0:00 Okay, thanks to one. And thanks for inviting me. This is actually my first CDFAM. All the other ones have been in parts of the world that are way too far away. So I never bothered to go but this this one’s in my neighborhood. So I’m going to talk about my favorite topic implicit modeling. Usually I talk about how fabulous implicit modeling is and it is fabulous but like anything it has some downsides to and I’m going to talk about those today.

0:26 Specifically the problems with connecting implicit modeling systems to the to the mainstream ugly world of engineering. Recorded at the CDFAM computational design symposium in Tokyo, October 2026. Learn more at CDFAM.com. Let’s see if this works. Nope. Okay, introduction. You won’t know what bridges and islands are all about but but you will in a few minutes. A little bit about me. I’m a mathematician or at least that’s what I write on my tax return every year.

1:09 I spent 40 years or so working on Unigraphics and NX CAD systems. I I’m really a I’ve done all kinds of things but I but geometry is my real area of expertise. I’ve been at nTopology since 2019 and I’m based in Okinawa, Japan which is a beautiful little island about halfway between here and Taiwan. And I mentioned that because we’re going to discuss islands quite a bit in this in this talk.

1:42 This is nTopology or it used to be called nTopology. It’s not really a startup anymore. It’s been around since 2015. Got 400 odd customers. It’s based in New York City which is way too far away from where I live but that’s kind of a good thing. We’ve spent $150 million developing implicit modeling. I hope it was worth it. These are some of the customers, you know, when you’re in the software business, it’s kind of annoying that your customers won’t ever let you tell anyone that they’re customers and using our software, but anyway, these are the few of the ones that don’t care.

Traditionally traditionally nTopology focused on design for additive manufacturing. So we’re really good at lattices and lightweighting and and stuff like that. But then about about a year ago, we decided that the additive manufacturing market wasn’t big enough for us and we decided we would expand into other areas of product design outside of additive. And the the the product area that we focused on mostly for the last year is is aerospace design for a couple of reasons.

2:57 One is aerospace companies have huge piles of money as the Honeywell presentation explained this morning. And secondly, because our our CEO Brad is is crazy about airplanes, which is a good reason for chasing a market. I I I I’ve sort of taken this slide out and put it back in again about three times but just just to make sure we all understand what boundary representations are. The idea here is that you represent a solid object by taking a bunch of faces which are surfaces bounded by loops of edges and you glue them all together with topology information.

3:36 In In other words, you represent the object by its outside skin or its boundary. So that’s the old way of doing it. The way and this is how all current CAD systems work. It was invented around 1974 by Ian Braid, Braid, and apparently there’s no connection whatsoever between Ian Braid, the inventor of B-reps, and Braid Tech, the sponsors of this conference, which I think is it’s a small world.

4:10 Okay, so that’s the old way of doing things. The new way of doing things is this implicit modeling stuff, which several people have explained, but I’m going to do it yet again. So the idea here is to represent a solid object, you you somehow fabricate a function, which is negative inside the object and positive outside. And the nice thing about this is that in order to do modeling operations, things like Booleans and offsetting and filleting, you just have to fiddle with these functions.

4:39 You just have to com- compose them in different ways. So there’s no computation to do. So these modeling operations cannot fail, and they’re blazingly fast, because it’s cheating. You’re not doing anything. So that’s you know, in software they you always say the software that has the least bugs is the software that isn’t there. So so it it’s 100% reliable, it’s extremely fast because it’s well, because it doesn’t do anything, and because it’s GPU friendly, and it’s the scalability is very good.

5:15 So you know, lattices with millions or tens of millions of cells are are no problems for the no problem for this technology. Where we fit into the overall engineering process is shown here. Several people have shown this sort of iterative loop, and this is my version of it. Actually not the best, I don’t think, but anyway, everybody has this picture of an iterative loop. So the idea here is you’ve got a you’ve got complex requirements, you’ve got a highly engineered product, you’re searching around the design space for feasible or optimal solutions.

5:51 So, it’s a process of iteration. So, what do you need if you’re going to iterate effectively? Well, first of all, you need reliability because if one of those iterations fails, then the process grinds to a halt. And secondly, you need speed because if each iteration takes too long, then the whole process takes forever. And, you know, we have exactly that. We have reliability and speed. So, nTop is very well suited for these for this iterative loop.

6:22 The only problem is that the nasty world of legacy engineering is over here and it’s it’s separated from this nice little world of that nTopology deals with. Okay, so we need better bridges. What does that mean? Well, here’s nTop and and other implicit modeling systems. Here’s the the legacy mainland, if you like. So, nTop implicit modeling is an island. The legacy systems are sort of the mainland of of engineering and somehow we got to get from the island to the to the mainland.

6:59 In other words, we have to convert implicit models into into meshes and boundary representations because that’s what the downstream applications in legacy systems want to consume. So, we need better bridges. We need a way to get from from the implicit island to the legacy mainland. So, the the obvious Well, the obvious answer is well, you just convert an implicit into a mesh or into a B-rep. Well, yeah, that’s basically what we have to do, but it’s it’s somewhat more complicated than that, as I will explain.

7:44 The first point is that the downstream applications well, there’s lots of them, and they have different needs. I’m not going to go through all the details of this, but the color coding shows you that depending on the downstream application you’re trying to address, you might need a different kind of mesh or or B-rep data. So, it’s it’s not just make meshes and B-reps, there’s different kinds of meshes and different kinds of B-reps, as I will explain.

8:12 So, the first step usually is going from an implicit to a to a triangle mesh. And this is sort of textbook stuff, you know, you look it up and there’s an algorithm called marching cubes, which is invented in the 1980s, and it’s the standard way of converting a converting a a an implicit model into a into a triangle mesh. The problem is it doesn’t work very well.

8:35 It it does a very poor job of preserving sharp edges. And there are some other algorithms that do a slightly better job, but they have other problems. So, we had to work pretty hard to convert implicits into meshes and preserve the sharp edges. While we were working at that, trying to figure out how to do it, of course our customers are smarter than we are, and they said, “Well, if the sharp edges are are problem, let’s just get rid of them.

9:01 Let’s put little rounds on all the sharp edges, and then everything will be fine.” And it is fine. So, that’s one way of doing things, and in some industries, it’s a perfectly reasonable thing. On castings and forgings, every edge is rounded anyway. And fortunately for us, on airplanes, everything is smooth, there aren’t any sharp edges. So, the sharp edge problem had to be solved, but at least for airplanes, it’s it’s not that big of a deal.

9:30 Then, if you’re going to produce meshes and B-reps, there’s lots of different kinds. There’s there’s these things which I call uniface meshes. So, you’ve got a bunch of triangles that that that comprise one single face that’s the whole object. And then sometimes you want to break up that collection of triangles into individual faces, and then there’s other times when you want to replace some of those faces with analytic surfaces to make so-called mixed models.

10:02 The multi-face and mixed models are not very common not very widely supported in CAD systems and in data exchange standards, but in systems that are based on Parasolid Parasolid is a thing called convergent modeling, and what it means is they support these kinds of multi-face and mixed models. So, CAD systems that are based on Parasolid do support these kinds of of models and they’re and they’re very useful.

10:28 So, that would be NX SolidWorks, Onshape, Shape a 3D, B Plasticity. There’s lots of systems that based on Parasolid. Okay, so that’s a little bit about producing mesh models, but very often what you want is a is a B-rep that that consists of curved surfaces. So, very often NURBS surfaces. So, the standard way of doing this is you you make a triangle mesh, then you convert that to a quad mesh, and then in each little quadrangle you stick in a NURBS surface, and you try to make them all join smoothly, and you end up with a a NURBS surface model.

11:07 The problem is the quad meshes are always sort of distorted, which means that the NURBS surface models also come out sort of funny-looking and distorted, and people don’t like them. They don’t like these patchy NURBS surface models because they don’t look anything like what a human being would produce. So, people turn up their noses with these things. There’s actually very little wrong with them. They’re watertight. They’re very smooth.

11:35 You can add new shapes to them. You can, you know, add holes and fillets and what have you. So, they’re for a lot of purposes, they’re perfectly fine, but but people don’t like them. So, So, we have choices about which kinds of B-reps to produce. There’s these patchy things that I just talked about. We can use meshes instead of the NURBS surfaces. And there’s this kind of B-rep model, which is the kind you would probably produce if you’re a human being using a CAD system.

12:06 So, it’s the surfaces are trimmed. There’s fillets and so forth. It’s It’s It’s quite different from the from the ones our algorithms produce. So, we we spend We’ve spent a lot of time and effort trying to figure out how to produce boundary representations from implicit models. And to me personally, this is getting increasingly frustrating because the older I get, the less I like boundary representations. So, spending, you know, spending months or years of development time trying to figure out how to produce them is really kind of annoying, and I wish they would go away, but they won’t.

12:47 So, here’s a couple of things that annoy me. First one is, you can’t leave out any of the edges. You have to make edges all over the place. We don’t have them in implicit models, so we somehow have to fabricate edges. And you have to get all of them. It’s not enough to get 99%. You have to get all of them. Because if you leave out an edge, the B-rep data structure is corrupt, and the model is completely useless.

13:10 So, look at this thing here that There’s two This is a fairly obvious kind of natural kind of design. It’s It’s two two pipes merging into one. So, there’s a This There ought to be an edge here. You have to put an edge here in a to make a valid B-rep model. Trying to compute this edge is horrendously difficult because the two surfaces are coincident and it’s pretty much useless from an from an application point of view.

13:36 The user doesn’t care about this edge. It’s it’s no use in applications. So, we have to work really really hard to compute this edge which is no use to the user. And it’s only it’s only purpose is to make the boundary representation data structures happy. So, it’s annoying. The second annoyance is that the kinds of boundary representations that that CAD systems typically produce are kind of messy, you know, and they don’t correspond to what to the way users think about these models.

14:11 If a user builds a model like this, he’s and and you listen to the user talk about this model, he’s going to say, “Well, it has some walls and a floor and it’s got a fillet.” But, that’s not what the boundary representation consists of. It consists of all these tiny little cylindrical and toroidal surfaces. It’s a it’s a giant mess. So, it’s it really doesn’t correspond very well to the user’s view of of what he’s designing.

14:40 So, my two pet peeves. But, it doesn’t matter that the B-reps annoy me. We still have to produce them because customers want them. So, our latest efforts have been aimed at producing boundary representations that are more similar to ones that human beings would produce and this is a work in progress, but it’s kind of working. Okay. A bigger island. Well, the for the last few minutes I’ve been talking about building a bridge between this little island here and and the mainstream over here.

15:17 Wouldn’t it be nice if we didn’t have to build our build a bridge between our little island and the mainland. And in order to make that possible, we have to get more people to come and live on our little island and work with us. In other words, we have to have more applications that can directly consume implicit models so that we don’t have to convert them into meshes and B-reps.

So, we’ve been trying to do this and the approach we’ve taken is that there’s a function in ANTOPT that that exports an implicit body and then there’s a a library of functions that we provide to people and these functions are able to process implicit bodies, do useful calculations on them. So, the idea is that people will write applications that call these functions and and consume implicit models directly.

16:13 And, you know, simple calculations like distances and intersections and so forth. So, if if you do that, then there’s there’s no meshes or B-reps involved. These implicit files are tiny, thousands of times smaller than than meshes and you’re doing calculations on something that’s exact as opposed to a mesh which obviously is an approximation. So, there’s a lot to be said for this way of doing things and we’re doing our best to persuade people to to work this way.

16:52 And we’ve had some success. There’s a fair number of applications that have adopted this ANTOPT core library and are using it to do calculations on on on models on on implicit models directly. Okay. So, bigger island is another solution. So, what I’ve talked about is is a connection between nTopology and traditional CAD systems, but there’s a new kind of connection that’s almost as important, and that’s the connection between nTopology and AI systems.

So, this is very new. Just a few weeks ago, we implemented a an API which AI agents can call to construct and process nTopology models. We call it the notebook API. So, it I don’t there’s nothing really very creative or original here. It’s not very different from the feature script idea that was described yesterday, and in fact, you could probably do this with any CAD system that’s got a decent API, which basically means all of them.

But this this idea is is is has had remarkable impact. We released this internally about 3 weeks ago, and our our CEO, Brad, has used it extensively, and he said he’s made more he’s made more models in the last 3 weeks than in the last 10 years. So, it gives you a very, very effective way of of making models. You just converse with a with your favorite AI agent, and the and the agent calls the nTopology API to to build the models.

18:40 So, Brad has built all kinds of things. This is interesting. One of our sales guys built this. This guy has no engineering background at all. He has a bachelor’s degree in music, and he designed this by using Claude code in he said 5 minutes. Is it a good impeller with good engineering properties? Probably not, but the fact that a guy with a music degree can design any well, anything at all in 5 minutes is is spectacular, I would say.

19:10 NTopology is meant for designing mechanical parts, but Brad, our CEO, had the bright idea of asking, Astra to design a new office layout for us. So, it did. It, produced this office layout, produced, produced, architectural layouts, produced a nice rendering showing what the office is going to look like. So, again, you can do spectacular things. 15 minutes ago I told you how hard it is to convert implicit models into boundary representations.

19:44 So, last week we had the bright idea of, well, you know, if we can’t do it, maybe Astra can do it. So, we asked Astra to write a conversion from implicit to step, and it did. I mean, it took, I don’t know, a few hours of prompting, but it did. And, the results it produced, I think they’re, it’s too early to say, but they sort of look better than than the algorithm that we wrote.

So, it’s, we’re living in a whole new world here. Another interesting thing is happening in that, you know, there’s lots of lots of companies that are doing AI-first engineering, or what whatever you’re going to call it. They all need, geometry capabilities, and very often they come to us and say, “Can we use your geometry kernel, for our in our AI-based process?” And, of course, the answer is yes.

20:38 And I think nTop is very well suited to this kind of thing because, you know, the AI model is the AI system is driving the geometric model, and you need, again, you need reliability, and you need speed, which is exactly what we provide. So, could we become the sort of the the center of the AI engineering world? It’s sounds like something made up by a marketing guy, right?

But, and I’m English, so I’m skeptical. But it it sounds sort of plausible. I mean, if not us, then who? B-rep systems don’t have the reliability and speed, and we’re the we’re the company that has spent the most money developing implicit modeling technology. So, we’re sort of a natural choice, and we’ll see what happens. This is just a repeat of everything I said, so I’m out of time, so I’m going to skip it.

21:35 But the the the punchline here is that boundary representation systems have problems with reliability, performance, and scalability. Implicit modeling systems have a problem, too, connectivity. Which of those two problems is easier to solve? I spent 40 years trying to solve the B-rep problems. I give up. So, I’ve spent the last 7 years trying to solve the implicit modeling problems, and I’m betting that those are easier. I certainly hope they are because I don’t have long left to work, so.

22:07 All right, thank you. And if I really did for talk for 28 minutes, I apologize. I I think it I think it kept itself of my talking of VCs was part of the 8 minutes, so you’re good. Recorded at the CDFAM Computational Design Symposium in Tokyo, October 2026. Learn more at CDFAM.com.