subtract

Difference of two polyshape objects

Syntax

polyout = subtract(poly1,poly2)

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

___ = subtract(poly1,poly2,'KeepCollinearPoints',TF)

Description

polyout = subtract(poly1,poly2) returns a polyshape object whose regions are the geometric difference of two polyshape objects. The output polyout contains the regions of poly1 minus any part of poly2 that overlaps with poly1. The input arguments poly1 and poly2 must have compatible array sizes.

[polyout,shapeID,vertexID] = subtract(poly1,poly2) also returns vertex mapping information from the vertices in polyout to the vertices in poly1 and poly2. The subtract 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 difference. vertexID maps the vertices of polyout to the vertices of poly1, poly2, or the difference.

___ = subtract(poly1,poly2,'KeepCollinearPoints',TF) specifies whether to keep or remove collinear points in polyout for any of the previous syntaxes.

Examples

Difference of Two Polygons

Create and plot two polygons poly1 and poly2 that partially overlap.

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

Subtract poly2 from poly1. The resulting polygon is poly1 minus any part of poly2 that overlaps with poly1.

polyout1 = subtract(poly1,poly2)

polyout1 = 
  polyshape with properties:

      Vertices: [8x2 double]
    NumRegions: 1
      NumHoles: 0

plot(polyout1)

Now subtract the two polygons in the opposite order, that is, subtract poly1 from poly2. The resulting polygon is poly2 minus any part of poly1 that overlaps poly2.

polyout2 = subtract(poly2,poly1)

polyout2 = 
  polyshape with properties:

      Vertices: [4x2 double]
    NumRegions: 1
      NumHoles: 0

plot(polyout2)
xlim([-0.2 1.4]);
ylim([-0.2 1.2]);

Vertex Mapping

Create two polygons, and compute and plot their difference. Display the vertex coordinates of the difference and the corresponding vertex mapping information.

poly1 = polyshape([0 0 1 1],[1 0 0 1]);
poly2 = translate(poly1,[0.5 0.5]);
[polyout,shapeID,vertexID] = subtract(poly1,poly2);
plot(polyout)
axis equal

[polyout.Vertices shapeID vertexID]

ans = 6×4

         0    1.0000    1.0000    1.0000
    0.5000    1.0000         0         0
    0.5000    0.5000    2.0000    4.0000
    1.0000    0.5000         0         0
    1.0000         0    1.0000    3.0000
         0         0    1.0000    4.0000

The first, fifth, and sixth vertices of the difference originated in poly1, since the corresponding values in shapeID are 1. These vertices are the first, third, and fourth vertices in the property poly1.Vertices, respectively, since the corresponding values in vertexID are 1, 3, and 4. Similarly, the third vertex of the difference originated in poly2, and is the fourth vertex in the property poly2.Vertices. The second and fourth vertices of the difference were created from the subtraction computation because the corresponding values of shapeID and vertexID are 0.

Input Arguments

poly1 — First input polyshape

scalar | vector | matrix | multidimensional array

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

poly2 — Second input polyshape

scalar | vector | matrix | multidimensional array

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

TF — Collinear vertices indicator

false | true

Collinear vertices indicator, specified as false or true:

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

• true — Keep all collinear points as vertices.

When the 'KeepCollinearPoints' parameter is not specified, its value is assigned according to the values used when creating the input polyshape objects:

• If the value was true for each input polyshape when they were created, then the value for the output polyshape is set to true.

• If the value was false for each input polyshape when they were created, then the value for the output polyshape is set to false.

• If the values for the input polyshape objects do not match, then the value for the output polyshape is set to false.

Data Types: logical

Output Arguments

polyout — Output polyshape

scalar | vector | matrix | multidimensional array

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

The two input polyshape arguments 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.

shapeID — Shape ID

column vector

Shape ID, returned as a column vector whose elements each represent the origin of the vertex in the difference. The value of an element in shapeID is 0 when the corresponding vertex of the output polyshape was created by the subtraction. An element is 1 when the corresponding vertex originated from poly1, and 2 when it originated from poly2.

The length of shapeID is equal to the number of rows in the Vertices property of the output polyshape. The xor function only supports this output argument if the input polyshape objects are scalar.

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 difference.

The length of vertexID is equal to the number of rows in the Vertices property of the output polyshape. The subtract function only supports this output argument when the input polyshape objects are scalar.

Data Types: double