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    GeoRaptor 4.x Update 2 (Project has Stalled)
    Tip: Drop that Spatial Index!
    Convert Single Geometry to Multi-part Geometry in Oracle Spatial
    Optimized Rectangle to 5 Point Polygon
    Centroid Package now supports Y ordinate seeding
    Convert GeoJSON document to Sdo_Geometry objects
    Implementation Of Travelling Salesman Problem
    Create Polygon From Bearings And Distances
    Function That Returns a Compass Point From a Whole Circle Bearing
    Playing around with Centroids by using different seed values
    Simple Oracle C Sprintf or Java String.format
    Some Oriented Point Functions
    Extracting Inner Rings Changed Ordinate Ordering: A Trap For Players Who Don't Read Documentation!
    PLS-00306: wrong number or types of arguments in call to 'SDO_GEOMETRY'
    Converting Google Earth Formatted Longitude/Latitude points to decimal degrees
    Oracle Business Intelligence Warehousing and Analytics - Spatial Summit
    How far inside, is inside? Measuring actual distance.
    Noding and building a polygon from single, overlapping linestrings
    Analyzing Spatial Query Performance Improvements in Oracle Spatial and Graph 12c Through Cross-Vendor Comparison
    ST_VertexN / ST_PointN - Extracting a specific point from any geometry
    Convert Single Point stored in SDO_ORDINATES to SDO_POINT_TYPE
    Aggregate APPEND Islands and XOR polygons
    Circular Arcs in Geodetic Polygons
    Some SDO_GEOMETRY/DIMINFO handling functions
    Applying And Extending Oracle Spatial - Book Released
    Changing all DIMINFO sdo_tolerance values for all metadata records in one go.
    Building Polygons from Incomplete Linestrings using ST_PolygonBuilder
    Computing Cardinal Directions to nearby geometries
    Intersecting two aggregated polygon layers with SC4O
    Spatial and Oracle 12c
    Update Triggers and SDO_GEOMETRY Equality
    Duplicate Geometry data and Data Models
    CENTROID package update
    How to calculate cumulative length of a linestring
    Useful Package of Wrapper Functions for Sdo_Util.AffineTransforms
    Compute Location from known Lat/Long point using delta easting and northing in miles
    SDO_AGGR_SET_UNION
    Sorting SDO_GEOMETRY data using the ORDER BY clause of a SELECT statement
    Creating linestrings from points
    Rounding Coordinates or Ordinates in SDO_GEOMETRY
    Effects of Sdo_Geometry Ordinate Precision on Performance
    Effects of Sdo_Geometry Ordinate Precision on Storage
    The Spatial filtering of geometries: The effect of tolerances on relationships
    Application of Delaunay Triangulation and Inverse Distance Weighting (IDW) in Oracle for Soils Interpolation
    Selecting all SDO_GTYPE values for all tables/sdo_geometry columns in a schema
    CENTROID package - Tips for Use
    Announcing the Spatial Companion For Oracle (SC4O)
    Filtering Rings (Oracle Spatial)
    Splitting a polygon using one or more linestrings
    isValid, isSimple, Dimension and CoordDim methods for SDO_Geometry
    Line Merging or Collecting lines together: ST_LineMerger
    ST_DeleteVertex for Oracle SDO_Geometry based on Jaspa/JTS
    3D/4D and SRID aware Conversion functions for SDO_Geometry: WKT and EWKT
    Topological vs Non-Topological Simplification/Generalization of Aggregated Area Geometies in Oracle
    Filtering very short linestrings via bitmap function index
    CENTROID For Oracle
    Gridding a sdo_geometry line/polygon object (Oracle)
    Finding centre and radius of a circular geometry
    Constraining geometry type for sdo_geometry column in a table.
    CASE Statements and SDO_GEOMETRY
    The Power of Constraints and Indexes for Spatial Constraints: stopping duplicate points
    Replacement for SDO_GEOM.RELATE - ST_Relate based on JTS
    Changing Oracle Spatial Index Parameters on existing index
    Writing Excel Spreadsheets files from within the Oracle database using Java and PL/SQL
    Writing xSV (eg csv) files from within the Oracle database using Java and PL/SQL
    A simple spike finder for Spatial/Locator
    JTS Java class compilation for 11g and above
    Random Spatial Search Procedure
    Geometry Snapping using JTS in Oracle
    Exposing JTS's MinimumBoundingCircle functionality
    Exposing JTS's Densifier functionality
    Using JTS's Comparison Functions - HausdorffSimilarityMeasure & AreaSimilarityMeasure with SDO_GEOMETRY
    Free JTS-based Area/Length Functions
    Handy way of systematically fixing polygon geometries with 13349 and other errors
    Standalone CENTROID package now available for download
    Free Union, Intersection, Xor and Difference Functions for Oracle Locator - Part 4 Processing Geodetic data
    Configurable Buffer: JTS and Oracle
    Free Union, Intersection, Xor and Difference Functions for Oracle Locator - Part 3
    Free Union, Intersection, Xor and Difference Functions for Oracle Locator - Part 2
    Free Union, Intersection, Xor and Difference Functions for Oracle Locator - Part 1
    Building Lines into Polygons in Oracle Locator / Spatial
    Finding Intersection Points between Line and Polygon
    SDO2GeoJSON
    Free version of sdo_length
    Alternative to my SQL based GetNumRings function
    External Tables and SDO_Geometry data.
    layer_gtype keyword issue when indexing linear data on 11g
    String Tokenizer for Oracle
    Free Aggregate Method for Concatenating 2D Lines in Oracle Locator 10g
    Reducing 5 Vertex Polygon to Optimized Rectangle
    Square Buffer
    Converting decimal seconds to string
    SDO_GEOM.VALIDATE_GEOMETRY_WITH_CONTEXT - 13356 Issues
    Valid conversion unit values for Oracle sdo_geom.sdo_length()
    Removing Steps in Gridded Vector Data - SmoothGrid for Oracle
    Oracle Spatial DISJOINT search/filtering
    Creating SDO_Geometry from geometric data recorded in the columns of a table
    Concave Hull Geometries in Oracle 11gR2
    Projecting SDO_GEOM_METADATA DIMINFO XY ordinates
    Instantiating MDSYS.VERTEX_TYPE
    New PL/SQL Packages - Rotate oriented point
    GeoRaptor Development Team
    Fast Refreshing Materialized View Containing SDO_GEOMETRY and SDO_GEOM.SDO_AREA function
    Performance of PL/SQL Functions using SQL vs Pure Code
    Implementing the BEST VicGrid Projection in Oracle 10gR2
    Making Sdo Geometry Metadata Update Generic Code
    ORA-13011 errors when using SDO_GEOM.VALIDATE_LAYER_WITH_CONTEXT()
    Extract Polygons from Compound Polygon
    Detecting sdo_geometries with compound (3-point Arcs) segments
    GEOMETRY_COLUMNS for Oracle Spatial
    Convert GML to SDO_Geometry in Oracle 10gR2
    Spatial Sorting of Data via Morton Key
    Swapping Ordinates in an SDO_GEOMETRY object
    New To_3D Function
    Extend (Reduce/Contract/Skrink) Function for Oracle
    Loading and Processing GPX 1.1 files using Oracle XMLDB
    Loading Spatial Data from an external CSV file in Oracle
    Calling the Oracle Spatial shapefile loader from within the Oracle database itself
    Implementing SDO_VertexUpdate/ST_VertexUpdate for Oracle
    Implementing SDO_RemovePoint/ST_RemovePoint for Oracle
    Implementing SDO_AddPoint/ST_AddPoint for Oracle
    ESRI ArcSDE Exverted and Inverted Polygons and Oracle Spatial
    Funky Fix Ordinates By Formula
    Implementing a SetPoint/ST_SetPoint function in Oracle
    Implementing an ST_SnapToGrid (PostGIS) function for Oracle Spatial
    Generating random point data
    Implementing an Affine/ST_Affine function for Oracle Spatial
    Implementing a Scale/ST_Scale function for Oracle Spatial
    Implementing a Parallel/ST_Parallel function for linestring data for Oracle Spatial
    Implementing a Rotate/ST_Rotate function for Oracle Spatial
    Limiting table list returned when connecting to Oracle Database using ODBC
    ST_Azimuth for Oracle: AKA Cogo.Bearing
    Implementing a Translate/ST_Translate/Move function for Oracle Spatial
    Elem_Info_Array Processing: An alternative to SDO_UTIL.GetNumRings and querying SDO_ELEM_INFO itself
    Minumum Bounding Rectangle (MBR) Object Type for Oracle
    How to extract elements from the result of an sdo_intersection of two polygons.
    How to restart a database after failed parameter change
    Fixing failed spatial indexes after import using data pump
    generate_series: an Oracle implementation in light of SQL Design Patterns
    Multi-Centroid Shootout
    Oracle Spatial Centroid Shootout
    On the use of ROLLUP in Oracle SELECT statements
    Surrounding Parcels
    Spatial Pipelining
    Using Oracle's SDO_NN Operator - Some examples
    Converting distances and units of measure in Oracle Locator
    Split Sdo_Geometry Linestring at a known point
    Forcing an Sdo_Geometry object to contain only points, lines or areas
    Unpacking USER_SDO_GEOM_METADATA's DIMINFO structure using SQL
    Generating multi-points from single point records in Oracle Spatial
    Object Tables of Sdo_Geometry
    Oracle Locator vs Oracle Spatial: A Reflection on Oracle Licensing of the SDO_GEOM Package
    FAST REFRESHing of Oracle Materialized Views containing Sdo_Geometry columns
    Australian MGA/AMG Zone Calculation from geographic (longitude/latitude) data
    Loading Shapefiles (SHP) into Oracle Spatial
    Oracle Spatial Mapping and Map Rendering Performance Tips
    The significance of sdo_lb/sdo_ub in USER_SDO_GEOM_METDATA: Do I need it?
    Oracle Spatial Forum - Melbourne April 2007
    Layer_GTypes for spatial indexes
    Oracle's SQL/MM Compliant Types
    Tips and Tricks

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All Blog Articles, Data Models and Free Source Code by Simon Greener, The SpatialDB Advisor is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.

Multi-Centroid Shootout

Wednesday November 05 2008 at 01:00

(WARNING: I have completely re-written my centroid code since this article when I discovered that the algorithm I had been supplied by a Tino failed in one important case. Instead of fixing the existing algorithm I completely re-wrote it and have also added support for polygons and mutil-point geometries. I will edit all centroid related articles some time soon.)

This blog follows on from the first “Centroid Shoot Out” and the comment left by Andy. It covers two issues. Firstly it publishes the original centroid code written by Tino Delbourgo when he worked for a company based in Hobart, Tasmania called Geometry Pty Ltd ; secondly, it shows how the PL/SQL version of the Java code handles holes in polygons, multi-part polygons and the generation of multi-point centroids.

Original Java Code.

The original Java code is:

private static void calcParaCentroid(Geometry geometry, Double centroidX, Double centroidY)
{
   Enumeration segs = ((Polygon)geometry).getAllSegments();
   int segCount = 0;
   Envelope envp = geometry.getEnvelope();
   // Go half-way along bottom edge of bounding box to get our candidate point (x,y)
   double x = (envp.getMinX()+envp.getMaxX())/2.0;
   double y = envp.getMinY();
   // Go through each line segment in turn, working out crossing points from the
   // half-way along the bottom edge of the bounding box in a line due north.
   // We only need to keep the lowest and second lowest of these points.
   double lowestCrossing = 0.0;
   double secondLowestCrossing = 0.0;
   while (segs.hasMoreElements()) {
      segCount++;
      if (debugPinP)
         System.out.println("Considering polygon segment #"+segCount);
      LinearSegment seg = (LinearSegment)segs.nextElement();
      double coords[] = seg.getCoordArray();
      double x1 = coords[0];
      double y1 = coords[1];
      double x2 = 0.0;
      double y2 = 0.0;
      for (int i=2; i<coords.length; i+=2) {
         double ycrossing = 0.0;
         x2 = coords[i];
         y2 = coords[i+1];
         if (debugPinP)
            System.out.println("   Considering line segment: ("+x1+","+y1+") to ("+x2+","+y2+")");
         if ((x1<x && x2<x) || (x1>x && x2>x) || (y1<y && y2<y)) {
            // do nothing - segment is either wholly to left, to right or below our point
         } else if (y1>=y && y2>=y) {
            // the line segment is above our point with one end to the left and the other to the right
            // - this is a definite crossing
            if ((x1<=x && x<=x2) || (x2<=x && x<=x1))
               ycrossing = y1+((y2-y1)/(x2-x1))*(x-x1);
         } else if (x1==x && x2==x) {
            // do nothing - we are comparing with a vertical line (no crossing possible)
         } else if (y1==y && y2==y) {
            // we are dealing with a horizontal line going through our point - a definite crossing
            ycrossing = y;
         } else {
            // we are dealing with a line above our point with our point being within the line's bounding box
            // - we need to project up to the line to see if it crosses
            double ytest = y1+((y2-y1)/(x2-x1))*(x-x1);
            if (ytest>y)
               ycrossing = ytest;
         }

         // If it crosses, then see if it is the crossing with the lowest or second lowest y-value
         if (ycrossing!=0.0) {
          if ( ycrossing  lowestCrossing ) {
            lowestCrossing = ycrossing;
            } else if ( ycrossing  secondLowestCrossing ) {
              secondLowestCrossing = ycrossing;
	       } else if (lowestCrossing==0.0 || 
                  ycrossing <  lowestCrossing) {
              secondLowestCrossing = lowestCrossing;
              lowestCrossing = ycrossing;
            } else if (secondLowestCrossing==0.0 || 
                       ycrossing < secondLowestCrossing) {
               secondLowestCrossing = ycrossing;
            }
         }
         // Go round the loop again with next segment
         x1 = x2;
         y1 = y2;
      }
   }
   if (secondLowestCrossing==0.0 || lowestCrossing==0.0)
      throw new RuntimeException("Para-centroid calculation failed, couldn't find two crossing points up from centre bottom edge of bounding box");
   centroidX = new Double(x);
   centroidY = new Double((lowestCrossing+secondLowestCrossing)/2.0);
}

You will note that the code requires some functions in the old sdoapi.jar from 9i (the api was changed with the 10g release). The function it needs from this jar file is one that “vectorizes” an sdo_geometry polygon into simple start/end 2 point linestrings (or vectors): getAllSegments().

I have looked at deploying this code inside the Oracle database JVM with PL/SQL wrappers. It is possible but because the sdoapi.jar file is deprecated I decided the only long term solution was to use the Java Topology Suite and to build a vectorisation function using it. I have not time to do this. There are also other issues such as the conversion of Sdo_Geometry/JGeometry to JTS via GeoTools (I think that the current converter does not support circular arcs).

When I converted the Java to PL/SQL, I had to build my own vectoriser (see my article on spatial pipelining). I also added in support for rectangles, circles and compound linestrings/polygons with three point circular arcs. I added the ability to choose the largest part of a multi-part geometry object (SdoGType x007). All these could be added to the Java code but have not been done. In creating the PL/SQL version I found a few centroid use cases that the original Java code didn’t implement. I have added these to the PL/SQL version (compiled and tested) and the Java version (never compiled or tested).

Multi-Part Polygons: Single Centroid

As indicated in the previous paragraph the PL/SQL implementation supports generating a centroid for multi-part polygons (SDO_GTYPE = x007). The method I use is simple: firstly, choose the largest part; secondly, generate the centroid as normal. The algorithm used gets the minimum bounding rectangle of each outer shell and selects the largest. Of course, this may still not be correct as in certain situations area would be better. Perhaps one day I will add this in.

Multi-Part Polygons: Multiple Centroids

The PL/SQL version has support for generating a multi-point sdo_geometry (SDO_GTYPE = x005) holding the centroid of each and every outer shell (EType 1003) of a multi-part polygon (Sdo_Gtype x007). The algorithm simple extracts each outer shell as a single (2003) polygon and passes it to the standard centroid function: each centroid created is appended to a multi-point sdo_geometry object. Once all parts have been processed the resultant multi-point geometry is returned.

Holes

There is little that I can say other than the code will never put a centroid into any of the holes (SDO_GTYPE = 2003) of any part of a polygon of any type.

Data and Diagram

Putting it all together. I have created a single, complex, multi-part polygon (SDO_GTYPE = 2007) object (see below). For this polygon I have generated a centroid from the standard Oracle function sdo_geom.sdo_centroid, my own geom.sdo_centroid function and finally I have generated a single multi-point geometry via my geom.sdo_multi_centroid function.

codesys@XE> CREATE TABLE MultiCentroidShootOut AS
SELECT 
SDO_GEOMETRY(2007, 28355, NULL, 
SDO_ELEM_INFO_ARRAY(
 1, 1003, 1, 
25, 2003, 1, 
35, 2003, 1, 
45, 2003, 1, 
63, 1003, 1, 
87, 1003, 1, 
99, 1003, 1), 
SDO_ORDINATE_ARRAY(
17.0158371, -492.10068, 
60.6568627, -602.4868, 
186.445701, -612.75528, 
378.979638, -712.87293, 
740.943439, -712.87293, 
669.064103, -515.20475, 
835.926848, -284.16403, 
879.567873, -140.40535, 
645.96003, 16.188914, 
299.398944, 13.6217949, 
76.0595777, -171.21078, 
17.0158371, -492.10068, 
386.680995, -576.81561, 
396.949472, -366.31184, 
602.319005, -489.53356, 
566.379336, -651.26207, 
386.680995, -576.81561, 
91.4622926, -474.13084, 
168.475867, -399.68439, 
307.100302, -481.8322, 
181.311463, -558.84578, 
91.4622926, -474.13084, 
176.177225, -209.71757, 
299.398944, -86.495852, 
561.245098, -30.019231, 
692.168175, -94.19721, 
789.718703, -171.21078, 
633.124434, -340.64065, 
376.412519, -255.92572, 
214.684012, -361.1776, 
176.177225, -209.71757, 
69, 9.5, 
206, 86.5, 
397, 185.5, 
553, 189.5, 
698, 143.5, 
920, -7.5, 
853, 105.5, 
704, 259.5, 
537, 307.5, 
403, 271.5, 
183, 134.5, 
69, 9.5, 
412.352187, -158.37519, 
468.828808, -225.12029, 
592.050528, -237.95588, 
661.362745, -202.01621, 
568.946456, -89.062971, 
412.352187, -158.37519, 
886, -424.5, 
999, -357.5, 
1153, -208.5, 
1201, -41.5, 
1165, 92.5, 
1028, 312.5, 
903, 426.5, 
980, 289.5, 
1079, 98.5, 
1083, -57.5, 
1037, -202.5, 
886, -424.5)) as geom
from dual;

codesys@XE> select sdo_geom.sdo_centroid(geom,0.05) from MultiCentroidShootout;
SDO_GEOM.SDO_CENTROID(GEOM,0.05)(SDO_GTYPE, SDO_SRID, SDO_POINT(X, Y, Z), SDO_ELEM_INFO, SDO_ORDINATES)
-----------------------------------------------------------------------------------------------------------------------------------
SDO_GEOMETRY(2001, 28355, SDO_POINT_TYPE(545.679984, -227.04292, NULL), NULL, NULL)

codesys@XE> select geom.sdo_centroid(geom,0.05) from MultiCentroidShootout;
GEOM.SDO_CENTROID(GEOM,0.05)(SDO_GTYPE, SDO_SRID, SDO_POINT(X, Y, Z), SDO_ELEM_INFO, SDO_ORDINATES)
-----------------------------------------------------------------------------------------------------------------------------------
SDO_GEOMETRY(2001, 28355, SDO_POINT_TYPE(448.3, -657.6, NULL), NULL, NULL)

codesys@XE> select geom.sdo_multi_centroid(geom,0.05) from MultiCentroidShootout;
GEOM.SDO_MULTI_CENTROID(GEOM,0.05)(SDO_GTYPE, SDO_SRID, SDO_POINT(X, Y, Z), SDO_ELEM_INFO, SDO_ORDINATES)
-----------------------------------------------------------------------------------------------------------------------------------
SDO_GEOMETRY(2005, 28355, NULL, SDO_ELEM_INFO_ARRAY(1, 1, 4), SDO_ORDINATE_ARRAY(448.3, -657.6, 494.5, 242.1, 536.9, -167.8, 1043.5, -248.2))

Hope all this helps in understanding how the centroid functions in my PL/SQL packages work.

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