It is kinda neat, but OpenSCAD's limitations are the main thing that motivated me to write this Python library to generate 3D meshes used signed distance functions:
Just started using OpenSCAD recently and love it. While most CAD tools have a million features to learn, OpenSCAD is completely described by a cheat sheet you could print on a piece of A4 (like most programming languages).
I would really recommend using the git master than the latest release though. The last release was 2021 but they are still actively working on it and it's much faster now.
I also have to recommend the BOSL2 library which means you don't have to implement all of those one million features from typical CAD software yourself. Its definitely got a bit of a learning curve but the fact that you can always default back to vanilla OpenSCAD and that you can actually see how stuff is implemented makes it much more satisfying to me to learn than learning what all the traditional CAD GUI buttons do.
> I would really recommend using the git master than the latest release though.
This. The master version is so much further ahead of the last tagged version. The render time can be orders of magnitude faster for more complex models.
Commenting off of you since I wrote all of this and then realized it's basically exactly what you're saying. But to +1 everything you just said in my own words:
I love OpenSCAD. I've been 3D printing for a while, but I never really got to a place where I could design interesting parts until I started to get the precision of doing models in code. Sometimes it is slower, for sure.
Every time I've used as a CAD GUI program I would get to this point where I would need to alter a single dimension by 0.25mm and realize that _all_ of my fastener holes, cutouts, etc have to be nudged with the keyboard or mouse to accommodate it. The input devices lack precision for that kind of task, and having to repeat the operation dozens of times (or bulk select) gave me a terrible sinking feeling, and I'd often just step away and give up on the design at that point out of frustration. I try to approach everything in OpensSCAD in a way that means I never have to experience that feeling again.
I will also say that doing everything from scratch in OpenSCAD would be it's own special kind of hell. Libraries like [BOSL2](https://github.com/BelfrySCAD/BOSL2) provide a good set of core ideas and preferences that help set you on a good path. A good example: BOSL2 shapes tend to have a "center origin" by default, which is different than the OpenSCAD default, but makes doing transforms later way easier.
Anyway, happy to see OpenSCAD getting some attention here :)
> Every time I've used as a CAD GUI program I would get to this point where I would need to alter a single dimension by 0.25mm and realize that _all_ of my fastener holes, cutouts, etc have to be nudged with the keyboard or mouse to accommodate it.
There seems to be some fundamental misunderstanding of CAD here. I can't imagine how you could even design something in CAD in a way that you would end up in this situation.
A properly parameterized model shouldn't have the issue with having to nudge everything manually after a trivial change.
I had the change the height of an entire enclosure to accommodate a taller than anticipated PCB, and simply edited the sketch at the top of my design tree that defined the overall dimensions.
It took about 5 minutes to adjust the odd broken fillet and change some mates in assembly and it was done. No fidgety mouse movements. I actually do a lot of mech design on a laptop with a trackpad, arrow keys for view changes and numeric dimensioning for 95% of everything else.
> Every time I've used as a CAD GUI program I would get to this point where I would need to alter a single dimension by 0.25mm and realize that _all_ of my fastener holes, cutouts, etc have to be nudged with the keyboard or mouse to accommodate it.
I am just starting to learn CAD and FreeCAD - also dabbled a bit in OpenSCAD. But I do know that FreeCAD has Spreadsheets [1] and Configuration Tables [2] which allows you to define your model parameterically and changes values as needed.
>Every time I've used as a CAD GUI program I would get to this point where I would need to alter a single dimension by 0.25mm and realize that _all_ of my fastener holes, cutouts, etc have to be nudged with the keyboard or mouse to accommodate it.
What.
This makes no sense. This isn't PowerPoint; your holes and cutouts are supposed to be parameterized. How are they even supposed to be at the proper position in the first place?
As a CAD user, this is like e.g. a coder seeing someone write code with global variables everywhere.
The great thing about OpenSCAD is that it makes it easy to 3D model things which may be described using spheres, cylinders, and cubes which are stretch, and/or rotated, and arranged in 3D space.
The awful thing about OpenSCAD is that what one can model in 3D is limited by one's ability to mathematically stretch, rotate, and/or arrange spheres, cylinders, and cubes in 3D.
For folks who want "real" (read mutable in normal terms of scope) variables there is a Python-enabled fork (which should become part of the main release presently:
> The great thing about OpenSCAD is that it makes it easy to 3D model things which may be described using spheres, cylinders, and cubes which are stretch, and/or rotated, and arranged in 3D space.
It also has hulls and minkowski sums, which are powerful once you understand them.
Aren't hulls just a direct connection of the edges of two shapes (which could be simulated by a series of duplications) while Minkowski is "just" a matter of putting spheres along the edges of an object to round the straight edges?
So, spheres and cylinders and cubes placed, rotated, stretched and placed mathematically.
Not just that but it also positions everything in absolute coordinates and does not have the ability to reason about solids, just surfaces. Basically if you want to model something like a bolt you need to create a cylinder for the shaft, a separate head of the bolt, and then a thread profile you can rotate around the cylinder. You must ensure there is enough overlap between these three separate parts so the resultant object is a single surface and not three separate ones.
You can use modules to create a semblance of relative measurements but you still cannot do things like “attach this surface of object A to that surface of object B)”. In practice this means that if you want to create something like a spacer or a bracket you can do that easily enough. But if you want to make a part that matches some real world design you are stuck doing a lot of caliper measurements and math to try to create a part that lines up correctly. The you 3D print it and find that you positioned some hole based on its edge and not center and so nothing quite fits.
OpenSCAD is easy to start but difficult to scale because of these limitations and because once you hard-code any measurement you are stuck with it. The “proper” way to do this is to give everything a variable but honestly that makes reasoning about how to line things up even more difficult. “Does base_width include the width of the vertical walls? What about the margin to make the parts fit together?”
I have never been able to understand how things like FreeCAD lay out their UI. TinkerCAD is relatively simple but clearly a lot less powerful. I did try cadquery which solved a lot of OpenSCAD’s issues by having all offsets be relative by default but also introduces a few issues of its own.
One tip I will give about OS: grab a copy of the latest beta/dev release. The renderer is several orders of magnitude faster.
Another interesting option is FreeCAD, which is scriptable in Python but its primary interface is a GUI. So you can use a script to create things programmatically, edit graphically, or both.
FreeCAD sounds great but in practice it’s sooo slow.
If you are coming from SolidWorks, Fusion360, Inventor, or OnShape, it won’t take long before you start finding that there are a lot of things missing from it.
I'm coming from Fusion, advanced hobbyist, I can't find anything missing. </anecdata>
There is a problem though - sometimes what you want requires deep understanding. It's less user friendly, polished, and documented. That's also relevant to the performance - it's easy to cause performance issues. But I remember the same was also applicable to Fusion.
From my testing, the CSG operations, with post-processing, don’t produce watertight meshes. And being focused on printing, it doesn’t support different colors for the CSG operands. My use case is animation/games, so I’m reimplementing the CSG with a watertight b-rep.
Don't people think this is one tool that would greatly benefit from using the very fastest languages available? Where's the C++, Rust, maybe even FORTRAN version?
This is only the language for describing the volumes. That's not heavy, rather the importance is that you can express the ideas you want. The heavy lifting of rendering and computing how volumes interact etc is already implemented in native code.
I ended up adding the https://github.com/BelfrySCAD/BOSL2 library to OpenSCAD and it had some reasonable options for some gear and rack-and-pinion modeling that I needed to do.
(3D printing a sacrificial gear for a seat position adjustment mechanism)
For me as a casual 3d-modeler, my favorite thing about OpenSCAD is that I don't have to learn a new application the size of Photoshop with everything hidden 7 levels deep in some menu that is probably intuitive for some people who learned CAD in the 80s.
Instead it's basically like graphics programming, with a couple of basic primitives, some linear transformations and a bit of set theory. When I do a model a month and get back to previous work, I read a few lines of code and know exactly how I achieved the result.
I was once a big OpenSCAD user myself but I'm really skeptical that there are many use cases where it's actually more intuitive than a traditional CAD program, even if you're a programmer. It's true CAD programs have a huge amount of features but the basic sketch, extrude, revolve, and loft tools aren't conceptually difficult and are basically the same between Onshape, Fusion, Solidworks, etc. Those tools are sufficient to make 99.99% of OpenSCAD models I'm seeing.
I also have the opposite experience about understanding previous scripts. Unless it's dead simple I'm usually thinking why the hell did I multiply this thingy by sqrt(3)/2 plus this other thing. Maybe a documentation problem, but it's inescapable that sometimes you need a lot of math for what are trivial constraints in an interactive sketch. A real CAD program will let you roll back to any feature to figure out how it's constructed step by step so there's really nothing to decipher.
I've been trying to model joints for woodworking, and in traditional tools, the shapes I wish to arrive at verge on nightmarish, while I was able to knock them out in OpenSCAD in pretty short order --- except that when I sent a 1" x 2" x 1" test joint to a CAM program, it took some 18 minutes and generated a ~140MB G-code file, hence my working on:
I went from OpenSCAD -> cadquery/build123d -> Zoo/KCL
It still is early days, and it needs some more helper functions but it's really nice having two-way capabilities (not just code -> model, but also the reverse).
Of course having Text-to-model as a first class citizen is also nice.
I have played with this but been underwhelmed. However I do think probably on the right track.
I know the ecosystem not-at-all (sum total knowledge of the CAD ecosystem is that my kids got a Bambu printer for Hanukkah) but it feels to me that current LLMs should be able to generate specs for something like https://partcad.readthedocs.io/en/latest/, which can then be sliced etc.
Curious to know what others think? I come at this from the position of zero interest in developing the fine design skills needed to master but wanting to be able to build and tweak basic functional designs.
Mind you, it can't export to step file. That makes it impossible to re-use the models in other CADs to make assimblies. Also it's tedious to use for 3d printing when you want to include modifier objects with your model. Otherwise it's great and good enough for part modeling
It's super useful, been using with my 3D printer to print things such as an adapter to connect a Canon EF lens to night vision tube and parts to link motorised linear stages together.
If you are a programmer OpenSCAD is likely for you. It certainly has benefits in things that are repeating patterns (gears and such)...and if your mind is good at visualizing things in "code" things will likely go a lot faster.
I personally do better with CAD software such as fusion or freecad since my mind doesn't work in the code realm since I have more of a hardware mindset. Translating the picture in my head to code is more difficult than drawing it using the standard CAD set of tools.
My opinion on OpenSCAD is that it is a very useful piece of software which many have used to make some very interesting things. If you have a background in code I recommend giving it a go. I largely view it as "the coder's CAD".
It’s still strictly worse than what these models are capable of for general-purpose coding, but for simple tasks where precision isn't the bottleneck, it's surprisingly decent.The "aha" moment for me was an image-to-object workflow: found a geometric design on the web --> generated OpenSCAD to match the image --> 3D printed it. Going from seeing a JPEG to holding the physical object in a few hours.
I find myself using OpenSCAD regularly to 3D print little things for the house. (Most recently: hooks to attach Christmas lights to our roof deck's glass walls)
And when something gets too trick, ChatGPT is amazing at writing in it. Often it nails the whole design in the first try, like https://bsky.app/profile/bradfitz.com/post/3maelwomyw22n to mask off certain Raspberry Pi pins to make reassembly of projects easier later.
This is important and should be a given. But the more interesting challenge is to highlight the object you’re editing (where your cursor is). It’s not clear even how to exactly visualize it (it could be inside subtract of union of subtract etc).
OpenSCAD has become my go to with my 3-D printer for dumb little things. And the best part is LLMs are getting decent / pretty good with it!
My favorite thing I’ve printed is a little downsize coupler for the cool shirt system I built for my spec miata. It’s realllly silly & small thing, but it saved me!
openscad is quite nifty for small geometric projects. unfortunately it lacks some Features that make most bigger cad programs really useful... for example: - the ability to select faces/paths from a render, which can be hugely helpful when modifying complex models. - the ability to do constrained sketching in both 2d and 3d - caching at intermediate render levels - nested Projects and joining parts with mechanical constraints. it's still pretty nifty but very niche. I personally would dream of having the tools of a tool like fusion 360 or Catia, but in a gilly textual progemmatic way, while keeping the ability to select objects from the rendrr view.
OpenSCAD is great! I used it to create a bunch of things to cut on a CNC router over the years. Best achievements were a scale model of Mount Rainier and some one-piece picture frames with text cut into them.
Yes. The "official release" is just so old as to be useless at this point. They should either update it or take it down and point people at github or something, IMO.
I use the latest version all the time. The newer renderer ("manifold", IIRC) is much faster, and there are newer facilities that make it possible to build 3MF files containing multiple objects for multi-color printing, though that takes a bit of thought to do correctly.
Yes everything this person said is correct. The Manifold backend is no joke, probably 100x faster.
To do multi-color printing it’s pretty easy now, just turn on the poorly named feature in preferences called “lazy-unions”. This will make it so that each top level object in your file gets exported as a separate subobject in the 3mf file.
Yes, but the main downloads on the site are very old for some reason. Just get the nightly version instead, and then in Preferences -> Advanced -> Backend change it to “Manifold”. It will make your models “render” 10x faster (or more!).
I love the model, it's nice to be able to generate things parametrically instead of grabbing knots with the mouse. so I use scad pretty often.
but it has real problems -
the language is weird and unfortunate. not anything super fatal, just the obvious product of evolution that would be more cohesive if it were architected wholesale
epsilons are really unfortunate. you have to expect that after getting what you want in the whole, you're going to have to scan over the whole thing and look for cracks or collision where there shouldn't be
performance is quite sad. here you are happy going back and forth between the view and text windows, but as you go on, it starts taking .. minutes.. to update the view once you have a reasonably complicated geometry
high-level operators would also be nice. I made the mistake of using a thread library once, not only did that make my model unrenderable, there was so much noise in the model and the manufacturing process I had to make 3 expensive test prints in sintered nylon to get the fit right. (I'm thinking an annotation on a cylinder that says 'standard 1mm thread')
It actually renders things incredibly fast if you get the nightly version and set the backend to Manifold. It is probably 100x faster (!!). In fact it renders so fast that I put a render() command at the top of my hierarchy so that everything just renders all the time, it’s faster and more performant. I make incredibly complex models with it too, with hundreds of holes, complex svg files with text in them, etc.
I'm a programmer. I once had an idea stuck in my head for a 3d model that I just needed to get down somewhere. I tried learning the basics of AutoCAD but after 2 days of tutorials I still felt overwhelmed.
I looked into alternatives and learned about OpenSCAD. The immediate visual feedback makes picking up the language a breeze. Within an hour of downloading I familiarized myself with the language and had manifested my idea into a 3d model
I think that's a perfect example of a use-case where OpenSCAD shines. It's extremely easy to pick up if you have programming experience and it might even be a good thing to learn before moving onto more professional CAD software. From a teaching perspective, being able to have almost immediately-useful output is priceless
The thing is, I've crashed-and-burned every time I've tried to do traditional 3D CAD --- the closest I've come to success was making it all the way through the tutorial for Dune 3D:
OpenSCAD "just works", even on quite limited hardware, and if one has trouble modeling something, well, arriving at a solution is just a matter of learning the appropriate mathematics.
https://github.com/fogleman/sdf
One big plus to doing it this way is that it's "just" Python and you can use arbitrary logic to help construct your model.
You can even load an existing 3D mesh and operate on it as an SDF. Great for hollowing, chopping, eroding/dilating, etc. existing models.
I should probably do more with this project. I think there's a lot of interest in this space.
I would really recommend using the git master than the latest release though. The last release was 2021 but they are still actively working on it and it's much faster now.
I also have to recommend the BOSL2 library which means you don't have to implement all of those one million features from typical CAD software yourself. Its definitely got a bit of a learning curve but the fact that you can always default back to vanilla OpenSCAD and that you can actually see how stuff is implemented makes it much more satisfying to me to learn than learning what all the traditional CAD GUI buttons do.
This. The master version is so much further ahead of the last tagged version. The render time can be orders of magnitude faster for more complex models.
I love OpenSCAD. I've been 3D printing for a while, but I never really got to a place where I could design interesting parts until I started to get the precision of doing models in code. Sometimes it is slower, for sure.
Every time I've used as a CAD GUI program I would get to this point where I would need to alter a single dimension by 0.25mm and realize that _all_ of my fastener holes, cutouts, etc have to be nudged with the keyboard or mouse to accommodate it. The input devices lack precision for that kind of task, and having to repeat the operation dozens of times (or bulk select) gave me a terrible sinking feeling, and I'd often just step away and give up on the design at that point out of frustration. I try to approach everything in OpensSCAD in a way that means I never have to experience that feeling again.
I will also say that doing everything from scratch in OpenSCAD would be it's own special kind of hell. Libraries like [BOSL2](https://github.com/BelfrySCAD/BOSL2) provide a good set of core ideas and preferences that help set you on a good path. A good example: BOSL2 shapes tend to have a "center origin" by default, which is different than the OpenSCAD default, but makes doing transforms later way easier.
Anyway, happy to see OpenSCAD getting some attention here :)
There seems to be some fundamental misunderstanding of CAD here. I can't imagine how you could even design something in CAD in a way that you would end up in this situation.
I had the change the height of an entire enclosure to accommodate a taller than anticipated PCB, and simply edited the sketch at the top of my design tree that defined the overall dimensions.
It took about 5 minutes to adjust the odd broken fillet and change some mates in assembly and it was done. No fidgety mouse movements. I actually do a lot of mech design on a laptop with a trackpad, arrow keys for view changes and numeric dimensioning for 95% of everything else.
I am just starting to learn CAD and FreeCAD - also dabbled a bit in OpenSCAD. But I do know that FreeCAD has Spreadsheets [1] and Configuration Tables [2] which allows you to define your model parameterically and changes values as needed.
How good this is, I don't know yet.
[1] https://wiki.freecad.org/Spreadsheet_Workbench [2] https://wiki.freecad.org/Configuration_Tables
What.
This makes no sense. This isn't PowerPoint; your holes and cutouts are supposed to be parameterized. How are they even supposed to be at the proper position in the first place?
As a CAD user, this is like e.g. a coder seeing someone write code with global variables everywhere.
The awful thing about OpenSCAD is that what one can model in 3D is limited by one's ability to mathematically stretch, rotate, and/or arrange spheres, cylinders, and cubes in 3D.
For folks who want "real" (read mutable in normal terms of scope) variables there is a Python-enabled fork (which should become part of the main release presently:
https://pythonscad.org/
It also has hulls and minkowski sums, which are powerful once you understand them.
So, spheres and cylinders and cubes placed, rotated, stretched and placed mathematically.
You can use modules to create a semblance of relative measurements but you still cannot do things like “attach this surface of object A to that surface of object B)”. In practice this means that if you want to create something like a spacer or a bracket you can do that easily enough. But if you want to make a part that matches some real world design you are stuck doing a lot of caliper measurements and math to try to create a part that lines up correctly. The you 3D print it and find that you positioned some hole based on its edge and not center and so nothing quite fits.
OpenSCAD is easy to start but difficult to scale because of these limitations and because once you hard-code any measurement you are stuck with it. The “proper” way to do this is to give everything a variable but honestly that makes reasoning about how to line things up even more difficult. “Does base_width include the width of the vertical walls? What about the margin to make the parts fit together?”
I have never been able to understand how things like FreeCAD lay out their UI. TinkerCAD is relatively simple but clearly a lot less powerful. I did try cadquery which solved a lot of OpenSCAD’s issues by having all offsets be relative by default but also introduces a few issues of its own.
One tip I will give about OS: grab a copy of the latest beta/dev release. The renderer is several orders of magnitude faster.
Manifold backend also eliminates the need to avoid coincident faces.
Which avoids using the OpenSCAD language, but also means you can't use BOSL2. Might as well use FreeCAD.
If you are coming from SolidWorks, Fusion360, Inventor, or OnShape, it won’t take long before you start finding that there are a lot of things missing from it.
There is a problem though - sometimes what you want requires deep understanding. It's less user friendly, polished, and documented. That's also relevant to the performance - it's easy to cause performance issues. But I remember the same was also applicable to Fusion.
https://openjscad.xyz/
https://github.com/jscad/OpenJSCAD.org
https://replicad.xyz/
If you wish to use Rust for 3D modeling directly there is:
https://fornjot.app/
(the developer of which is actually working on a BREP kernel)
(3D printing a sacrificial gear for a seat position adjustment mechanism)
Instead it's basically like graphics programming, with a couple of basic primitives, some linear transformations and a bit of set theory. When I do a model a month and get back to previous work, I read a few lines of code and know exactly how I achieved the result.
I also have the opposite experience about understanding previous scripts. Unless it's dead simple I'm usually thinking why the hell did I multiply this thingy by sqrt(3)/2 plus this other thing. Maybe a documentation problem, but it's inescapable that sometimes you need a lot of math for what are trivial constraints in an interactive sketch. A real CAD program will let you roll back to any feature to figure out how it's constructed step by step so there's really nothing to decipher.
https://github.com/WillAdams/gcodepreview
I went from OpenSCAD -> cadquery/build123d -> Zoo/KCL
It still is early days, and it needs some more helper functions but it's really nice having two-way capabilities (not just code -> model, but also the reverse).
Of course having Text-to-model as a first class citizen is also nice.
I know the ecosystem not-at-all (sum total knowledge of the CAD ecosystem is that my kids got a Bambu printer for Hanukkah) but it feels to me that current LLMs should be able to generate specs for something like https://partcad.readthedocs.io/en/latest/, which can then be sliced etc.
Curious to know what others think? I come at this from the position of zero interest in developing the fine design skills needed to master but wanting to be able to build and tweak basic functional designs.
Currently I'm playing with a gear library which is part of BOSL2 (https://github.com/BelfrySCAD/BOSL2/wiki/gears.scad), to make something to rotate a polariser in my microscope.
I personally do better with CAD software such as fusion or freecad since my mind doesn't work in the code realm since I have more of a hardware mindset. Translating the picture in my head to code is more difficult than drawing it using the standard CAD set of tools.
My opinion on OpenSCAD is that it is a very useful piece of software which many have used to make some very interesting things. If you have a background in code I recommend giving it a go. I largely view it as "the coder's CAD".
https://github.com/rahulgarg123/openscad-mcp
It’s still strictly worse than what these models are capable of for general-purpose coding, but for simple tasks where precision isn't the bottleneck, it's surprisingly decent.The "aha" moment for me was an image-to-object workflow: found a geometric design on the web --> generated OpenSCAD to match the image --> 3D printed it. Going from seeing a JPEG to holding the physical object in a few hours.
And even if it’s not perfect it saves a lot of time looking up the documentation and generally gets the relationships between objects right.
https://makerworld.com/en/models/2040939-accessible-christma...
And when something gets too trick, ChatGPT is amazing at writing in it. Often it nails the whole design in the first try, like https://bsky.app/profile/bradfitz.com/post/3maelwomyw22n to mask off certain Raspberry Pi pins to make reassembly of projects easier later.
My favorite thing I’ve printed is a little downsize coupler for the cool shirt system I built for my spec miata. It’s realllly silly & small thing, but it saved me!
https://github.com/gumyr/build123d
Ok if you want to generate a couple of cubes, but if you want anything advanced the kernel quickly falls apart
Which you can also use directly instead by writing C++. Trivial operations are two orders of magnitude faster and complex ones every faster.
https://github.com/WillAdams/gcodepreview
It's neat that I can tell the computer what I want in words and then have that object come out of the 3D printer
I use the latest version all the time. The newer renderer ("manifold", IIRC) is much faster, and there are newer facilities that make it possible to build 3MF files containing multiple objects for multi-color printing, though that takes a bit of thought to do correctly.
To do multi-color printing it’s pretty easy now, just turn on the poorly named feature in preferences called “lazy-unions”. This will make it so that each top level object in your file gets exported as a separate subobject in the 3mf file.
That said, there are often times software gets so stable that not having a new release for years is fine. Maybe this is one of them?
(I'm very new to OpenSCAD so I haven't run into bugs yet... But maybe it's pretty solid?)
https://openscad.org/downloads.html#snapshots
but it has real problems - the language is weird and unfortunate. not anything super fatal, just the obvious product of evolution that would be more cohesive if it were architected wholesale
https://pythonscad.org/
The big distinction is that those work implicitly, while OpenSCAD requires you to be implicit.
I looked into alternatives and learned about OpenSCAD. The immediate visual feedback makes picking up the language a breeze. Within an hour of downloading I familiarized myself with the language and had manifested my idea into a 3d model
I think that's a perfect example of a use-case where OpenSCAD shines. It's extremely easy to pick up if you have programming experience and it might even be a good thing to learn before moving onto more professional CAD software. From a teaching perspective, being able to have almost immediately-useful output is priceless
https://www.blockscad3d.com/editor/
I just wish that they'd add the balance of the language/fix some bugs.
https://news.ycombinator.com/item?id=37979758
https://news.ycombinator.com/item?id=40228068
OpenSCAD "just works", even on quite limited hardware, and if one has trouble modeling something, well, arriving at a solution is just a matter of learning the appropriate mathematics.