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Monotonicity Issues and Solutions

As we know, finding a monotonic projection for a polygonal chain or a tree is the same as finding in which direction the polygonal chain or every branch of the tree is monotonic. We are going to give theorems and proofs on the subject and try to explain the complexity of the algorithms used in such a field. All the proofs are not simple but understandable. To make them as clear as possible, we try to illustrate some ideas we got from the paper [1], to give the reader a vision of how things work.

1. Polygonal Chains
2. Trees
3. Simple Polygons

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