I need suggestions for algorithms to choose. In a grid-world, suppose i start at any point and start claiming grid-cells. I want to do this in a way such that i always maintain some convex shape. Imagine there is a 10x10 world with 100 cells of size 1x1. I start at any point in the interior.A trickier variant of this problem is to suppose that i am living in a polygonal shape in this grid-world. And i start on any point on the edge of this polygon, convex or concave, and start claiming cells inside the polygon. How can i now ensure that the area claimed by me is some convex shape at every expansion?I am not able to devise an algorithm on my own and could not find useful resource by browsing. Maybe my choice of keywords are faulty. I assumed i can compute a convex hull and then perform some checks to check convexity of the shape. But i could not figure how. Help would be appreciated.
Growing tree on a grid-world while maintaining convexity
ds.algorithms;cg.comp geom;computational geometry