Building elliptical entasis

- So in this movie we'll continue looking at the entasis of the profile curve in our column profile. And to get started we left off in the previous movie where we talked about the standard formula for an ellipse and I have provided that formula here in a text file. And all you have to do is select that formula and copy it with control c to your clipboard and then back here in Revit I'm in a file called "Shaft Profile_Start". And this is where we will continue building our Shaft Profile. So our ellipse needs to start right here at the end of this line and it needs to end up right about here, let me zoom in on that area, it needs to end at this intersection right here between these two reference planes. Now, to make that a little bit clearer, I'm going to just select this reference plane and kind of stretch it out of the way, select this reference plane, stretch it out of the way. So this is the intersection that we need to make sure that our ellipse passes through. That's that x, y point from the diagram. Now how are we going to get there? Well the first thing is let's understand the formulas that are already here in this file. So I'm going to move this out of the way and I'm going to open up Family Types. Now here in Family Types there already are some parameters here obviously and the first one that I'm going to talk about is, let me just make this a little wider so we can actually see what's going on here, the Entasis Total. Now you can see that Entasis Total is taking the Shaft Height and multiplying that by 2/3. So remember we're dividing the overall height into thirds and then that becomes our Entasis Total. However, because we are stopping here and the profile continues up to here, and then there is some additional moldings up here, notice where the dimensions are. So all of this space up in the top needs to be accounted for and thats all these various parameters right there. So what I've done is created a parameter called "Top Minus" and I've just added together all of these parameters over here. The values of all those parameters, it yields 6.5000 and so from the 2/3 of the shaft I'm subtracting the Top Minus. And that gives us this value here which is our Entasis Total or letter y in our formula. Now letters x and b are the two radii. So our Top Radius is taking the Top Diameter divided by 2. Our Base Radius is taking the Base Diameter divided by 2. Now Base Diameter is our standard parameter that we've been using all along. The Top Diameter is down here and in the case of the son capital that works out to be Part Length times 53 which is roughly that 85% of Base Diameter that we discussed. So the only thing that's missing is our Semi Major Axis. Now I've already created the parameter, It's just a simple length parameter, and I've set it to 100 just to start off with but this is where we need to put the formula in. Now if I come in here and I do control v that will paste that formula that we took out of the text file and then when I click somewhere else it'll run the calculation and that ends up being 684 and some change. So let's click OK there. And then the next step is I want to take any one of these reference planes, so I'm going to take this reference plane right here and I'm going to copy it up to about right there. I'll click in the name field and I'll call this "Semi Major Axis". Now I want to add a dimension from here to, and you need to zoom out, to the bottom 2/3 here. So remember that this needs to start right here, right at this location. So this is the Semi Major Axis. The center of the ellipse is going to be right there, so this is going to be half of that. Now I'm going to zoom out so you can see this happen. When you take this dimension and label it with the Semi Major Axis it will move that reference plane up to the top there. So gets up where we need to be and then the next thing we want to do is actually create the ellipse. Now to make this a little bit easier I'm going to select with my control key just the reference planes that I care about and then I'm going to come down to the sunglasses and do Isolate Element. So we want to start here at this intersection and end here with our elliptical arc. And that's the location of our Semi Major Axis. So now I'm going to go to Create, click on Line, and I'll choose the elliptical arc or Partial Ellipse tool. And the way that this works is you draw across one axis and then half of the other axis. So since I've got two points here to snap to I'll go from left over to right to draw my Minor Axis first and now you can see I'm drawing half of the Major Axis. We now where that should be. It should be right up here at the intersection of that reference plane and I'll click. And so you can see that that long thin ellipse now snaps perfectly to that location. Now couple things we want to do here. When you select an ellipse or an elliptical arc two temporary dimensions will appear half of the axes. This temporary dimension right here is showing us the Semi Major Axis, this one's showing the Semi Minor. They both have this "Make temporary dimension permanent". So I'm going to click that and click that. I'll select this dimension and label it with the same parameter, Semi Major Axis. This one I will label with the parameter for the Base Radius. That will make sure that our ellipse flexes properly in order to keep it's shape as the overall column flexes. Now the only thing we still need to do is we don't want a full half ellipse here, we want to do just part of it. So I'm going to select it, click this little grip point right here, drag it up around the top, and then I'll just let go close by that intersection. I'll zoom in and you can already see that the ellipse is passing right through that intersection, let me drag that grip again until it snaps perfectly right there. Then I'm going to go to my align command, align and lock the endpoint, align and lock the endpoint. I'll zoom out, do the same thing at the other end, align, lock the endpoint, and align, and lock the endpoint. And now all that remains is to flex our ellipse. So I will come over here to Family Types, let me reduce the size of this so we can see it, let me make it a little bit larger, so let's try 80, click apply. You can see the ellipse is flexing perfectly. Let's try 45, click apply. It's flexing perfectly and then back to 60. So if you can find the mathematical formula that describes the shape that your looking for all you have to do is translate that formula into a format that Revit understands. And then you can use that to drive the shapes in your geometry, like the elliptical entasis curve that we're using here to define our column shaft.