ProGuide Relational Operations

Language:      C#
Subject:       Geometry
Contributor:   ArcGIS Pro SDK Team <arcgisprosdk@esri.com>
Organization:  Esri, http://www.esri.com
Date:          04/04/2024
ArcGIS Pro:    3.3
Visual Studio: 2022

This ProGuide shows how the Relate method of the GeometryEngine class can express existing relational operations. In this example, you're expressing the Overlap method by creating a pattern matrix string as described in the Geometry ProConcepts. Imagine polygon geometries in the following configuration:

In this example of testing the relationship between geometries, you're expressing the relationship where A-B evaluates to true and A-C evaluates to false.

Create overlapping geometries

You'll create polygon geometries similar to the configuration in the previous image. The coordinates in this example are in Redlands, California, and WebMercator is the projected coordinate system.

// create polygon A by creating a list of the corner coordinates
List<Coordinate2D> coordinatesPolygonA = new List<Coordinate2D>();
coordinatesPolygonA.Add(new Coordinate2D(-13046461, 4036405)); // top-left coordinate
coordinatesPolygonA.Add(new Coordinate2D(-13046423, 4036405)); // top-right coordinate
coordinatesPolygonA.Add(new Coordinate2D(-13046423, 4036380)); // bottom-right coordinate
coordinatesPolygonA.Add(new Coordinate2D(-13046461, 4036380)); // bottom-left coordinate

Polygon polygonA = PolygonBuilderEx.CreatePolygon(coordinatesPolygonA, SpatialReferences.WebMercator);

// create polygon B by creating a list of the corner coordinates
List<Coordinate2D> coordinatesPolygonB = new List<Coordinate2D>();
coordinatesPolygonB.Add(new Coordinate2D(-13046436, 4036421)); // top-left coordinate
coordinatesPolygonB.Add(new Coordinate2D(-13046410, 4036421)); // top-right coordinate
coordinatesPolygonB.Add(new Coordinate2D(-13046410, 4036395)); // bottom-right coordinate
coordinatesPolygonB.Add(new Coordinate2D(-13046436, 4036395)); // bottom-left coordinate

Polygon polygonB = PolygonBuilderEx.CreatePolygon(coordinatesPolygonB, SpatialReferences.WebMercator);

// create polygon C by creating a list of the corner coordinates
List<Coordinate2D> coordinatesPolygonC = new List<Coordinate2D>();
coordinatesPolygonC.Add(new Coordinate2D(-13046432, 4036372)); // top-left coordinate
coordinatesPolygonC.Add(new Coordinate2D(-13046420, 4036372)); // top-right coordinate
coordinatesPolygonC.Add(new Coordinate2D(-13046420, 4036360)); // bottom-right coordinate
coordinatesPolygonC.Add(new Coordinate2D(-13046432, 4036360)); // bottom-left coordinate

Polygon polygonC = PolygonBuilderEx.CreatePolygon(coordinatesPolygonC, SpatialReferences.WebMercator);

Test the spatial relationship

In the previous image, consider the relationship of interiors, boundaries, and exteriors for the combination of polygon A to polygon B and for polygon A to polygon C. The result should be similar to the following matrix. The union of interiors must be true and the union of the exterior and the interior must evaluate to true.

// test the spatial relationship by considering the following DE-9IM matrix
//       | I(B) | B(B) | E(B)
// ------|------|------|------
//  I(A) |  T   |  *   |  T
// ------|------|------|------
//  B(A) |  *   |  *   |  *
// ------|------|------|------
//  E(A) |  T   |  *   |  *

// returns true, as polygon A and B do overlap
bool doTheyOverlap = GeometryEngine.Instance.Relate(polygonA, polygonB, "T*T***T**");

// returns false, as polygon A and C do not overlap
doTheyOverlap = GeometryEngine.Instance.Relate(polygonA, polygonC, "T*T***T**");