Intersection points for lines or polygon edges (2024)

[xi,yi] = polyxpoly(x1,y1,x2,y2)

[xi,yi,ii] = polyxpoly(___)

[xi,yi] = polyxpoly(___,'unique')

[xi,yi,ii] = polyxpoly(___) returns a two-column array of line segment indices corresponding to the intersection points. The k-th row of ii indicates which polyline segments give rise to the intersection point xi(k), yi(k).

To remember how these indices work, just think of segments and vertices as fence sections and posts. The i-th fence section connects the i-th post to the (i+1)-th post. In general, letting i and j denote the scalar values comprised by the k-th row of ii, the intersection indicated by that row occurs where the i-th segment of the first polyline intersects the j-th segment of the second polyline. But when an intersection falls precisely on a vertex of the first polyline, then i is the index of that vertex. Likewise with the second polyline and the index j. In the case of an intersection at the i-th vertex of the first line, for example, xi(k) equals x1(i) and yi(k) equals y1(i). In the case of intersections between vertices, i and j can be interpreted as follows: the segment connecting x1(i), y1(i) to x1(i+1), y1(i+1) intersects the segment connecting x2(j), y2(j) to x2(j+1), y2(j+1) at the point xi(k), yi(k).