 * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any  line segment located interior to  simple polygon amid both  vertex insertions and deletions to  simple polygon.
<clarity>  * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any  line segment located interior to  simple polygon amid both  vertex insertions and deletions to  simple polygon.
 * Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon . * Answering weak visibility polygon query corresponding to any line segment located interior to the simple polygon amid both vertex insertions and deletions to simple polygon.