Hmwk2 - where d is a constant Show that the convex hull of...

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COT5520 Computational Geometry Homework Assignment # 2 Due: September 15, 2003 1. Change the code of Algorithm FindIntersections (and of the procedures that it calls) such that the working storage is O instead of O . ( ) n ( ) k n + 2. Let S be a set of n triangles in the plane. The boundaries of the triangles are disjoint, but it is possible that a triangle lies completely inside another triangle. Let P be a set of n points in the plane. Give an O algorithm that reports each point in P lying outside all triangles. ( n n log ) 3. Suppose that a doubly connected edge list of a connected subdivision is given. Give pseudocode for an algorithm that lists all faces with vertices that appear on the outer boundary. 4. Let S be a set of N points in the plane with integer coordinates between 1 and N d ,
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Unformatted text preview: , where d is a constant. Show that the convex hull of S can be obtained in linear time. 5. Design an efficient algorithm to solve the following problem: Given n boy robots and n girl robots, whose positions are specified by points in the plane, such that the boy robots are separated from the girl robots by a vertical line. Find a matching of the boys with the girls by straight line-segments so that no two segments intersect. Intuitively, this corresponds to the paths the boys will have to make to pick a girl to go square dancing with. If more than one pair of boys and girls become collinear, their paths may have to overlap, but what will be a gentleman’s etiquette to avoid collision? What is the complexity of your algorithm? (Hint: Use convex Hulls)....
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