This command returns true if the two line segments intersect and false if they do not.  It does so using four calls to PointOrientation.

If the intersection option is given and the segments do not intersect false will be returned, otherwise the coordinate of the intersection will be returned.

If one segment is completely contained within the other, the list of endpoints of the smaller segment will be returned.

$\mathrm{with}\left(\mathrm{ComputationalGeometry}\right)\:$

$\mathrm{SegmentsIntersect}\left(\left[\left[0\,0\right]\,\left[1\,1\right]\right]\,\left[\left[0\,1\right]\,\left[1\,0\right]\right]\right)$

$\mathrm{true}$

$L≔\left[\left[1\,0\right]\,\left[1\,5\right]\right]\:$

$K≔\left[\left[\left[1\,-2\right]\,\left[1\,-1\right]\right]\,\left[\left[0\,1\right]\,\left[0\,3\right]\right]\,\left[\left[2\,1\right]\,\left[2\,3\right]\right]\,\left[\left[1\,6.5\right]\,\left[1\,8\right]\right]\,\left[\left[1\,6\right]\,\left[1.5\,8\right]\right]\,\left[\left[0.5\,4\right]\,\left[1.5\,7\right]\right]\,\left[\left[0.5\,0.5\right]\,\left[1\,-0.75\right]\right]\,\left[\left[1\,5\right]\,\left[1.5\,6\right]\right]\,\left[\left[1\,4.5\right]\,\left[1.5\,5\right]\right]\,\left[\left[0.5\,3.75\right]\,\left[1.5\,3.5\right]\right]\,\left[\left[1\,2.5\right]\,\left[1\,3.5\right]\right]\,\left[\left[0.5\,1.5\right]\,\left[1\,2\right]\right]\,\left[\left[1\,0\right]\,\left[1.5\,-2\right]\right]\,\left[\left[1\,0.5\right]\,\left[1\,-0.5\right]\right]\right]\:$

$\mathrm{plots}:-\mathrm{display}\left(\mathrm{plottools}:-\mathrm{line}\left(L\left[\right]\,\mathrm{legend}=''L''\,\mathrm{color}=''Red''\right)\,\mathrm{seq}\left(\mathrm{plottools}:-\mathrm{line}\left(K\left[i\right]\left[\right]\,\mathrm{legend}=''K''\Vert i\,\mathrm{color}=''Blue''\right)\,i=1..7\right)\,\mathrm{seq}\left(\mathrm{plottools}:-\mathrm{line}\left(K\left[i\right]\left[\right]\,\mathrm{legend}=''K''\Vert i\,\mathrm{color}=''Green''\right)\,i=8..14\right)\,\mathrm{axes}=\mathrm{boxed}\right)$

$\left\{\mathrm{seq}\left(\mathrm{SegmentsIntersect}\left(L\,K\left[i\right]\right)\,i=1..7\right)\right\}$

$\left\{\mathrm{false}\right\}$

$\left\{\mathrm{seq}\left(\mathrm{SegmentsIntersect}\left(L\,K\left[i\right]\right)\,i=8..14\right)\right\}$

$\left\{\mathrm{true}\right\}$

$M≔\mathrm{Array}\left(\left[L\left[\right]\,\mathrm{seq}\left(k\left[\right]\,k\mathbf{in}K\right)\right]\,\mathrm{datatype}=\mathrm{float}\left[8\right]\,\mathrm{order}=\mathrm{C\_order}\right)$

$M≔\begin{array}{c}\left[\begin{array}{cc}1.& 0.\\ 1.& 5.\\ 1.& \mathrm{-2.}\\ 1.& \mathrm{-1.}\\ 0.& 1.\\ 0.& 3.\\ 2.& 1.\\ 2.& 3.\\ 1.& 6.50000000000000\\ 1.& 8.\\ ⋮& ⋮\end{array}\right]\\ \hfill \text{30 × 2 Array}\end{array}$

$\mathrm{SegmentsIntersect}\left(M\,\left[1\,2\,3\,4\right]\,\mathrm{intersection}\right)$

$\mathrm{false}$

$\mathrm{SegmentsIntersect}\left(M\,\left[1\,2\,25\,26\right]\,\mathrm{intersection}\right)$

$\left[\begin{array}{cc}1.& 2.\end{array}\right]$

$\mathrm{SegmentsIntersect}\left(M\,\left[1\,2\,23\,24\right]\,\mathrm{intersection}\right)$

$\left[\left[\begin{array}{cc}1.& 2.50000000000000\end{array}\right]\,\left[\begin{array}{cc}1.& 3.50000000000000\end{array}\right]\right]$

$\mathrm{SegmentsIntersect}\left(M\,\left[1\,2\,29\,30\right]\,\mathrm{intersection}\right)$

$\left[\left[\begin{array}{cc}1.& 0.\end{array}\right]\,\left[\begin{array}{cc}1.& 0.500000000000000\end{array}\right]\right]$

The ComputationalGeometry[SegmentsIntersect] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.