4 ms·

> This is why most geometry kernels (see open cascade) sport things like "fuzzy boolean operations" [0]) that lean into epsilons. These epsilons mask the error-

> This is why most geometry kernels (see open cascade) sport things like "fuzzy boolean operations" [0]) that lean into epsilons. These epsilons mask the error-prone supply chain of these meshes that arrive in your program by allowing some tolerance. They don’t just lean into epsilons, the session context tolerance is used for almost every single point classification operation in geometric kernels and many primitives carry their own accumulating error component for downstream math. Even then the current state of the art (in production kernels) is tolerance expansion where the kernel goes through up to 7 expansion steps retrying point classification until it just gives up. Those edge cases were some of the hardest parts of working on a kernel. This is a fundamentally unsolvable problem with floating point math (I worked on both Parasolid and ACIS in the 2000s). Even the ray-box intersection example TFA gives is a long standing thorn - raytracing is one of the last fallbacks for nasty point classification problems.

MarkusQ 6mo ago
> They don’t just lean into epsilons, the session context tolerance is used for almost every single point classification operation in geometric kernels and many primitives carry their own accumulating error component for downstream math. The GP wasn't wrong. To "lean in" means to fully commit to, go all in on, (or, equivalently, go all out on).
- vouwfietsman 6mo ago
  I think his point is: rather than "leaning into" it as in, masking through epsilons, he argues that tolerance is fundamental to the problem space, not a way to resolve edge cases.
  - MarkusQ 6mo ago
    Right. And my point is that "leaning in" doesn't mean masking, it means committing to. Taking seriously. Exactly the sort of thing he's describing. I'm wondering if people have heard the expression "leaning in" from people who were insincere/lying, and assumed that that was what the phrase means?
    - juped 6mo ago
      I think you should revisit the word "just", its presence in the comment you're trying to discuss, and how it's used.
      - MarkusQ 6mo ago
        To me it seems it's used with the intent "They don’t just <do X>, they <do Y>," implying that Y is a proper superset of X. My point is that X is in fact a superset of Y, making the most charitable reading "They don’t just <do X>, they <do X in more words>." Is there another potential reading of "just" that I'm missing?
jstanley 6mo ago
> This is a fundamentally unsolvable problem with floating point math It's a fundamentally unsolvable problem with B-reps! The problem completely disappears with F-reps. (In exchange for some other difficult problems).
- alterom 6mo ago
  >(In exchange for some other difficult problems). Ahhaha. (I used to work in nTop, and boy is this an understatement when it comes to field based solid modeling)
  - jstanley 6mo ago
    I was working on an SDF-based CAD tool but gave up when I couldn't find a good way to do fillets. It's very deceptive because the easy way works so well (Use smoothmin instead of min and you get smooth blends for free! You can even use a circular approximation of smoothmin and get proper fillets!). But when you want the user to be able to pick a couple of surfaces and fillet between them, it gets really hard. This is the best I got: https://www.youtube.com/watch?v=LOvqdlDbkBs https://www.youtube.com/watch?v=LOvqdlDbkBs It worked by rewriting the expression tree so that the blend arguments become sibling nodes and then applying the blend to the union/intersection that is their parent. That works every time if you only want 1 single targeted blend, but if you want several of them then you can run into unsatisfiable cases where the same object needs to blended with several others and can't be siblings of all of them. So I gave up :(. For me, CAD without fillets and chamfers is no CAD at all. (Also, apropos for this thread: the discontinuity in the chamfer was a floating point precision problem...)
    - alterom 6mo ago
      Well, user picking a couple of surfaces is literally an operation on a boundary representation, so of course it's a PITA with fields :) I think the future is CAD is combined fields and breps. They're literally dual, one is covariant, the other contravariant (breps facilitate pushforwards, fields facilitate pullbacks). One without the other is necessarily going to be limited in some way.
vouwfietsman 6mo ago
Nice thanks, gotta love knowing a bit about a niche and then encountering someone who knows a great deal more. That's the beauty of HN. Could you point to any literature/freely available resource that comes close to the SOTA for these kinds of operations? I would be greatly helped.

MarkusQ 6mo ago

> They don’t just lean into epsilons, the session context tolerance is used for almost every single point classification operation in geometric kernels and many primitives carry their own accumulating error component for downstream math. The GP wasn't wrong. To "lean in" means to fully commit to, go all in on, (or, equivalently, go all out on).

vouwfietsman 6mo ago
I think his point is: rather than "leaning into" it as in, masking through epsilons, he argues that tolerance is fundamental to the problem space, not a way to resolve edge cases.
- MarkusQ 6mo ago
  Right. And my point is that "leaning in" doesn't mean masking, it means committing to. Taking seriously. Exactly the sort of thing he's describing. I'm wondering if people have heard the expression "leaning in" from people who were insincere/lying, and assumed that that was what the phrase means?
  - juped 6mo ago
    I think you should revisit the word "just", its presence in the comment you're trying to discuss, and how it's used.
    - MarkusQ 6mo ago
      To me it seems it's used with the intent "They don’t just <do X>, they <do Y>," implying that Y is a proper superset of X. My point is that X is in fact a superset of Y, making the most charitable reading "They don’t just <do X>, they <do X in more words>." Is there another potential reading of "just" that I'm missing?

jstanley 6mo ago

> This is a fundamentally unsolvable problem with floating point math It's a fundamentally unsolvable problem with B-reps! The problem completely disappears with F-reps. (In exchange for some other difficult problems).

alterom 6mo ago
>(In exchange for some other difficult problems). Ahhaha. (I used to work in nTop, and boy is this an understatement when it comes to field based solid modeling)
- jstanley 6mo ago
  I was working on an SDF-based CAD tool but gave up when I couldn't find a good way to do fillets. It's very deceptive because the easy way works so well (Use smoothmin instead of min and you get smooth blends for free! You can even use a circular approximation of smoothmin and get proper fillets!). But when you want the user to be able to pick a couple of surfaces and fillet between them, it gets really hard. This is the best I got: https://www.youtube.com/watch?v=LOvqdlDbkBs https://www.youtube.com/watch?v=LOvqdlDbkBs It worked by rewriting the expression tree so that the blend arguments become sibling nodes and then applying the blend to the union/intersection that is their parent. That works every time if you only want 1 single targeted blend, but if you want several of them then you can run into unsatisfiable cases where the same object needs to blended with several others and can't be siblings of all of them. So I gave up :(. For me, CAD without fillets and chamfers is no CAD at all. (Also, apropos for this thread: the discontinuity in the chamfer was a floating point precision problem...)
  - alterom 6mo ago
    Well, user picking a couple of surfaces is literally an operation on a boundary representation, so of course it's a PITA with fields :) I think the future is CAD is combined fields and breps. They're literally dual, one is covariant, the other contravariant (breps facilitate pushforwards, fields facilitate pullbacks). One without the other is necessarily going to be limited in some way.

vouwfietsman 6mo ago

Nice thanks, gotta love knowing a bit about a niche and then encountering someone who knows a great deal more. That's the beauty of HN. Could you point to any literature/freely available resource that comes close to the SOTA for these kinds of operations? I would be greatly helped.