Geometrical design of ornamental stone slabs cutting using the neutral region concept

This paper presents a study of the geometrical design of optimum cutting shapes in granite or marble slabs with the aim of improving cutting operations and reducing tailings in ornamental stone sawshops. To do so, a theory is developed to determine the neutral region of a planar domain using polygonal balls. The neutral region of a planar domain is defined on the basis of geometrical concepts such as the oriented directional distance, the polygonal ball and equidistance with respect to a polygonal ball. Starting out from said neutral region, a polygonal pattern of maximum area may be situated within the polygonal boundary that delimits the ornamental stone. A computational algorithm is implemented to solve this problem is presented, along with some practical examples of cutting granite slabs to validate the theory developed here.

► Geometrical design of optimum cutting shapes in rock slabs.
► Presentation of a theory to calculate the neutral region of a planar domain.
► Classic medial axis problem is a particular case of theory presented.
► Application of the theory to a practical case.