Taming Parametric Curved Geometry in Revit Family Editor

PAUL F. AUBIN: Welcome to Taming Parametric Curved Geometry in the Revit Family Editor. My name is Paul Aubin. And I'm happy to be here with you today.

Just briefly a little bit about me-- I am an author and consultant with an architectural background going back 20-some, 30 years. I'm also a proud husband and father of three adult children who are beginning their careers around the country, even as we speak.

As far as authoring goes, my two most recent books are these-- Revit Essentials for Architecture, which assumes no prior background to Revit and starts you at the beginning and is a tutorial manual 100% through two projects, two about early CDs, and then my deep dive into the Revit Family Editor, which is a little bit older a book. It's been around since 2014 release, but still pertinent because a lot of the Family Editor content is still valid. And so if you're interested in either of those books, you can learn more on my website.

The reason I mention Renaissance Revit in particular is a lot of today's content is actually drawn from that book. Chapter 4 in particular is where I talk about taming parametric curved geometry. So it's a good follow up if you're interested.

Also, if you're thinking, boy, this guy's voice sounds really familiar and I can't quite place it, perhaps you've seen some of my LinkedIn Learning videos. I've got lots of Revit content there. So feel free to look up my name there and check it out, including some of today's content, of course, on curved geometry.

Now, the handout for this session and an accompanying data set is provided. You can find it on the Autodesk website. But you can also find it at my website. So here's a QR code to my website or just simply wherever you found this recording. There should be some links accompanying it where you can download a ZIP file with the sample Revit files that I'll be working through in this session, as well as the PDF handout, which I did structure as a step-by-step handout. So even though I'll be going through the material relatively quickly on my end here in this presentation, you'll be able to do it at your own pace if you follow along in the handout later on after the session.

So parametric curvature-- just what are we trying to solve here? Well, let's talk about that a little bit. Suppose you had a curve in Revit. Now, the act of drawing the curves are not difficult. You can just draw arcs or circles or ellipses or even splines. There's a number of different curved forms that are supported.

Well, that's not the difficult part. If you're working in the Family Editor and you want that curvature to flex or reshape in some way and you want to be able to control that reshaping or flexing behavior, well, in that case, you could end up with some weird behavior like this, where the curves misbehave and you end up with these kinks or these little strange areas. That's what we're talking about when I say taming parametric curves. I want to give you some tools that you can use in your own family content to be able to control that behavior so that it stays smooth and continuous and gives you desired results.

So in line with everything that we're trying to accomplish, let me just talk about what I'm assuming from you. I am assuming that you have some background in the traditional Family Editor. Now, it's not absolutely required. If you're a complete novice when it comes to creating family content, you're still welcome to watch this course, of course. But some of the material might be a touch more advanced for you.

I'm assuming you're familiar with reference planes, dimensions, and parameters. These are the basic bones and muscle/skin analogy that we talk about in the Family Editor. And it's what drives the geometry, makes everything work. So I'm assuming you've seen that or at least heard of that before.

Obviously, I'm assuming that you've got some basic knowledge of solid and void forms, which we have in the Family Editor. And even though everything that I'm going to show you would be able to be used in the Conceptual Massing Environment, just for simplicity's sake for today, I'm not going to be covering the Conceptual Massing Environment. But again, all of the stuff that I will share with you would apply there. But there are several other additional techniques that I'm not going to be getting into as well.

So I'm mainly focused on the tools that you see over there on the right-hand side of my slide, just basic arcs and elliptical shapes that you can draw in the traditional Family Editor. And of course, the most important assumption I'm making is that you want your curves to flex in a predictable way. So that is the assumptions going in. And with that, let's switch over to Revit.

So here I am in Revit. And I'm just going to cancel this for a minute. This is that form that I showed you at the start in the slide. And I want to just show you this thing is based on a multiplier here. And I want to just show you how it would misbehave horribly if I don't have the curves constrained properly. So again, just to remind you of what we're trying to solve here, all of the examples that we're going to look at here this afternoon are going to address that issue.

So let's go ahead and get started here. And I'm going to open up my first starter file. This is just what I'm calling a seed file. It is a family file that I've started already. I added some basic reference planes for the right and the left and the front and the back. And I added this simple extrusion right here.

Now, I've also got a width and a depth parameter. So if we were to flex either of those parameters, of course, the size of that box would adjust. And let me just Control-Z to undo that.

What I'm going to do is take this box, edit the extrusion, remove the straight lines, and let's start with the simplest curve form of all. And that is a circle. So I'm going to draw a circle. Start right here at the center. Pull it out to here. And I'm going to finish that. And of course, the trouble with that is that simply drawing a circle and snapping to reference planes does not constrain that circle in any way. So it's not going to force that circle to flex when we do that.

So let me undo that and re-edit this. How would we go about flexing this circle? Well, even something as simple as a circle-- we're already running into the first time when we have to break one of the rules of the Family Editor. So if you've done any work in the Family Editor, you know there's this so-called bones, muscle, skin analogy. So you start with the reference planes. You add dimensions to those reference planes to make them flexible and adjustable. And then you pin the geometry to that armature, that framework, of reference planes so that when the reference planes move the bones, it takes the skin, the muscles and the skin, with it. So that's the idea that we want.

Well, that's the general rule of thumb. But like all rules, we sometimes need to break those rules. We need to make exceptions in order to get the behavior we want. And curvature is usually one of the places where we have to start thinking about an alternative approach and breaking some of those rules.

So if I select this circle, a temporary dimension appears here for the radius. And there's the "Make this temporary permanent." I'm going to click that. And now if I click away from it, I have this dimension here. But of course, this dimension is breaking the rule because it's dimensioning directly to the geometry rather than the reference planes. But you can't have a curved reference plane. So that's the problem here.

So I'm going to take this dimension. And I'm going to label it with a new parameter that I'm going to call "Radius." And then I will click OK. And then I will simply finish this. And now, of course, I could flex the radius. And it will adjust the shape of that geometry.

Now, of course, it's not changing the width or the depth. So if you want to tie all that together, then some simple formulas will do the trick. So in the case of a circle, you probably want width to equal depth. So we can do that. And then, of course, I could make either one of those tied to the radius.

Now, of course, the radius is half of the width or the depth. So I could do something like width divided by 2. And then let's apply that just to make sure. It's telling me I've got instance parameters here. So that's one thing I forgot-- is that my radius needs to be an instance parameter in order for a formula to work. Now I can apply it just fine. And I'll change the radius. I'll click OK. And now you're going to see that the circle will change to double the size. And the width and the depth will adjust along with it.

So-- pretty simple example. But it actually already covers some of the fundamental basics that we need to know about flexing curved geometry-- is that you have to think a little differently about how you apply the rules.

Now, I'm going to delete this circle. And in its place, I'm going to do an ellipse. And an ellipse is, admittedly, slightly more complex than a circle. Now, initially, it looks exactly like a circle. Now, it's offering me these two dimensions right here and here. So I'm going to go ahead and take advantage of that. And then instead of "Radius," I'm going to label this one just simply "Y." And let me go ahead and make that an instance this time. And then this one I'm going to label. And I'll simply call that "X" and also make that instance.

Now, what I've done is basically given two radii to this ellipse. But now we need to do a little bit of work here in the family types. I no longer want the depth and the width to be equal to one another. So I'm going to remove that formula there. And then we don't really care about the radius anymore. In fact, you could delete that parameter entirely if you wanted to. And as far as the X and Y, this is where we would want to do the formula.

So the X is running horizontally. So that's going to be my width divided by 2. And then the depth is running vertically. And that's going to be my depth divided by 2. And we'll click Apply just to make sure we don't get any errors this time. And then finally, let's try flexing. And now, of course, you're going to see that it only flexes in one direction. And I'll try flexing this way. And it flexes in one direction.

And of course, if you think about it mathematically, well, all an ellipse-- or rephrase that. If you think about it mathematically, all a circle is is a special case of the ellipse. So if you have an ellipse where both axes are equal, then you have a circle. So if you wanted to, you could use this exclusively for both forms.

Now, there is an alternative to these extra parameters and these half-formulas. And that is that I could remove these dimensions. And I could place the dimensions a little bit differently. So I could go to this reference plane. And then if you use your Tab key here, you should be able to find an endpoint. And you're going to need to do this on all four sides. And then you simply lock these.

Now, it's almost a "six of one, half-dozen of the other" kind of situation. In other words, this is largely a matter of personal preference. But now that means I no longer need X. I no longer need Y. But I still have control over this entire thing. And I can flex it by taking the width and changing it, taking the depth and changing it. And it would-- oops, that was the height. And it will apply, like so. So it's two different approaches to the same thing.

Now, I'm going to finish this example off by just setting the width and the depth back to the same value. And then I'm going to delete this form. And if you happen to be doing a circle, you can use the same trick. So I could do a dimension. And then I get nearby the edge of the circle. And I tab. And it will let me do a 0 dimension there. And this you only need to do on three sides.

Now, you could do the fourth side if you wanted to. It's not going to hurt anything. But mathematically, we really only need three. And when I click Finish here-- and now if I change here, you definitely want to tie these two together. Otherwise, you're probably going to generate an error. So I'll make the depth and the width equal to one another. And then when I apply, you're going to see that works as well.

So those are a couple of techniques that you can use to start controlling your parametric curvature there. Now, those are simple circles, ellipses-- complete, enclosed forms. Well, let me delete this extrusion. And to keep this example a little bit simpler here so I don't have to make another solid form, the next one I'm going to do with just a model line.

So I'm going to go to Create here. And I'm going to choose Model Line. And I'm going to draw an arc now. And this arc I'm just going to draw in this first little quadrant right there. Now, it did offer me some lock icons. I chose not to click those just yet because what I want to show you here is if I flex this-- and right now, I've got the width and the depth equal to one another. If I flex this, you can see that it's doing the correct thing. So at first, you might be thinking, well, gee, that's working just fine. Why would I need to do anything else? Well, sometimes it does. Sometimes, it doesn't.

So let me show you some scenarios where that might not be the case. For example, suppose I put the radius on here. So I'm going to go ahead and select this. And I'm going to call this "Radius." And again, I'll make it Instance. Just last time, I forgot.

Well, now what happens if we flex this radius? Well, now you're going to see it's going to behave a little bit differently because suddenly, that radius is taking on a little bit more hierarchy, we can say, than what was implied earlier. And now if I flex the width and the depth, it's not guaranteed that those are going to have an impact on the overall shape of that arc. So notice that the arc is ignoring what's going on with the width and depth now.

So the bottom line is here there's some underlying rules that are taking place in this family. And you can use those rules if you want to if they're giving you what you want. But if they're not giving you what you want, then the trick is you need to know why. And the reason why is something called Automatic Sketch Dimensions.

So you can see those in visibility graphics. So I'm going to type "VG." And then I'm going to go to the Annotation Categories tab here. And I'm going to check this little box here. Now, in most family templates that you create family content from, that is turned off by default.

Now, what is an Automatic Sketch Dimension? It's really like Revit taking its best guess on what you intended. What was I thinking here-- or rather, Revit saying, what was the "you" thinking when you built this family? What were you trying to achieve? And it tries to guess that using Automatic Sketch Dimensions. So if I turn these on, do you see this little 0 right here and this other 0 right here? Those are the Automatic Sketch Dimensions. So it's taking its best guess on what my intention was.

Now, suppose I took the radius and I deleted it. Well, now, suddenly, I get another one right here. So there's a couple of things you want to know about Automatic Sketch Dimensions. They are automatic, which means the flip side of that is you can't control them. They are making assumptions. And they can change frequently depending on what's going on with the geometry at any given time.

For example, if I took this arc and I started to stretch it out, you see the Automatic Sketch Dimension is changing, changing, changing. At some point, it might flip allegiance, so to speak. So at some point-- you see it right there, how it actually jumped over to an entirely different reference plane.

Now, if you've even built a little bit of Revit Family content, then you know that if your dimensions and your parameters were jumping from reference plane to reference plane-- that you probably wouldn't get very predictable results. So even though, in the case where it's 0, it's logically assuming maybe what I intended, this one-- not so much. So this is why it's important in most cases, certainly with curves, for you to eliminate as many of those Automatic Sketch Dimensions as possible.

Now, how exactly do we go about doing that? Well, what I'm going to do is delete this arc and make a new one just to be easier to start over again. And I'll do it from here to here. And this time-- let me cancel out of there-- notice the Automatic Sketch Dimensions.

Now, as I've already said, it'll probably flex in a way that seems logical because the 0's are giving us what we want here. Well, if I were to go to the Align command, select this reference plane, there's an endpoint right here. And I can lock. And I'll do it in this direction as well. Do you notice how the temporary dimensions are disappearing as I do that? What happens is if you don't want the temporary dimensions, you can't just simply delete them. What you need to do is create rules that make them no longer necessary. So either by adding your own dimension or by aligning and locking, you can remove the necessity of those dimensions.

Now, here's the thing. What happens if I flex this time? Well, it's doing the correct thing. It's giving me an obvious thing until I do something like this. If I take this and I apply the radius to it, and now let's flex that again, well, now that may not be what you had in mind. Well, it's doing exactly what I asked for. It's locking both endpoints to these intersections. And it's maintaining the three-foot radius or the three-unit radius. I forget whether this file is in feet or inches. But it's whole numbers. So it's maintaining that radius.

So that's up to me. As the designer of this family, as the creator of this family, I get to make those decisions. So let me show you a more practical example of when this might be pertinent. Let's think about arches.

So what I'm going to do is actually close this file-- not going to save it. And I've got another sample file in here. This one I have called-- let's see. Where is it here? I've got this face-based one. So I'm going to open that one up. And the only reason I'm using a face-based here is because if I'm doing an arch, it's probably something I want associated with a wall, maybe, or some sort of a horizontal surface. So using a face base is an easy way to do that.

Now, there's already an extrusion in here. I'm going to remove that. And this bottom reference plane-- I don't want that, either. And then I'm going to take this top reference plane here. And actually, it's already named correctly. It's this one that I want to rename. And I'm going to call that "Springline."

And then this, which used to be an equal-equal dimension-- I'm going to rename that or label that, rather, with a new parameter called "Rise." And I think everything in here is instance-based as well. So let's keep it instance-based. And then I'm going to flex this 0.75.

Now, what I want is-- this is the overall size of the arch. So I'm going to create this arch, in this case, with a sweep. So I'm going to go to Sweep, sketch the path. And there's all my curves again. So I'm going to do this three-point curve from here to here to here. And then I'll click the Modify tool.

Now, I've already got Automatic Sketch Dimensions turned on in this file, as you can see. And you can see that they're all appearing in lots of different locations. And we're getting one to this weird point right here because if you imagine where the center of this is-- I forgot to show you a neat little trick we can do with curved geometry-- we can turn on the center mark. So if I do that, that's where those mysterious dimensions are pointing to. So even though the center mark wasn't turned on, Revit still knows where it is. And that's what it's dimensioning to. So again, it's taking its best guess here.

Here's what I want to do. I'm going to go to my Align command again. Now, if you're using a modern version of Revit, 22 or 23, like I am, the Lock feature is right here. So instead of having to pick the reference plane, pick the point, and-- oh, I missed it there. Let me try that again. Pick the reference plane. You want to pay attention to what it's saying here. That says Automatic Sketch Dimension. So I want to tab until it says Sketch. Click the point and lock.

Do you see how the dimension went away? Well, I can save a step if I turn this on ahead of time. So now I'll pick the Springline. And I'll tab and tab again until it says Sketch. And it locks automatically.

So that saves you an extra click. Now, if you're doing this a lot, those clicks add up. So that can be a nice thing. Let me see. For some reason, it's not letting me get to that one. Oh, there it was. I just wasn't paying attention.

Now, notice that I've eliminated most of the Automatic Sketch Dimensions. But there's still one right here to the center because, as you saw in the previous example, just having the endpoints pinned down isn't enough. So most arcs need three things. It can be two endpoints and a radius. It can be the curvature and two endpoints. It can be the angle. There's a number of things you can choose from. But you typically need to lock down three parameters, mathematically speaking, in order to keep that arc behaving.

So I could calculate, using math, where the center line-- or where the center point needs to be. But if we go back to the first example I showed you with the circles and the ellipses, what we can do alternatively is simply put a dimension and tab in right there and lock that. And if you don't like doing a 0 dimension, then you can do it this way from the Springline and tab it right there and then select this and label it with the Rise parameter. Both of those will do exactly the same thing.

And so now if I were to flex this, and let's say that we flex the width of this to 3, you're going to see it spread out a little bit. I'll change it back to 2. If we change the rise to 1, it becomes more of a Roman arch, a half-circle. If we change the Rise to something greater than 1, it becomes more of a amorous kind of shape. And if we go less than 1-- 0.5, 0.75-- then it's got more of that eyebrow shape, that segmental shape. So this same construct could be many different types of arches because we've now made it flexible in all those ways.

Now, this is the path of the sweep. So I can click Finish here. And then I can go to the profile, edit the profile, open up a view. And I'll just draw a simple rectangle to represent the geometry and finish that. And then when we look at it in 3D, we have our arched form right there, which, again, you can flex to any of those ways to adjust that arch.

So it's creating all these techniques. You want them to apply to something practical. And so arches are very common in many different forms of buildings. And so that is certainly one of the practical forms.

Now, as well as those techniques work, and I've got lots of others that I'm skipping over here-- but I'm going to jump right to one of my go-to forms, and my apologies if this is going to bring back any old memories for any of you. But we're going to do a trigonometry example now.

So I know that some of you may not have liked math in high school and you were happy to be done with it and you probably said to yourself, when will I ever use this again? Well, here you are using Revit. Here's an example.

So what I'm going to do is jump back over to my PowerPoint here for a minute and just show you the trigonometry example. So I've got it mapped out here so we can see what we're after. The first thing I want to show you is a handout that's-- or a page that's included at the end of the handout. It's a cheat sheet for trigonometry. And here's just some clippings from that.

Now, I adapted this from a forum post on the RevitForum.org. And Klaus Munkholm was very gracious enough to let me reproduce it. But you can go to that URL at the bottom of the page there if you want to read the entire post. There's lots of good formulas on there. So if you're serious about Revit formulas, you should definitely check out that post. It's still valid today even though it was written, like, 20 years ago. And it's got lots of great formula examples that you can use in your content, including trigonometry.

So what you do with the cheat sheet is you determine which two parts of the triangle you know, either two sides or an angle or something like that. And then it tells you what formula to use in Revit. And the first one we're going to do is make an ovolo curve. And if you're not sure what an ovolo curve is, it's this. It's just a simple-- you would think of it as a quarter round, like if you went to a lumber yard and you picked up some moldings. You would think of it as a quarter round. But a quarter round is equal in both directions. An ovolo is not. An ovolo has a slightly narrower side and a slightly taller side. And therefore, the center of it is shifted off-center.

Now, on the left side of the screen, I'm showing an image from a book by Robert Cheetham, who was one of the sources for Renaissance Revit that I relied on heavily in that book. And then my diagram on the right is in Revit. And the idea is that we're going to ask the end user two questions. We're going to ask them what the depth and the height is of this molding. And we'll figure out the rest. And what we're trying to do is calculate the point right there which that diagonal line is going through. And that's where we need to put a reference plane to mark the center of this arc. And that's going to move depending on the width and the depth. So we need to calculate that location.

And we could have done the same thing with the arch a moment ago when I said the center was floating and we could adjust it. And I chose to do it by putting the dimension directly in the geometry. The alternative would be to calculate where the center ought to be. And that's another option.

So anyway, to find this reference plane, it turns out that the X and Y that we're asking for forms a triangle. So using one of those trigonometry formulas, we can easily figure out the diagonal of that triangle. And then it turns out that this other triangle here is a similar triangle. Now, mathematically, a similar triangle is one that's proportional to the original, but has all the same relationships. So if we take half of the diagonal, that becomes the small side on this other triangle. And then we can take this angle here. And the corresponding angle is right there. And we can use trigonometry, again, with that half-diagonal and that angle to calculate this distance, which is the radius, which you can see turns out to be the long side, or the hypotenuse, of that smaller triangle.

So we just apply a few of these trig formulas. And we get to where we need to go. Here's the formulas. So we're trying to find that point. And we're going to use the Pythagorean theorem to figure out D. Then there it is right there. And we're going to just do simple division to get Half D, right there. And then we are going to look for-- do a little trig here. So we're going to use the atangent function on angle A in order to figure out what the-- to figure out the angle, rather. Sorry. We're going to use the atang function with the height and depth to figure out angle A. And then once we have angle A, we can use the cosine function and Half D to figure out the radius.

So that's how we're going to analyze what we're dealing with. We start with those two inputs, X and Y. And we end up where we need to go. Oops. I did not want to cancel out of the PowerPoint-- my apologies. I pressed my Escape button. It's a Revit habit that I'm sure we're all in. And let's jump back over here.

So the file that I want to open here I have forgotten. Forgive me. Let me go to my notes here. Seed Profile-- so this one. And one thing I forgot to mention here-- the remainder of the session, we're going to be creating profile families. The reason for that is that profile families I like because you can reuse them. So we can do the shape that we want, including all the flexible curves, in a 2D profile family. And then we can use that profile family to create our solid forms, sweeps and swept blends.

Now, if you need extrusions or revolves or blends, there's a pretty good chance that you can emulate those same forms using sweeps or swept blends. So most of the time, you can do most of your geometry using sweeps or swept blends. And therefore, you can rely heavily on profiles because extrusions, revolves, and blends, unfortunately, don't support profiles. So your choices with those forms would either be emulate them with the sweep or swept blend or do the sketch directly in the form, which means you'd have to repeat yourself if you wanted the shape multiple times. So because I'm thinking I want to use this ovolo shape in other circumstances, I'd rather have it as a profile.

So there's a little triangle in here just as a placeholder. I'm going to delete that. I'm going to draw two reference planes, one here and another one a little further out. And just to keep these straight, I'm going to name this one "Projection." And I'm going to name this one "Radius."

So this one is the one that we're using trigonometry to figure out. For the projection, that's just going to be another parameter. So I'm going to put a parameter there. And let's put this over here.

So we're going to label this. I don't think I have "Radius" in here yet. No. So we're going to label this "Radius," or I-- did I use "R"? I think I just did "R" in the handout. So I'll do "R," make it instance-based. And then this one I'm going to call "Projection." And the "Projection"-- I'll do it instance as well. Let me just make that a whole number. So I'll just go with 5 there.

Now, I'm not going to worry about R yet because we're going to calculate that. So what we want to do now is go to our Family Types window here. And let me just make this a little bit larger. And I'm going to add the parameters that I need. And I would love to say I had these all memorized, but I don't. So let me turn to the page-- there we go-- that I need for this. And this is all in the handout if you're-- are following along later.

So I'm going to do a D parameter. That's my diagonal. I'm going to do a Half D parameter, HD. And actually, I want to put these under Constraints. That's just something I like to do because I don't like having everything under Dimensions. But that's not at all required. You can put these in any group that you like. So there-- and then I also need A.

Now, it's very important with A that you pay attention because it defaults to length. And I want A to be an angle. And I also want that in Constraints, instance-based. And I needed one more, R, which I already have. So let's take R. And because we're calculating that, as well-- anything that I'm calculating I like to move to Constraints. So I'm just going to move it up there. So those are the four parameters.

Now, let me change the order. D we're going to calculate first. Then we're going to calculate Half D, From D, and then A, and then, finally, R. So D was Pythagorean theorem, which is SQRT, open/close parentheses.

I'm going to arrow in, open/close again, plus open/close again. The reason I do that is I want to make sure I don't miss any of the parentheses because that will generate errors. And what we're going to do is take X squared.

Now, the way you do square-- the way you square things in the Family Editor is to do the little caret symbol, which is Shift-6, and then the number 2 or whatever power you want to raise it to because you could raise it to the third power or the fourth power or the fifth power.

So I'm going to do caret 2 again. Whoops. There we go. And that calculates that distance. And it's funny. I got it really close, didn't I? I can't see it. But I think it was 16-something already. So that was just dumb luck.

D divided by 2-- that one's easy. This one is the atan function. So again, I do atan, open/close parentheses. Then I'm going to arrow into the parentheses. And it was Y divided by X.

Now, again, I don't have all this memorized. I'm using that trigonometry cheat sheet to remind me. So I just thought about what do I have. I have my X and Y. And I'm trying to calculate an angle and figure that out.

Right now, my X and Y are equal. So you can do a quick gut check. And it's working because if you have two equal sides, you have to have a 45-degree. So it's working. So you can see that right there.

And then finally, the last formula is HD divided by the cosine of A. So it's not too bad-- yeah, a little high school math there, but it's not so painful.

Now, it's very important that you type the parameter names exactly. So I used uppercase in my names over here. I had to use uppercase over here as well.

So if I click OK, you'll see that my radius has flexed. Something doesn't seem right there, though. What did I do wrong? Oh, no. It is saying it's 12. So let's change that. So let's do 8 for the X. And we'll click OK. And do you see how that just adjusted?

Now, instead of having to keep going in and out of the dialog, let me just position these next to each other. Let's flex the Y, too. Click Apply. And you'll see everything adjust.

Now, in order to really see this, let's put some lines. Now, remember, I'm in a profile family. So I'm not creating extrusions or blends yet. I'm just creating the shape. So I'm going to do a center-ends arc. The center point is right there, the intersection of R and that top reference plane. And then I want it to swing from here to here.

I'll click Modify to cancel a whole bunch of temporary sketch dimensions. I'm going to select the arc, turn on the center mark. Then I'm going to go to my Align command.

Now, I previously turned on Lock. It remembers that. So I'm going to align and lock that top endpoint in both directions, align and lock the bottom endpoint in both directions. And then I'm going to align and lock the center line in both directions. And now that arc is locked in three locations. And it should flex perfectly no matter what I adjust these numbers to. So I'm just going to try a few values. And you can see that everything is working.

So to finish off, remember, this is not a profile. So it has to be a closed shape. I'll just draw straight lines. And I want to go to that intersection right there, that intersection right there, and finish it off there, Align command. Align and lock that. Align and lock that. And align and lock that.

Now, I have a testing file that we can test this out in. And it is called-- what is it called? It is called Sweep Flex, 05 Sweep Flex. I'm going to open that up. And I can load in the one that I just created into this file-- whoops-- here. I can load that in. But I actually already had the-- I already had the files here or the profiles already here in this file. So if I just adjust some of these, I can select this sweep and come over here to the profile. And you can see I've already loaded them all in.

So you can use the ones that I've already provided or you can use the one that you loaded yourself. So let's try the one that I just loaded, which is still called "Seed Profile" because I forgot to Save As. And you can see it will come in. And it looks beautiful and smooth and-- nice, clean geometry. That's what I'm going for. It's very important to me that I have nice, clean geometry. I don't like a bunch of gaps. I don't like weird, little angles when it breaks in some strange way. So that's what I'm after.

So I'm going to go back to PowerPoint once more here. And let's just advance here through all this again. And then we're going to go to this one. So this is a slightly more complex curve. There's two arcs now that need to meet at a tangent. And it's kind of the same thing. We're going to find not only a diagonal, but a center there and then the halfway points of each of those. And I had this little happy discovery that it turns out that that's actually a regular hexagon when you do that. So that's kind of cool.

And then you've got a triangle here, again, between X and Y. That gives us a D. But because we're dealing with a regular hexagon, we've actually got six regular triangles within that hexagon, which means that any side of the hexagon is actually also the radius of these arcs.

So we're going to find these two centers points here and here. We're going to need to calculate this little triangle to help us do that. And of course, there's angle A again. A regular triangle has 60-degree angles. So that's going to be easy enough. Here's angle B. But with the combination of angle A and 60 degrees, we'll be able to figure out B very easily.

So again, we're going to do a Pythagorean theorem to get D. Then we're going to just do simple division to get R. So in this case, R is just half of D, as you can see there with my little PowerPoint animation. And then we're going to do some trig to figure out angle A, just like we did in the last one. Then we're going to just do some simple arithmetic.

Now, if you go, wait a minute, how is that 120 minus A, let's explain that. So right here, a total line is 180 degrees, half-circle. We're subtracting angle A from that. But we're also subtracting 60 degrees from that. So if you take 60 degrees and you push it over to the other side, what you get is that B plus A equals 120. And then if you simplify it further, you get that B equals 120 minus A.

So that's how I came up with that. So that's our simple arithmetic. And then to find the center here, now we have to go to our X1 and our Y1. And that's just going to use the cosine function with our radius again and then some more trig here to give us Y1, which is the sine function of the same angle.

So anyway-- oops, went too far. I'll save that one for later. So let's close this guy. And we're not going to save it. Let me just make these full screen again. Open up the starter file here, which is the Cyma Start. I've already done-- I'm not going to do all the work over again. I've already done some of the work here.

So here's the reference planes and the offsets. And basically, we just have to add in the required formulas, some of which are already here. So you can just type in those formulas and then flex it. So rather than watch me do all of that, in the interest of time, and it's all in the handout, I'm going to open up the final version here.

So if you want to do it yourself, you can start in that file. But if you just want to skip to the end, here's what it looks like. And you can see there's an arc here and an arc here with their center lines at that-- those locations. It's all been aligned and locked. And here's those formulas that I mentioned in the PowerPoint, which makes the whole thing flexible. And just to prove that, we can try putting in a different value. And you can see it adjust. And more importantly, it stays nice and tangent, which means that if you load this into this file and you take this and you change the profile that it's using to the Cyma profile, you can see that you get beautiful, smooth geometry, no seam right here.