So here is our diagram
This would be a straight overhead shot of my and my neighbor's house. In the picture, up is west, left is south, down is east, right is north. My house is H1, my neighbor's, where my cat liked to hang out, is H2. As the front yard is the primary focus of this mission, the details of the backyards have been left out.
In the diagram, the road is up at the top, and the red boxes indicate houses/unsafe firing directions. There are houses to my west, north, and south, but no houses to the east. Only very thick woods for about half a mile, and then a road.
The brown represents commonly used foot paths. The green represents trees or shrubs, and the yellow represents safe shooting paths, from the position of the pink circles. I have only two safe shooting paths, and the safest is the one on the right, as I would be shooting straight towards woods, with no houses on the left or right. The position on the left has a very narrow safe shooting path, so it would be less than ideal.
Dogs commonly track through the footpath directly to the north of my house, which is directly to the right of H1 in the diagram. The brown dogs I saw yesterday morning were there. Ideally, the target would be in that area, and I would come up from the left side of my house, go up through my front yard and try to get in the position of the pink circle on the right, to take a safe shot, and take out the target.
Of course, things change considerably when one elevates one's self ....