intersect

Boolean intersection of 3-D geometries

Since R2025a

Syntax

g3 = intersect(g1,g2)

g3 = intersect(gv)

Description

g3 = intersect(g1,g2) returns the overlapping part of the 3-D geometries g1 and g2 as the combined geometry g3.

In R2026a: g3 = intersect(gv) returns the Boolean intersection of all geometries specified by the vector gv. The resulting geometry g3 consists of points that belong to every geometry specified in gv.

Examples

Intersect Cylinder and Cuboid

Find a Boolean intersection of a cylinder and a cuboid.

Create and plot a hollow cylinder geometry.

gcyl = multicylinder([3 4],10,Void=[true,false]);
pdegplot(gcyl,CellLabels="on")

Create and plot a single cuboid geometry.

gcube = multicuboid(sqrt(50),sqrt(50),10);
pdegplot(gcube)

Convert both geometries to fegeometry objects.

gcyl = fegeometry(gcyl);
gcube = fegeometry(gcube);

Find the intersection of the geometries by using the Boolean intersection operation.

g = intersect(gcyl,gcube);

Plot the resulting geometry with cell labels.

pdegplot(g,CellLabels="on",FaceAlpha=0.3)

Intersect Multiple Geometries

Since R2026a

Intersect multiple cubes.

Create a geometry representing a unit cube.

gmcube = fegeometry(multicuboid(1,1,1));

Create a vector of geometries by rotating the cube by 30 and 60 degrees.

angle = [0 30 60];
for k = 1:numel(angle)
    gv(k) = rotate(gmcube,angle(k));
end

Find the intersection of the geometries specified in the vector.

gm = intersect(gv);

Plot the result.

pdegplot(gm)

The resulting geometry has one face wrapped around the side. To create a geometry with multiple faces, first create a triangulation object from the resulting geometry gm.

tr = triangulation(gm);

Convert the triangulation object back to an fegeometry object, and specify a small FeatureAngle value, such as, 15 degrees. The default value is 44 degrees.

gm = fegeometry(tr,FeatureAngle=15);
pdegplot(gm)

Input Arguments

g1 — 3-D geometry

fegeometry object | vector of fegeometry objects

3-D geometry, specified as an fegeometry object or a vector of fegeometry objects.

g2 — 3-D geometry

fegeometry object | vector of fegeometry objects

3-D geometry, specified as an fegeometry object or a vector of fegeometry objects.

gv — 3-D geometries to intersect

vector of fegeometry objects

Since R2026a

3-D geometries to intersect, specified as a vector of fegeometry objects.

Output Arguments

g3 — Combined geometry

fegeometry object

Combined geometry, returned as an fegeometry object.

Limitations

• intersect works only on 3-D geometries. Use decsg to intersect 2-D geometries.

Tips

• When creating a geometry, intersect uses the default threshold of 44 degrees for the dihedral angle between adjacent triangles. If the angle between the triangles exceeds the threshold, the edge becomes a topological (feature) edge separating two faces. If the angle does not exceed the threshold, intersect does not create a topological edge with two separate faces, unless the function can create the edge based on other criteria. Instead, intersect creates one face.

  To use a different feature angle value, create a triangulation object from the resulting geometry g3, and then convert the object back to an fegeometry object. Specify the value of the FeatureAngle argument as a number between 10 and 90. The specified FeatureAngle value represents degrees.

  tr = triangulation(g3);
  g3 = fegeometry(tr,FeatureAngle=15)

  The triangulation function accepts only single-domain geometries, so g3 must have one cell.

Version History

Introduced in R2025a

R2026a: Intersect several geometries

The intersect function accepts one or two vectors of geometries to intersect.