intersect

Intersection of polyshape objects

Syntax

polyout = intersect(poly1,poly2)

polyout = intersect(polyvec)

[polyout,shapeID,vertexID] = intersect(poly1,poly2)

[polyout,shapeID,vertexID] = intersect(polyvec)

[in,out] = intersect(poly1,lineseg)

___ = intersect(___,Name=Value)

Description

polyout = intersect(poly1,poly2) returns a polyshape object whose regions are the geometric intersection of two polyshape objects. The intersection contains the regions of poly1 and poly2 that overlap. poly1 and poly2 must have compatible array sizes.

polyout = intersect(polyvec) returns a polyshape object whose regions are the intersection of all the polyshape objects in the vector polyvec. The intersection contains the regions where all the polyshape objects in polyvec overlap.

[polyout,shapeID,vertexID] = intersect(poly1,poly2) also returns vertex mapping information from the vertices in polyout to the vertices in poly1 and poly2. The intersect function only supports this syntax when poly1 and poly2 are scalar polyshape objects.

The shapeID elements identify whether the corresponding vertex in polyout originated in poly1, poly2, or was created from the intersection. vertexID maps the vertices of polyout to the vertices of poly1, poly2, or the intersection.

[polyout,shapeID,vertexID] = intersect(polyvec) returns vertex mapping information from polyout to each element of the vector of polyshape objects polyvec.

[in,out] = intersect(poly1,lineseg) returns the line segments of lineseg that are inside and outside of poly1. The matrix lineseg has two columns. The first column defines the x-coordinates of the line segments and the second column defines the corresponding y-coordinates.

intersect supports this syntax only when poly1 is a scalar polyshape and lineseg contains no self-intersections.

___ = intersect(___,Name=Value) specifies options using one or more name-value arguments in addition to any of the input argument combinations in previous syntaxes. You can use any of the output argument combinations in previous syntaxes. For example, polyout = intersect(poly1,poly2,Simplify=false) returns a polyshape object whose vertices have not been modified regardless of intersections or improper nesting.

Examples

Intersection of Two Polygons

Create and plot two polygons.

poly1 = polyshape([0 0 1 1],[1 0 0 1]);
poly2 = polyshape([0.75 1.25 1.25 0.75],[0.25 0.25 0.75 0.75]);
plot(poly1)
hold on
plot(poly2)

figure

Compute and plot the intersection of poly1 and poly2.

polyout = intersect(poly1,poly2)

polyout = 
  polyshape with properties:

      Vertices: [4×2 double]
    NumRegions: 1
      NumHoles: 0

plot(polyout)
xlim([-0.2 1.4]);
ylim([-0.2 1.2]);

Vector of Polygons

Create a vector containing two polygons.

polyarray1 = polyshape([0 0 1 1],[1 0 0 1]);
polyarray2 = polyshape([0.75 1.25 1.25 0.75],[0.25 0.25 0.75 0.75]);
polyvec = [polyarray1 polyarray2]

polyvec = 
  1×2 polyshape array with properties:

    Vertices
    NumRegions
    NumHoles

plot(polyvec(1))
hold on
plot(polyvec(2))

figure

Compute the intersection of the elements of poly1.

polyout = intersect(polyvec)

polyout = 
  polyshape with properties:

      Vertices: [4×2 double]
    NumRegions: 1
      NumHoles: 0

plot(polyout)
xlim([-0.2 1.4]);
ylim([-0.2 1.2]);

Vertex Mapping

Create two polygons and compute their intersection. Display the vertex coordinates of the intersection and the corresponding vertex mapping information.

poly1 = polyshape([0 0 1 1],[1 0 0 1]);
poly2 = polyshape([0.75 1.25 1.25 0.75],[0.25 0.25 0.75 0.75]);
[polyout,shapeID,vertexID] = intersect(poly1,poly2);

[polyout.Vertices shapeID vertexID]

ans = 4×4

    0.7500    0.2500    2.0000    1.0000
    0.7500    0.7500    2.0000    2.0000
    1.0000    0.7500         0         0
    1.0000    0.2500         0         0

The first two vertices of the intersection originated in poly2, since the corresponding values in shapeID are 2.These vertices are the first and second vertices in the property poly2.Vertices, respectively, since their corresponding values in vertexID are 1 and 2. The last two vertices of polyout were created from the intersection because the corresponding values in shapeID and vertexID are 0.

Intersection of Polygon and Line

Create a rectangular polygon and a line segment.

poly1 = polyshape([0 0 1 1],[1 0 0 1]);
lineseg = [0.5 0.5; 1.5 1.5];

Compute the intersection of the polygon with the line segment, and determine which sections of the line segment are inside or outside of the polygon.

[in,out] = intersect(poly1,lineseg);
plot(poly1)
hold on
plot(in(:,1),in(:,2),'b',out(:,1),out(:,2),'r')
legend('Polygon','Inside','Outside','Location','NorthWest')

Input Arguments

poly1 — First input polyshape

scalar | vector | matrix | multidimensional array

First input polyshape, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: polyshape

poly2 — Second input polyshape

scalar | vector | matrix | multidimensional array

Second input polyshape, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: polyshape

polyvec — polyshape vector

vector

polyshape vector.

Data Types: polyshape

lineseg — Line segment coordinates

two-column matrix

Line segment coordinates, specified as a two-column matrix. The first column defines the x-coordinates of the line segments and the second column defines the y-coordinates. lineseg must have at least two rows and contain no self-intersections.

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: polyout = intersect(poly1,poly2,Simplify=false)

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: polyout = intersect(poly1,poly2,"Simplify",false)

KeepCollinearPoints — Keep collinear points as vertices

true or 1 | false or 0

Keep collinear points as vertices, specified as one of these numeric or logical values:

• 1 (true) — Keep all collinear points as vertices.

• 0 (false) — Remove collinear points so that the output polyshape contains the fewest vertices necessary to define the boundaries.

If you do not specify the KeepCollinearPoints name-value argument, the function assigns its value according to the values used during creation of the input polyshape objects.

• If each input polyshape kept collinear points as vertices during creation, then the function sets KeepCollinearPoints to true.

• If each input polyshape removed collinear points during creation, then the function sets KeepCollinearPoints to false.

• If the collinear points of the input polyshape objects were treated differently, then the function sets KeepCollinearPoints to false.

Simplify — Modify polygon vertices to simplify output

true or 1 (default) | false or 0

Modify polygon vertices to simplify output, specified as one of these numeric or logical values:

• 1 (true) — Modify polygon vertices to produce a well-defined polygon when the output vertices produce intersections or improper nesting.

• 0 (false) — Produce a polygon that may contain intersecting edges, improper nesting, duplicate points, or degeneracies. Computing with ill-defined polygons can lead to inaccurate or unexpected results.

Output Arguments

polyout — Output polyshape

scalar | vector | matrix | multidimensional array

Output polyshape, returned as a scalar, vector, matrix, or multidimensional array.

• If you input two polyshape arguments, then they must have compatible sizes. For example, if two input polyshape vectors have different lengths M and N, then they must have different orientations (one must be a row vector and one must be a column vector). polyout is then M-by-N or N-by-M depending on the orientation of each input vector. For more information on compatible array sizes, see Compatible Array Sizes for Basic Operations.

• If you provide a single input argument polyvec, then polyout is a scalar polyshape object.

shapeID — Shape ID

column vector

Shape ID, returned as a column vector whose elements each represent the origin of a vertex in the intersection.

• The length of shapeID is equal to the number of rows in the Vertices property of the output polyshape.

• The elements of shapeID depend on the number of input arguments:

  • If you provide two input arguments poly1 and poly2, then they must be scalar polyshape objects. The value of an element in shapeID is 0 when the corresponding vertex of the output polyshape was created by the intersection. An element is 1 when the corresponding vertex originated from poly1, and 2 when it originated from poly2.

  • If you provide one input argument polyvec that is a vector of polyshape objects, then shapeID contains the element index of polyvec from which the corresponding output vertex originated. The value of an element is 0 when the corresponding vertex was created by the intersection.

Data Types: double

vertexID — Vertex ID

column vector

Vertex ID, returned as a column vector whose elements map the vertices in the output polyshape to the vertices in the polyshape of origin. The elements of vertexID contain the row numbers of the corresponding vertices in the Vertices property of the input polyshape. An element is 0 when the corresponding vertex of the output polyshape was created by the intersection.

The length of vertexID is equal to the number of rows in the Vertices property of the output polyshape. If you provide two input polyshape objects, then intersect only supports this output argument if they are scalar.

Data Types: double

in — Inside coordinates

two-column matrix

Inside line segment coordinates, returned as a two-column matrix. The first column of in contains the x-coordinates of the line segments inside the input polyshape, and the second column contains the corresponding y-coordinates.

Data Types: double

out — Outside coordinates

two-column matrix

Outside line segment coordinates, returned as a two-column matrix. The first column of out contains the x-coordinates of the line segments outside of the input polyshape, and the second column contains the corresponding y-coordinates.

Data Types: double

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Dynamic memory allocation must be enabled for code generation.

• Name-value pair must be compile time constant.

Thread-Based Environment
Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

Version History

Introduced in R2017b

R2024a: Control whether to simplify output

Specify the Simplify name-value argument to control whether the intersect function simplifies its output. By default, Simplify is true and intersect returns a well-defined polygon by resolving boundary intersections and improper nesting and also by removing duplicate points and degeneracies.

You can specify Simplify=false to gain performance when performing a series of unions or intersections. In this case, you can simplify the output once at the end either by specifying Simplify=true in the final function call or by using the simplify function on the final output polygon.