intersect

Intersection of shapes in geographic or planar coordinates

Since R2025a

Syntax

shapeout = intersect(shape1)

shapeout = intersect(shape1,shape2)

Description

shapeout = intersect(shape1) calculates the geometric intersection of the specified point, line, or polygon shapes.

• When you specify point shapes, the intersection is a point shape that contains the points in shape1 that overlap.

• When you specify line shapes, the intersection is a line shape that contains the line parts in shape1 that overlap.

• When you specify polygon shapes, the intersection is a polygon shape that contains the polygon regions in shape1 that overlap.

shapeout = intersect(shape1,shape2) calculates element-wise intersections by comparing the shapes in shape1 to the shapes in shape2.

Examples

Calculate Intersection of Shapes

Read a shapefile containing the coordinates of locations in Boston as a geospatial table. The table represents the locations using point shapes in planar coordinates.

GT = readgeotable("boston_placenames.shp");

Create a subtable that contains two table rows. Then, create a vector of polygon shapes by buffering the point shapes.

subGT = geocode(["BEACON HILL","COPPS HILL"],GT);
shape1 = buffer(subGT.Shape,1000)

shape1=2×1 mappolyshape array with properties:
              NumRegions: [2×1 double]
                NumHoles: [2×1 double]
                Geometry: "polygon"
    CoordinateSystemType: "planar"
            ProjectedCRS: [1×1 projcrs]

Calculate the intersection of the polygon shapes. The result is a scalar polygon shape in planar coordinates.

shapeout = intersect(shape1)

shapeout = 
  mappolyshape with properties:

              NumRegions: 1
                NumHoles: 0
                Geometry: "polygon"
    CoordinateSystemType: "planar"
            ProjectedCRS: [1×1 projcrs]

Display the original polygon shapes and the intersection on a map.

figure
geoplot(shape1)
hold on 
geoplot(shapeout)

Calculate Element-Wise Intersections of Shapes

Create two vectors of polygon shapes in geographic coordinates.

• The first vector contains polygon shapes that buffer the cities of Adelaide and Brisbane.

• The second vector contains polygon shapes that buffer the cities of Melbourne and Sydney.

GT1 = geocode(["Adelaide","Brisbane"]);
shape1 = buffer(GT1.Shape,6);

GT2 = geocode(["Melbourne","Sydney"]);
shape2 = buffer(GT2.Shape,3.5);

Calculate the element-wise intersections of the polygon shapes. The result is a two-element vector of polygon shapes.

• The first polygon shape is the intersection of the polygon shapes for Adelaide and Melbourne.

• The second polygon shape is the intersection of the polygon shapes for Brisbane and Sydney.

shapeout = intersect(shape1,shape2)

shapeout=2×1 geopolyshape array with properties:
              NumRegions: [2×1 double]
                NumHoles: [2×1 double]
                Geometry: "polygon"
    CoordinateSystemType: "geographic"
           GeographicCRS: [1×1 geocrs]

Display the original polygon shapes and the intersections on a map. Note that the intersect function did not calculate the intersection of the polygon shapes for Melbourne and Sydney.

figure
geoplot([shape1; shape2])
hold on 
geoplot(shapeout)

Input Arguments

shape1, shape2 — Input shapes

array of geopointshape objects | array of geolineshape objects | array of geopolyshape objects | array of mappointshape objects | array of maplineshape objects | array of mappolyshape objects

Input shapes, specified as one of these options:

• Array of geopointshape objects — Point shapes in geographic coordinates

• Array of geolineshape objects — Line shapes in geographic coordinates

• Array of geopolyshape objects — Polygon shapes in geographic coordinates

• Array of mappointshape objects — Point shapes in planar coordinates

• Array of maplineshape objects — Line shapes in planar coordinates

• Array of mappolyshape objects — Polygon shapes in planar coordinates

If you specify both shape1 and shape2 as input to the intersect function, then shape1 and shape2 must share these characteristics:

• The geometric types of shape1 and shape2 must match. For example, if shape1 is a polygon, then shape2 must also be a polygon. You can find the geometric type of a shape object by querying the Geometry property.

• The coordinate system types of shape1 and shape2 must match. For example, if shape1 is in geographic coordinates, then shape2 must also be in geographic coordinates. You can find the coordinate system type of a shape object by querying the CoordinateSystemType property.

• The coordinate reference systems (CRSs) of shape1 and shape2 must match, unless one of shape1 or shape2 is not associated with a CRS. For a shape object in geographic coordinates, you can find the CRS by querying the GeographicCRS property. For a shape object in planar coordinates, you can find the CRS by querying the ProjectedCRS property.

• The sizes of shape1 and shape2 must be compatible. For more information about compatible array sizes, see Compatible Array Sizes for Basic Operations.

Output Arguments

shapeout — Intersection of shapes

array of geopointshape objects | array of geolineshape objects | array of geopolyshape objects | array of mappointshape objects | array of maplineshape objects | array of mappolyshape objects

Intersection of the shapes, returned as an array of geopointshape, geolineshape, geopolyshape, mappointshape, maplineshape, or mappolyshape objects.

When you specify only shape1, the shapeout argument is a scalar. When you specify both shape1 and shape2, the size of shapeout depends on the sizes of shape1 and shape2. For more information about array sizes, see Compatible Array Sizes for Basic Operations.

The geometric type and coordinate system of shapeout matches the geometric type and coordinate system of the input shape or shapes. For example, if shape1 and shape2 contain maplineshape objects, then shapeout also contains maplineshape objects.

Version History

Introduced in R2025a

R2026a: Improved performance for element-wise intersections

The intersect function shows improved performance for element-wise intersections.

For example, in this code, the call to intersect is about 7.8x faster than in the previous release. The code performs these operations:

• Reads 51 polygons into the workspace.

• Creates 51 areas of interest (AOIs) by buffering a point in each polygon.

• Measures the time required to calculate the element-wise intersections of the polygons and the AOIs.

function t = timingTest
    % Read polygons.
    states = readgeotable("usastatehi.shp");
    shape1 = states.Shape; 

    % Create AOIs.
    points = geopointshape(states.LabelLat,states.LabelLon);
    shape2 = buffer(points,3);

    % Measure time to calculate element-wise intersections.
    shapeout = @() intersect(shape1,shape2');
    t = timeit(shapeout);
end

The approximate execution times are:

• R2025b: 0.39 s

• R2026a: 0.05 s

This code was timed on a Windows^® 11, AMD EPYC™ 74F3 24-Core Processor @ 3.19 GHz test system by calling the function timingTest.