S2E49 Lattice Structure 3D Printing – 3D printed COVID 19 Test Swab | Hardik Kabaria

In early March 2020, Carbon engineer Hardik Kabaria received a message about a sudden swab shortage. With his engineering background and knowledge of software, he led the team at Carbon to produce Lattice Structure 3D Printing – a 3D-printed COVID-19 Test Swab.

Hardik Kabaria is Director of Software Engineering at Carbon. In this role, he leads the development of Carbon’s Design Engine. He works on a variety of computational geometry and mechanics algorithms including surface and volumetric parameterization, parametrizing topology changes, working with an implicit neural representation of 3D geometry, linear algebra-mixed-integer solvers, PDE constrained optimization tools, and physics simulations based on finite element framework. Before Carbon, he completed his PhD at Stanford University in the field of generating tetrahedral discretization for changing geometries and evolving topologies.

Links:

Hardik Kabaria

Rafael Testai(co-host)

Articles discussed in the podcast:

Lattice Design Enables 3D-Printed Nasal Swab Production, Machine Design

https://www.machinedesign.com/medical-design/article/21162932/lattice-design-enables-3dprinted-nasal-swab-production

The Lattice Engine That Could: How a New COVID-19 Testing Swab Went from Concept to Launch in 20 Days

https://www.carbon3d.com/resources/blog/the-lattice-engine-that-could-how-a-new-covid-19-testing-swab-went-from-concept-to-launch-in-20-days/ 

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Transcript

Presenter: 0:00

The Being An Engineer Podcast is a repository for industry knowledge and a tool through which engineers learn about and connect with relevant companies technologies, people resources, and opportunities. Enjoy the show

Hardik Kabaria: 0:16

You have a lot of freedom on the geometry you can produce.

Rafael Testai: 0:32

Hello, everyone, welcome to the Being An Engineer Podcast. I am your co-host, Rafael Testai. Today we got another very special guest Hardik Kabria, and he is a director of software engineering at Carbon. In this role, he leads the development of Carbon's design engine, he works in a variety of computational geometry and mechanic mechanics algorithms, including surface and volumetric parameterization parameterizing, topology changes, working with implicit neural representation of 3D geometry. And if by all means, as I'm reading this description if your listeners if the listeners are wondering what some of these terms mean, we're gonna go over them rest assured, linear algebra mix integer solvers, PDE, constrained optimization tools, and physical simulations based on finite element framework. Before Carbon, he completed his PhD at Stanford University in the field of gender generating tetrahedral descritization, for changing geometries and evolving topologies. Sounds like I'm going to be speaking with someone extremely smart. Hardik, welcome to the show.

Hardik Kabaria: 1:40

Thanks for having me.

Rafael Testai: 1:41

Absolutely. So why don't you tell us a little bit about yourself? How did you decide to be an engineer? What's your story?

Hardik Kabaria: 1:48

Oh, how did I decide to be an engineer, I cannot even think of one sort of point in time where that decision may have happened. But it very early on. In my age, I was quite interested in paper airplanes. Had I remember having a book where there were like 100 different designs you could make, made a sort of a project out of it. And that got me interested in being an engineer, especially something related to mechanical aerospace. I didn't end up going in exactly any of those places. And fast forward did my bachelor's in mechanical engineering in India, and that led to a Master's and PhD here at Stanford, and I've moved around Clearbit started in mechanical engineering, then the got interested quite a bit in computational geometry. Did my PhD focus on that? And, and then the rest is history, 'sort of became a software engineer in that space with Carbon since 2015.

Rafael Testai: 2:50

Okay, so as I said before, I'm going to start defining your complex definition that you have on LinkedIn, your biography, piece by piece, so we can put it all together. So you work at Carbon, could you explain to our audience who Carbon is and what you do?

Hardik Kabaria: 3:09

Sure. So Carbon is a 3D printing company. In a little bit more elaborate way, we have created a new, fundamental way to manufacture products within the realm of additive manufacturing, a new process we call digital life synthesis. So we create this hardware, which is the printer, we are the inventor of the process. And we also invent the chemistry, which are the resins that you can use on this printer to create parts. sort of fundamentally different thing is our process is innovative. So you can print things significantly faster. These are all polymers, so plastics. And because we can print faster, we have allowed ourselves to use certain chemistry that enables us to create parts that have high end properties. That means it is not just for prototyping, it is for manufacturing. Fast forward a few years we have there are several high profile customers that are using our technology. Suddenly, printer resin, and software that drives the printer all together to create parts like reverse creates midsoles and these are at scale, in manufacturing environment, in factories, and these parts are real so that you can buy that from the consumers website like you can buy the 3D printed midsole powered shoes from Adidas website. So that's in a nutshell company carbon. We work at the intersection of saw hardware, software and material science, as I alluded to before, my role was in software team. Within that we early on, we realized that one of the ways we can accelerate how mechanical engineers find more and more applications that will be manufactured in our printer is we give them access to ways of designing for additive manufacturing. Just like you injection molding is a manufacturing processes very mature, there are many software tools around around the world that can help engineer design the parts that are right for them that can be produced robustly with a high yield. And without any error using injection molding processes new so it has its own constraints, it has its own freedom. So we wanted to create a design engine or design tool that specifically takes advantage of the manufacturing process that carbon had invented. Even more specific, we thought lattice structures are this structure that or architecture that can lead to very phenomenal or fascinating mechanical properties compared to a form or income burned material. And so if we give access to these lattice structures as a meta materials to mechanical engineers, they will be able to design cards that will have superior performance compared to incumbents, and hence, they might be interested in designing this way. So that started the idea of creating the protocol design engine. As we know today, I was the first engineer on the team.

Rafael Testai: 6:07

Before we go into that, you just unloaded a lot of information

Hardik Kabaria: 6:11

Yes

Rafael Testai: 6:11

Can I ask you some follow ups before we go into the details?

Hardik Kabaria: 6:14

Please, please.

Rafael Testai: 6:14

Okay, so if I understand correctly, just to recap, Carbon, it's a 3D printing company, not only you make the printers, but you make a a filament or a typo.

Hardik Kabaria: 6:27

So yes, it's basically liquid resin, and that the printer shines a UV light on it. And that starts a chemical reaction that converts the liquid into solid.

Rafael Testai: 6:39

Okay, and then once it solidifies, then you produce some very special properties, you said that could be used as soles of shoes, is that right?

Hardik Kabaria: 6:49

Yes. So this part is just about the process. So the process is rather, you can think about it in a very simple way, wherever you shine the light, the liquid becomes solid. So our printer is basically a very fancy projector, where the UV light is shining this light in particular places where the liquid turns into solid. The beautiful thing about that is you have a lot of freedom on the geometry you can produce. That means you can produce really complicated geometry using this manufacturing method compared to what you might do with other traditional methods of manufacturing. So I'll pause there first. And if that makes sense, I can elaborate further on why lattice structures could play an important role in that argument.

Rafael Testai: 7:31

That was actually going to be my next follow up question because I design in SolidWorks

Hardik Kabaria: 7:36

Yeah

Rafael Testai: 7:36

And I use Markforged a lot here at Pipeline, teampipeline.us, where I work at, the sponsor of this podcast. And we always think about the 45 degree angles that we need to use in order to avoid using supports in additive. So how is designing it for carbon different than that?

Hardik Kabaria: 7:55

So in some ways, it certainly is similar, that you do need support if there are big overhangs or islands as we like to call it. But our process is also a little bit more complicated. Because we have a pool of resin out of which you're pulling the part out. So you can create a lot of suction pressure at the same time, there is heat being generated by this chemical reaction, so the parts could warp as well. So we have created design guidelines, that is accessible to all the engineers in carbon sequel systems that help them design the part or maybe alter the design. So that's sort of at the high level, yes, this manufacturing process that lives any anything else has its own constraints, and it has its own freedom. The biggest freedom I think is you, just like you may have experienced with Markforged or any other printer is that the you can create very complicated structures and one of the things that academics in this area has been excited about is lattice structures.

Rafael Testai: 8:52

Lattice structures? What's that?

Hardik Kabaria: 8:53

Yeah, and I want to define a little bit. So, lattice structures are basically a repeated pattern that you can fill the 3D area with. And each structure has a unique shape, right. So, you can say a few few cylindrical beams coming together is one structure and depending upon the size of the beam, the angle of the beam and the diameter and how they connect together depending upon how low how much load you apply, it may perform or bend differently, right. So that's sort of our simple mechanics ideas. Given the 3d printing technique, like manufacturing process, we have can allow for very complicated structures to be manufactured, you can really take the idea to the top that basically means you can define more and more complicated structures and still the manufacturing process can successfully produce them at yield with the right amount of repeatability and all the other things that come with manufacturing process. So that has given birth to this idea of design. Based on lattices, then by any means, I wouldn't say that carbon is the one that introduced it. lattice structure based design, I would say has been studied in academia since 1980s. But it hasn't really led to a plastic product that is available specifically in consumer world that is designed based on larger structures. And it's available to people. So it's available to mass that means it's manufactured at scale. So I would say that is something that carbon did it first. And the example is one of the example is the midsole that is created in partnership with Adidas. So midsole traditionally is done with form, you have a form that does the job of cushioning and giving support to the person that is running or standing or walking in the shoes. In this case, that form part is replaced with a set of structures, which are repeated structures. These are engineered structure, they're supposed to do a particular job. That means you can engineer them to your liking, you can say that if I compress it from the top, it's going to propel towards forward. So that means it gives you sort of a positive kickoff or momentum or boost. You can

Rafael Testai: 11:16

You mean, in performance, in sports, wouldn't that be cheating? Just playing devil's advocate.

Hardik Kabaria: 11:22

So 100% I cannot talk about how a particular body of sports could think about performance of any particular product. As a technologist, what I think about is, what we want to do is you have a set amount of space, how thick a midsole can be, or how thick a helmet can be, how heavy a helmet can be. Within that constraints, what is the best thing we can do? Can we create a superior helmet by designing the structure so that they are the safest? Or they would reduce the linear or rotational impact the most? In terms of shoe? Can it give the right amount of energy recovery? So yes, I, by any means I'm neither expert nor I would say, I have no authority to comment of what sports body would think about these products. But from pure engineer technology perspective, I think this is a fascinating area, because we can achieve a better tuned mechanical properties out of a part to what an engineer might want.

Rafael Testai: 12:26

I see, I encourage, I agree with you. This is very interesting. I encourage all the listeners if you're not driving too quickly open up a browser and just type in lattice structure 3D printing, or 3D printing Adidas, Adidas shoes, so you can visualize what it is that we're talking about here. Talking about, I went to one of the biggest medical device shows called MD&M West, just last month, and I happen to see the Adidas shoes that you're talking about with the printed soul. There were over $300. Is there something why is this technology so expensive, or it seems to be expensive, is there a reason why?

Hardik Kabaria: 13:06

So I cannot comment on the consumer price. So first of all, make it clear that Adidas is a partner with which we have the make metals at the end the end goods, the product, which is the midsole and the upper and the final shoe that is sold is the product of Adidas, but you are raising one interesting question is that when we replace this foam midsole with a ladder structured by midsole is it same at the manufacturing cost, because that's something that we are really interested in. So 100% not, it is more expensive today and partially is because of the volume and the scale, the scale at which the the amount of material that has been consumed is still miniscule compared to the form industry. And as we all know, up to a point things get cheaper, as more and more of the same material is consumed. So and that is already we see that happening already. That basically means we have the same material or the similar same raw material components being used across many different application by several of our customers to produce lattice based design, whether it's midsoles for readers, saddles, biking helmets, enhance overall the cost of the raw material comes down and hence slowly the same component will become cheaper, and so on so forth. So that sort of expands the total applications or different mechanical components that can be made with the same technology being the printer and the resin we have and the software that AIDS mechanical engineers to design parts. At the same time. There's also the aspect of performance. It's quite possible there are higher performing shows higher performing helmets, and the companies that sell these goods might be interested in creating a premium segment. So like I said, we do not go in the price, nor we influence it, what our customers sell the products at it is their business, they understand each of these products and markets much, much better than us. We are a tool in the toolkit, what we extend them is yet on an innovative manufacturing process, at the same time, an awesome way to design so they can design parts that aesthetically look cool, that achieved the mechanical performance, maybe even one up than what they have been aiming to achieve, right and do that very, very fast. So that means we try to reduce the time from the product conceptualization to the market, because in additive manufacturing, you don't have tooling cost or the tooling time. So that's sort of our vision and ideas.

Rafael Testai: 15:50

Yeah, thank you for making the distinction between the pricing of Adidas and in Carbon is two different subjects. I should have been more specific in my question. And also when I said cheating, I should rephrase it to more of an advantage, if you want is trying to maybe propel him or herself forward.

Hardik Kabaria: 16:07

Yeah, as an engineer, I think about you have the constraints. And within those constraints, everything I do is hope if I can make the lives better, whether it's for the athlete or patients, then it's a fair game. But anyhow, again, this I have no legal authority of no, no sports body authority. Yeah, where it's a pure engineering mindset.

Rafael Testai: 16:29

So I come from a biology background, my degrees in microbiology and genetics. And now I'm working on my second degree in mechanical engineering. And this is why I'm going to ask you this question.

Hardik Kabaria: 16:39

Sure

Rafael Testai: 16:39

It may come out of nowhere. I haven't even asked you this question before the podcast started, but it popped in my head, the great fruit. If we look at biomimicry, what she is using nature as inspiration for engineering or any kind of technology advancements, when they look at their pomelo, the grapefruit and the skin of the grapefruit that the white part is very thick. And scientists have used it to emulate it because it's a great shock absorber, and that your technology of carbon, it kind of reminds me of the familiar skin it is does it look to you like or no?

Hardik Kabaria: 17:14

Yeah, so that's certainly a good point. And I would say there's a whole field around it, where people are actually trying to design stuff that is inspired from nature. And I'll give you some more example that has come my way as I have delved into lattice structures is you have woodpecker, and they have sort of a design around the brain that has they keep packing the wood, it still protects the brain, in the same amount of torque or force or jerk was applied to human brain, it would suffer concussion. So clearly there is a lot in the nature that we can inspire common design, quite often that we have seen is that the scale at which nature has backed engineering, this design is is amazing. What I mean by that is whether you take the skin of the fruit or woodpecker or any of these examples, it is very, very intricate design once you put it on the microscope, and I do not think we always have the right manufacturing technology to create design at this high resolution. So that's sort of number one, we are slowly getting there 100% We have metal 3d printer that can print not a carbon, but in the world, where they can print a very high resolution with carbon, we are trying to sort of taking a step towards that we are bringing a slightly higher resolution design availability for polymer products. I by no means we are there, right by no means we are still in millimeter scale. But it still means that you can design very complex parts that may have inspired from that has inspiration from nature, and could those designing and I'll give one more idea where our own design ideas have stemmed from. There are these polymer called a block copolymer. And there's a whole area that has studied these structures, they have these block copolymer have phenomenal energy absorption properties. And there are scientists who studied their structures at nanometer scale that has led to the area of triply periodic minimal surfaces. And what we do is take advantage of those inputs help them put in lattice structures at a different scale, significantly different scale, but they still, the structure that was actually found in other material is very useful at an absorbing energy or postponing stain densification and it's helping some of our customer design very phenomenal parts. So we will transition right there.

Rafael Testai: 19:45

So when we look at lattice structure, 3D printing, for those of you that are listening and maybe driving who have not had the chance to maybe look at a picture of that, I'm going to try my best to describe it, I think of is like maybe a pile of toothpicks or something like that. Just, how could you give our listeners a quick visual before I ask my question?

Hardik Kabaria: 20:04

That's certainly one way to think about it, I was going to say you have a pile of toothpicks, but a very diligent engineer that is replacing each toothpick nicely. And is also maybe selecting toothpicks with different diameters and creating this web. But this web is may look organic, or may look stochastic, haywire, chaos, but it is not. It is engineered, and it is engineered to do a particular purpose, whatever that purpose of the product might be. And I will say that pays in maybe a couple sentence word lattice designers.

Rafael Testai: 20:39

Okay, very well said. So, when I think of when I looked online of lattice structure, 3D printing, they all look like what we just described. So I think to myself, is there a disadvantage for looking that way? And not being a traditional, maybe like a slab of 3D printing material? Imagine like a slice of bread or something like that. That's continuous? Because it has holes in the material, right? When it's, what's the word we use? lattice, it has the holes between it, is this advantage or no?

Hardik Kabaria: 21:10

Yeah, so I think it's both advantage and disadvantage, like, I would be a miss if I say this is free. It's about quite often lattice structures are used to reduce the weight, like you don't need a full blob of material for every task you needed to do, right? Imagine is supposed to support some weight and not collapse. And you only have a few materials to select from. So you're going to choose a material that is slightly safer side so slightly in our care. And at that point, you could choose to have a full slab of material, or you can optimize for stiffness to mass ratio, which is most often we engineers do, even if we are not using 3d printing, right? The 3D printing in large sectors, that idea has one more degree of freedom, that means you can choose the right structure and the right level of fidelity, right, whether it's a big hole small holes, is the same size of holes everywhere, same topology everywhere. To optimize the purpose, whatever is the purpose, and I may push back on this loaf of bread loaf of bread is not continuous either, it actually has holes. It's exactly like lattice structure.

Rafael Testai: 22:19

It is a porous surface

Hardik Kabaria: 22:21

It is a porous surface, it's actually very good example for a lattice structure would be but a different scale than what we do for carbon.

Rafael Testai: 22:28

Alright, so I came across the term 'topology optimization,' which it really caught my eye a couple years ago, I am someone that optimization really resonates with me, even the way that I have things around my house, where I put my clothes in my room. So for instance, if I do my break, I'm almost finished with my example. But if I'm doing a breakfast in the morning, I'll put my oatmeal next to my honey and next to the cinnamon in the same drawer, because I know I'm going to do it all together. So topology optimization has been something that really resonated with me and I wanted to ask you is how and perhaps a passionate topology optimization, something that led you to where you are now? Is that how you started the journey?

Hardik Kabaria: 23:11

I wouldn't say that, I will say I, I got deeper into topology optimization more during my work at Carbon. My sort of the way I came about here is more about geometry, processing geometry. And there was like creating tools for people who do topology optimization. So I'll give a very simple example. So quite often people make propellers, propellers for engines and submarines and whatnot. So one of the things people have looked at for ages and they continue to look for is having the right shape of the propeller to do the job is supposed to do. And this part of it is some idea of either topology or shape optimization. And what I did during my master's PhD is create tools, so that whoever is doing this job of optimizing, it's easier for them to perform physical simulation, specifically in the context of finite elements analysis. So I would say topology optimization wasn't really my field, I wouldn't say I'm expert in the field even today. But I have had to go deeper into it as part of the trade.

Rafael Testai: 24:26

Okay, processing geometry. So if I understand this correctly, if you download a geometry into the software that you will make, I'm making a lot of assumptions here in a second, please correct me everything I say. But if you download a geometry into a software that's going to optimize it for its purpose. How does the software know that you're the person behind that that codes everything?

Hardik Kabaria: 24:50

Yeah, so geometry processing, sort of a wide term and I'll tell what the term is and then I'll tell you what we do at Carbon. Yeah, pick your favorite CAD tool. You, you draw, let's say a few different objects and you, you sort of Boolean them. So intersection union difference, you can create a CSG, tree or graph. Geometry processing, in a way is what's happening behind the scene when you do that. Right. Now that area is I would say up to an extent, pretty well figured out. Because you see SolidWorks, you name it to all of these tools very successful. Entertaining the needs of a mechanical engineer in all the different industries. However, this problem is a little bit more complex when you start designing with even more complicated structures, where instead of having a 1050 different beams like this toothpick example, in lattices, now we have 10,000 different beams. So the number of parts are significantly higher if you think about your primitives in lattice structures compared to other traditional designs. And hence, now the same geometry processing, you have to do it on a very different scale, you have to do it very fast. And you have to do it so that you can handle so many different parts. And that's sort of the job we do so for geometry processing for us is doing the simple operations on primitive. And the but we want to do it for the type of designs that are often used in additive manufacturing, which may lead to have, which often have like 10s of 1000s of different primitives instead of like 100 or 1000.

Rafael Testai: 26:25

Okay, perfect. I want to take a quick moment to remind our listeners that they're being an engineer podcast is brought to you by Pipeline Design & Engineering. Pipeline partners with medical and other device engineering teams on a turnkey equipment, such as cycle test machines, custom test fixtures, automation, equipment, assembly jigs, inspection stations, and more. You can find us on the web, www.teampipeline.us. And I'm here with Hardik that works at Carbon. And I want to ask you, this is the story of how we found you there's an article on a very famous magazine called Machine Design, you can find them on machinedesign.com. And the article talks about how you, there at Carbon, developed a viable swab prototype within a couple hours. So first, could you define to us, give us a visual, what do you mean by a swab, because when I think of a swab, I think of like a Q-tip.

Hardik Kabaria: 27:23

Yeah, and I was complete, I had no idea what swab was either, before this problem hit us. But as we all know, early on, in the pandemic, there was a shortage of a COVID-19 test swab. And this particular swab, the technical term is nasal pharyngeal swab. If you or anybody has gone through COVID-19 test, you sort of remember it as a not so happy experience, there is a swab, that's pretty long, that goes quite a bit in your nasal cavity. And the person who is doing the test will roll the swab a few times before the direction and try to collect the mucosal content. And they try to detect a virus or wider content in that biological sample. The swabs as I knew, then, I still know is a very simple object. But because the supply chain was broken, there was a shortage of the swab. And that led to one institute, specifically, Beth Israel Deaconess Medical Center in Boston, to think about, can there be alternative swabs which are 3D printed, because the normal supply chain for the golden swab that is traditional is broken, and there is a shortage of? That's where the problem was introduced to us and many other 3D printing companies as well. We, we started looking into it like what swab looks like, what's the purpose of it, how does it function, and we did think of an idea that maybe we can design the tip of the swamp using lattice structure. So that basically, when you when somebody sort of rotates it around the axis, it will collect the mucosal content within it, and then you'll be able to pull it out and do the test as it is. We have developed this tool called design engine, which is specific for lattice design for additive manufacturing. We use the same tool to create this design. And we started printing prototypes on the printer that we have. So within days, we created a few prototypes. And we we sent it out to a couple of clinical institutions where we got some feedback like, oh, this this thing is working. This is not working. This is how you might want to change design. And we started the design iterations for the swab. So that's sort of the rough story how we came about working on this project.

Rafael Testai: 29:52

So before the original swab is a can at the bottom, at the end?

Hardik Kabaria: 29:58

Yeah, yeah.

Rafael Testai: 29:59

Okay. For some reason, it just seems like it would be a little more painful to put us 3D printed swab, right?

Hardik Kabaria: 30:08

100%, 100%, we all felt the same, the first design got the same feedback that the material you have is pretty stiff, it is not a pleasant experience. But we were able to iterate. And there are many different ways to create a flexible design, specifically using these ideas of lattices, even when the material is stiff. So we applied this concept. And we went through those user studies, to get to a place where the swab we designed, went through a clinical study, and it was perceived as its equivalent experience. So it's not any worse. Then the golden swab, which is what was used at.

Rafael Testai: 30:50

Changing subjects here, first, congratulations on that to you and the whole Carbon team for helping with COVID. So I received as I'm here in the middle of my second degree in mechanical engineering, some of my mentors and advisors and some of my mentors actually have been guests on the show, I'm very fortunate to have access to such high profile guests. It's truly a blessing. And I share a lot of the tips that I received on my personal LinkedIn, everyone feel free to follow. But I've been given a tip that we should expose yourselves as mechanical engineers, this is what I'm training to become, to the more subjects the better, because then we'll realize what we want to be what we want our niche to become, as we grow older, and we specialize. How did you decide that you wanted to take this route of, of software engineering, because if I'm not mistaken, your degree is in mechanical engineering, right?

Hardik Kabaria: 31:41

100%. Okay, I mean, I would say, up till finishing masters, that was the path I was on. But when I started pursuing a particular problem in my PhD, the problem I ended up choosing was more about generating tetrahedral mesh, as a discretization of a geometry for to enable a particular type of physics simulations, right. And in that there are two components, I would say one is like coming up with the algorithm, and the proof of the algorithm is going to work, which is more of a geometry concept. But it is not very useful unless it's implemented somewhere. And it's usable by somebody. So just because I was in that area, it was evident that I had to learn to code the same algorithm that I came up with. And in geometry, processing speed is really important. As in almost every software gets measured on two axes, not every algorithm, like how fast it is, and how robust it is, and robustness, you can work on with theoretical concepts, but speed, you cannot just theorize, at the end, you have to code the algorithm, and you have to run it on some computer hardware, whatever, and prove that it is better on particular examples or what have you. So I would say I learned coding as part of that. And I still am kind of doing the same thing if you asked me. So it is to me that a lot of our team members are also the same, which degree you have a sort of less important, then at carbon a case, then what you do with the knowledge you have and how you pursue it. So I would say at least for me, it was a organic growth.

Rafael Testai: 33:27

So a great snippet to use for maybe the introduction of the podcast right there. Jumping back to your bio, it says, well, this is almost fate, because I had electromagnetism class physics this morning. And my professor from physics said that linear algebra was single handedly the most important math class he took in his entire career. And he encouraged us, everyone after this course, enroll in Linear Algebra. And what do I know, when I read your LinkedIn bio, it says that use linear algebra mixed integer solvers. May I ask how do you use linear algebra in Carbon to solve problems?

Hardik Kabaria: 34:09

I mean, I'll give it so many different places. But I'm going to give an example from this week. So linear algebra is basically a big field of study. And again, I'm not a by any means the top of the world or even anywhere close to that to comment on it. But I'll tell you, within geometry, a lot of geometry algorithms turned into a linear algebra problem. That basically means you will end up solving a linear system of equations. So you have a matrix X equal to B that you want to solve. You want to solve that very, very fast. Just this week, we do lattice population, that means we have a part and we populate with lattice. And within that a problem turned into a eigenvalue problem. That basically means we have a lot of small four by four matrices. Then you want to find the eigenvalues of those. And those eigenvalues are particular meaning and that helps us produce a very good looking lattice. So yeah, linear algebra for us is sort of a very core bread and butter for the geometry related algorithms we design, and I certainly find it a fascinating area. It's very well developed, there are a lot of libraries out there to get started from. Yeah. 100%.

Rafael Testai: 35:26

Okay. What's something that I haven't asked you that I should have asked you?

Hardik Kabaria: 35:32

Oh, definitely. Not really something that comes to my mind. I'd say, if you're thinking about like, as an engineer, what, what sort of is that important to me? Like, what skills to have? What skills not to have? I would say, don't worry about that. Find the problems that you like and pursue it. I would say that it's a case been my journey. I never thought competition or geometry would have a career. And specifically not in 3D printing. But it certainly was. It was a good opportunity. And so far, it has been, it seems very rewarding opportunity. And if you are an engineer out there interested in exploring these ideas, then we certainly have a growing software team. You should reach out to us.

Rafael Testai: 36:23

Okay, I want to dig a little bit deeper on that one. So don't worry about the skills, find the problems you want to solve. That's very good advice that I heard before. Very reasonable. But then the follow up is how do you find the problems you want to solve?

Hardik Kabaria: 36:38

I agree, it's very hard

Rafael Testai: 36:39

Right?

Hardik Kabaria: 36:40

It is very hard. It is, yeah, it's very hard. And I would say the only way it often happens is through exposure. You talk to people around you look at the problems, quite as an engineer quite a bit of us are hammer a nail and totally I am like that. I had a hammer of genetic tetrahedral mesh. So I went looking around for nail. And turns out 3D printing was one of those nails and decided to apply it. With that also works. But basically, I would say expose yourself to a lot of problems, and something probably will appeal to you.

Rafael Testai: 37:20

Okay, I think that's a wonderful message for all of our audience, younger and older, it's never too late to follow what problem you want to solve. And if they have any last comments for our listeners.

Hardik Kabaria: 37:36

No, thanks for having me and it has been a great conversation.

Rafael Testai: 37:39

Of course. Thanks for joining us.

Hardik Kabaria: 37:41

Thanks.

Aaron Moncur: 37:45

I'm Aaron Moncur, Founder of Pipeline Design & Engineering. If you liked what you heard today, please share the episode. To learn how your team can leverage our team's expertise developing turnkey equipment, custom fixtures and automated machines and with product design, visit us at teampipeline.us. Thanks for listening.