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The convex hull of a simple polygon (blue). Its four pockets are shown in yellow; the whole region shaded in either color is the convex hull. In discrete geometry and computational geometry, the convex hull of a simple polygon is the polygon of minimum perimeter that contains a given simple polygon.
Convex hull ( in blue and yellow) of a simple polygon (in blue) The convex hull of a simple polygon encloses the given polygon and is partitioned by it into regions, one of which is the polygon itself. The other regions, bounded by a polygonal chain of the polygon and a single convex hull edge, are called pockets.
The convex hull of a simple polygon is divided by the polygon into pieces, one of which is the polygon itself and the rest are pockets bounded by a piece of the polygon boundary and a single hull edge. Although many algorithms have been published for the problem of constructing the convex hull of a simple polygon, nearly half of them are ...
Sequence of probes around the convex hull of a polygon to determine its diameter using Rotating Caliper method. In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding the width or diameter of a set of points.
Toussaint (1986), who provided an efficient algorithm for the construction of the relative convex hull for finite sets of points inside a simple polygon. [3] With subsequent improvements in the time bounds for two subroutines, finding shortest paths between query points in a polygon, [4] and polygon triangulation, [5] this algorithm takes time (+ (+)) on an input with points in a polygon ...
The convex hull of a simple polygon can also be found in linear time, faster than algorithms for finding convex hulls of points that have not been connected into a polygon. [ 6 ] Constructing a triangulation of a simple polygon can also be performed in linear time, although the algorithm is complicated.
The polygon is the convex hull of its edges. Additional properties of convex polygons include: The intersection of two convex polygons is a convex polygon. A convex polygon may be triangulated in linear time through a fan triangulation, consisting in adding diagonals from one vertex to all other vertices.
Conversely, if the convex hull consists of 7 or fewer vertices, at least one of them must lie within an edge of the hull's minimal enclosing box. [ 4 ] It is also possible to approximate the minimum bounding box volume, to within any constant factor greater than one, in linear time .