The relationship between a rectangle and a triangle

Abstract

A procedure is developed that decides for given rectangle and triangle whether the triangle is contained in the rectangle, the rectangle is contained in the triangle, the two figures overlap or whether they are disjoint. The procedure uses interval barycentric coordinates, which allow a very transparent description of the test, as well as concise proof of correctness and completeness. The numerical execution needs only a few interval and non-interval arithmetic operations. Representative numerical examples are given for some of the cases. Contrasting this interval approach, a direct approach is considered that requires fewer arithmetic and logical operations. The direct approach has the disadvantage of being logically involved, resulting in a large number of cases that must be distinguished, while being computationally less expensive.