Intersection of polyshape objects
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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
example
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.
example
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.
example
[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.
example
[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
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Intersection of Two Polygons
Open Live Script
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 onplot(poly2)
figure
Compute and plot the intersection of poly1 and poly2.
polyout = intersect(poly1,poly2)
polyout = polyshape with properties: Vertices: [4x2 double] NumRegions: 1 NumHoles: 0
plot(polyout)xlim([-0.2 1.4]);ylim([-0.2 1.2]);
Vector of Polygons
Open Live Script
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 = 1x2 polyshape array with properties: Vertices NumRegions NumHoles
plot(polyvec(1))hold onplot(polyvec(2))
figure
Compute the intersection of the elements of poly1.
polyout = intersect(polyvec)
polyout = polyshape with properties: Vertices: [4x2 double] NumRegions: 1 NumHoles: 0
plot(polyout)xlim([-0.2 1.4]);ylim([-0.2 1.2]);
Vertex Mapping
Open Live Script
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 0The 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
Open Live Script
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 onplot(in(:,1),in(:,2),'b',out(:,1),out(:,2),'r')legend('Polygon','Inside','Outside','Location','NorthWest')
Input Arguments
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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 outputpolyshapecontains 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
polyshapekept collinear points as vertices during creation, then the function setsKeepCollinearPointstotrue.If each input
polyshaperemoved collinear points during creation, then the function setsKeepCollinearPointstofalse.If the collinear points of the input
polyshapeobjects were treated differently, then the function setsKeepCollinearPointstofalse.
Simplify — Modify polygon vertices to simplify output
true or 1 (default) | false or 0
Modify polygon vertices to simplify, 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) — Do not modify output vertices regardless of intersections or improper nesting. Computing with ill-defined polygons can lead to inaccurate or unexpected results.
Output Arguments
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polyout — Output polyshape
scalar | vector | matrix | multidimensional array
Output polyshape, returned as a scalar, vector, matrix, or multidimensional array.
If you input two
polyshapearguments, then they must have compatible sizes. For example, if two inputpolyshapevectors 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).polyoutis 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, thenpolyoutis a scalarpolyshapeobject.
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
shapeIDis equal to the number of rows in theVerticesproperty of the outputpolyshape.The elements of
shapeIDdepend on the number of input arguments:If you provide two input arguments
poly1andpoly2, then they must be scalarpolyshapeobjects. The value of an element inshapeIDis 0 when the corresponding vertex of the outputpolyshapewas created by the intersection. An element is 1 when the corresponding vertex originated frompoly1, and 2 when it originated frompoly2.If you provide one input argument
polyvecthat is a vector ofpolyshapeobjects, thenshapeIDcontains the element index ofpolyvecfrom 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
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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.
See Also
polyshape | xor
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