Before revision: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}}  -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}}  -{\rm Kernel }_{\theta}(P) are maximum or minimum. These results extend previous works by Gewali, Palios, Rawlins, Schuierer, and Wood .
After revision: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}} -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}} -{\rm Kernel }_{\theta}(P) optimizes area or perimeter. Further, we show how the algorithms can be improved when P is a simple orthogonal polygon .