minkowskiSum

Compute the Minkowski sum of any two polygons or polyshapes, convex or concave.

The Minkowski sum of two polygons

https://en.wikipedia.org/wiki/Minkowski_addition

is simply computed for two convex polygons, but if they may be more general with concavities, the sum is slightly more complex. minkowskiSum will work for any pair of polygons (even self-intersecting polygons), returning a polyshape as a result.

Pa = polyshape([-1 2;0 2;-0.75 2.25;-1 3]);
Pb = polyshape([1 0;2 0;3 1;4 3;2 .3]);
plot(Pa)
hold on
plot(Pb)
MSumShape = minkowskiSum(Pa,Pb)
MSumShape = 
  polyshape with properties:

      Vertices: [8×2 double]
    NumRegions: 1
      NumHoles: 0