Intersection of polyshape objects - MATLAB intersect (2024)

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)

Intersection of polyshape objects - MATLAB intersect (1)

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))

Intersection of polyshape objects - MATLAB intersect (3)

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]);

Intersection of polyshape objects - MATLAB intersect (4)

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 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

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')

Intersection of polyshape objects - MATLAB intersect (5)

Input Arguments

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poly1First input polyshape
scalar | vector | matrix | multidimensional array

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

Data Types: polyshape

poly2Second input polyshape
scalar | vector | matrix | multidimensional array

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

Data Types: polyshape

polyvecpolyshape vector
vector

polyshape vector.

Data Types: polyshape

linesegLine 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)

KeepCollinearPointsKeep 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.

SimplifyModify 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 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

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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See Also

polyshape | xor

MATLAB Command

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Intersection of polyshape objects - MATLAB intersect (6)

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Intersection of polyshape objects - MATLAB intersect (2024)

FAQs

What is the intersection of Polyshapes in Matlab? ›

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.

How to use intersect function in Matlab? ›

C = intersect( A,B ,___,'rows') and C = intersect( A,B ,'rows',___) treat each row of A and each row of B as single entities and return the rows common to both A and B , with no repetitions. You must specify A and B and optionally can specify setOrder .

How do you find the intersection of two rectangles in MATLAB? ›

area = rectint(A,B) returns the area of intersection of the rectangles specified by position vectors A and B . If A and B each specify one rectangle, the output area is a scalar. A and B can also be matrices, where each row is a position vector.

How do you check if two polygons overlap in MATLAB? ›

TF = overlaps( poly1 , poly2 ) returns a logical array whose elements are 1 when the corresponding element pairs of two polyshape arrays with compatible sizes overlap. TF(i,j) is 1 when the ith polyshape in poly1 overlaps the jth polyshape in poly2 .

How do you find where two functions intersect? ›

Here's a step-by-step process:
  • Write down the equations of the two functions, f(x) and g(x).
  • Set the two functions equal to each other: f(x) = g(x).
  • Solve the equation for x. ...
  • For each x-value found in step 3, plug it back into either f(x) or g(x) to find the corresponding y-value.

What happens when two curves intersect? ›

This is their point of intersection. In mathematics, we call the place where two lines or curves meet their point of intersection. The point of intersection of two curves is significant in that it is the point where the two curves take on the same value. This can be useful in a variety of applications.

What is the intersection of two graphs? ›

The Intersection Between Two Graphs. You find the point where the graph of f and the graph of g intersects by solving the equation f ( x ) = g ( x ) .

How do you use intersect? ›

The basic syntax of SQL INTERSECT is quite simple. SELECT column_1, column_2 FROM table_1 INTERSECT SELECT column_1, column_2 FROM table_2; If you want to collate more datasets, simply write the INTERSECT keyword between each SELECT statement. Or use INTERSECT ALL if you want to include duplicates.

What is the area of a Polyshape in Matlab? ›

A = area( polyin ) returns the total area of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape . A = area( polyin , I ) returns the area of the I th boundary of polyin . The area of a hole boundary is negative.

What is the intersect method? ›

The intersect method is a drilling method that uses two drills, each at the far end of the bore path. By means of the intersect method, drilling is done from two sides towards each other. One of the biggest advantages of the intersect method is that you can double the maximum achievable drill length.

How do you find the intersection of two elements? ›

A ∩ B = {x : x ∈ A and x ∈ B}

That means x is an element of A ∩ B, if and only if x is an element of both A and B. Thus, we can use the word “AND” to represent the intersection of sets. Sometimes, the above expression can also be referred to as the intersection of sets formula.

How to find the intersection of two graphs in Matlab? ›

Direct link to this answer
  1. % define x Axis and evaluate functions.
  2. x_points = -5:0.1:5;
  3. function1 = -x+1;
  4. function2 = x+1;
  5. index_intersection = find(function1 == function2);
  6. x_value_intersection = x_points(index_intersection);
  7. y_value_intersection = function1(index_intersection);
  8. % plot functions and intersection point:

How do you find the intersection of two circles in Matlab? ›

[ xout , yout ] = circcirc( centerx1 , centery1 , radius1 , centerx2 , centery2 , radius2 ) finds the intersection of two circles with the specified centers and radii, in Cartesian coordinates.

How do you find the intersection of a circle in MATLAB? ›

[ xout , yout ] = circcirc( centerx1 , centery1 , radius1 , centerx2 , centery2 , radius2 ) finds the intersection of two circles with the specified centers and radii, in Cartesian coordinates.

What is the area of a Polyshape in MATLAB? ›

A = area( polyin ) returns the total area of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape . A = area( polyin , I ) returns the area of the I th boundary of polyin . The area of a hole boundary is negative.

What is intersection variable? ›

Therefore, the intersections variable counts the number of times that each imaginary line is intercepted for the trace of the digit (continues trace that define the digit). Due to we have two imaginary lines, the variable intersections has two values, that is the number of intersections of each line.

How to do intersection stats? ›

We can find the probability of the intersection of two independent events as, P(A∩B) = P(A) × P(B), where, P(A) is the Probability of an event “A” and P(B) = Probability of an event “B” and P(A∩B) is Probability of both independent events “A” and "B" happening together.

References

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