separating bichromatic polylines by fixed-angle minimal triangles

Separation of desired objects from undesired ones is one of the most important issues in the computational geometry. it is tended to cover the desired objects by one or a couple of geometric shapes in a way that all of the desired objects are included by the covering shapes, while the undesired objects are excluded. we study separation of polylines by minimal triangles with a given fixed angle and present o(n log n)-time algorithm, where n is the number of all the desired and undesired polylines. by a minimal triangle, we mean a triangle in which all of its edges are tangential to the convex hull of the desired polylines. the motivation for studying this separation problem stems from that we need to separate bichromatic objects that are modeled by polylines not points in real life scenarios.