 Okay, so now we want to plot some critical points and I'm going to go back to what you've already encountered in the textbook in chapter 7, Applying the Angles to Shadows and Tracking. So let's focus on shadows. The first example that we've got here is the example of a wing wall. The wing wall being an extension out from the side of a building that might be blocking the sun. In the case that we've got in the textbook, we've got a wall that is to the west of the site and so in our case that means that on this plot it's going to be a shadow that's going to be occurring on the west side in the afternoon sun and we'd like to plot when is that shading going to happen on our central point, our point of interest x, in this case x was in the center of a building. So we can imagine that this was a window that we wanted to understand or a central point in the window that we wanted to understand when is it being shaded versus not shaded. And so we did some basic trigonometry in the textbook to give us critical points between the central point x and three other shadowing critical points, a, b, and c. And those points are listed in the textbook and so what I'm going to do right now is just start plotting those out and so we had a, our points in that case listed as zero being the south. And so when I had plus 54 degrees, what I was having is an addition of 54 degrees onto the original 180 degrees, right? And so we're going to end up with some points at the bottom and they're going to go up to our critical point of a, which was zero degrees and altitude angle, excuse me, zero degrees altitude angle and 54 degrees to the west to the afternoon azimuth angle. And then point b was going to be a separate altitude angle upward of 35 degrees. And so let's go to approximately 35 degrees, we'll plot a second point right there. And our third point, so this was point x, a, this point was point x, b. And now we're going to need a third point that's going to be point x relative to the critical point c. And that was going to be 45 degrees up, so we count up 45 degrees and we're going to go up 45 degrees and we need to go into the west in the azimuth 114 degrees, right? So first we add 100 degrees and we're going to get about 114 degrees across to finally get our critical point c right here. And so if I want to connect these guys together, if I want to connect these guys together, first thing I know in an orthographic projection, and I'm just kind of telling you this, is that it's a vertical drop down. So lines connected together vertically will basically just have a vertical line down. The connection for the points here is going to be more like an arc, okay? And so we make sure that we have a nice arc tying these points together and it's going to extend continuously out towards the north. And then I'm going to shade, oops, then I'm going to shade that data in under here. So all of this region is going to be under shadows for our wing wall. So we understand that in December we get shading happening at about four o'clock in the afternoon. So four o'clock solar time, shading happens for the rest of the day. In the, on March 21st, shading is going to happen at about, we're going to say at about 250, right? And by the time we get to the end, the other extreme, the summer solstice of June 21st, that time is going to be about 345. So from 345 on to the end of the day, we're going to have shadowing occurring for this particular point X in the problem. And now if I were to take that same plot and show you what we did inside the textbook, it's going to look just like this. So something very much like what the textbook is just by plotting the points out and connecting those points together.