The algorithm makes convex partition of a polygon with holes using monotone chains,it includes three stages: the first one decomposes a polygon with holes into ordered monotone chains;the second one divides the original polygon with holes into monotone polygons through combinations and splits of ordered monotone chains;the third one partitions every monotone polygon into convex polygons.

The definition of generalized-trapezoid is by integrating the trapezoid with monotone chain, and the generalized-trapezoidal decomposition algorithm is based on vertex classification and a scan line approach.

The concept of monotone chain in computational geometry is extended at first and used to decompose the inner and outer loops of an arbitrary polygon.

Simple Polygon Distance Algorithm Based on Monotone Chains;

First the algorithm breaks down the connected segments into monotone chains.

Firstly,we should find an optimal direction to minimize the number of monotone chains,then find all the intersection among these monotone chains by extending the Bentley-ottmann s sweep line algorithm.

According to some relative definations, this paper proposed a triangulation of convex hull based on a monotonic chain.

Three methods were used to prepare the single chain particles and pauci chain particles.

Gene cloning and expression of single-chain antibody against Torpedo acetylcholinesterase;