
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| colout | numeric | Values of each cell|
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#### Example Usage
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```sql
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with data as (
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select
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ARRAY[7.0,8.0,1.0,2.0,3.0,5.0,6.0,4.0] as colin,
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ARRAY[ST_GeomFromText('POINT(2.1744 41.4036)'),ST_GeomFromText('POINT(2.1228 41.3809)'),ST_GeomFromText('POINT(2.1511 41.3742)'),ST_GeomFromText('POINT(2.1528 41.4136)'),ST_GeomFromText('POINT(2.165 41.3917)'),ST_GeomFromText('POINT(2.1498 41.3713)'),ST_GeomFromText('POINT(2.1533 41.3683)'),ST_GeomFromText('POINT(2.131386 41.413998)')] as geomin
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)
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select CDB_TINmap(geomin, colin, 2) from data;
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```
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+1
-1
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## Contour maps
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Function to generate a contour map from an scatter dataset of points, using one of three methos:
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Function to generate a contour map from an scatter dataset of points, using one of these three methods:
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* [Nearest neighbor](https://en.wikipedia.org/wiki/Nearest-neighbor_interpolation)
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* [Barycentric](https://en.wikipedia.org/wiki/Barycentric_coordinate_system)
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