Determining the new faces (subpolygons) when vertical lines intersect polygon

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Hi everyone,
If a polygon is inside a rectangle, and a set of vertical parallel lines where each of them pass through one vertex creating new faces.
Is there algorithm to determining the points of the new faces, when a vertical parallel lines cut polygon that lies inside rectangle?

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Image Analyst
Image Analyst 2014-3-22
If you want to do it numerically, sure. Just turn it into an array (an image) and use find() to find the intersections in each column. If you want to do it analytically, then it seems to be a theoretical math or geometry problem - not sure it's a MATLAB problem.
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