Star-shaped Polygon
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High Quality Content by WIKIPEDIA articles! A star-shaped polygon (not to be confused with star polygon) is a polygonal region in the plane which is a star domain, i.e., a polygon P is star-shaped, if there exists a point z such that for each point p of P the segment zp lies entirely within P. The set of all points z with the described property is called the kernel of P. Star-shaped polygons are of interest in computational geometry and its applications such as motion planning because of its relation to the notion of visibility: the star-shaped polygon may be informally defined as the one whos...
High Quality Content by WIKIPEDIA articles! A star-shaped polygon (not to be confused with star polygon) is a polygonal region in the plane which is a star domain, i.e., a polygon P is star-shaped, if there exists a point z such that for each point p of P the segment zp lies entirely within P. The set of all points z with the described property is called the kernel of P. Star-shaped polygons are of interest in computational geometry and its applications such as motion planning because of its relation to the notion of visibility: the star-shaped polygon may be informally defined as the one whose whole interior is visible from a single point, assuming that the polygon boundary is not transparent. Convex polygons are star shaped, and a convex polygon coincides with its own kernel. Point-in-polygon queries may be answered in logarithmic time after linear-time preprocessing.
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