3 ms·

Same, but I don't think it's possible without a large and sustained investment into a free geometric modelling kernel, which can probably be only done by a gove

by dgroshev 11mo ago

Same, but I don't think it's possible without a large and sustained investment into a free geometric modelling kernel, which can probably be only done by a government. Parasolid is powering practically every major CAD system. Its development started in 1986 and it's still actively developed. The amount of effort that goes into those things is immense (39 years of commercial development!) and I don't believe it can be done pro-bono in someone's spare time. What's worse, with this kind of software there is no "graceful degradation": while something like a MIP solver can be useful even if it's quite a bit slower than Gurobi, a kernel that can't model complex lofts and fillets is not particularly useful. 3D CAD is much harder than Blender and less amenable to open source development.

LoganDark 11mo ago
> Same, but I don't think it's possible without a large and sustained investment into a free geometric modelling kernel, which can probably be only done by a government. Fornjot has been attempting this: https://www.fornjot.app https://www.fornjot.app It's going to be years or decades before it's competitive though. Also, it looks like they switched to keeping progress updates private except to sponsors, which means I don't actually have any easily-accessible information about it anymore which is sad.
- dgroshev 11mo ago
  I'm very skeptical that one person can make a dent. Paging through the releases, they seem to focus on constructive solid geometry and code-driven shape generation, which I believe is a dead end. The tricky bit is having a G2 (or even G3) fillet that intersects a complex shape built from surface patches and thickened, with both projected into a new sketch, and keeping the workflow sane if I go and adjust the original fillet. I hope one day we'll see a free (as in speech) kernel that can enable that, until then it's just Parasolid, sadly.
  - throwrb 11mo ago
    Isn't their project boundary representation? I read a couple of your CAD comments, what an interesting space. It never occurred to me how complex computing 3d geometries is.
deleted 11mo ago
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dr_dshiv 11mo ago
> Same, but I don't think it's possible without a large and sustained investment into a free geometric modelling kernel, which can probably be only done by a government. Can you help me understand why this problem is so hard?
- dgroshev 11mo ago
  The way modern CAD systems work is by having a tree of features/actions that is then used to construct an analytical representation of a 3D object. The features/actions can rely on "sketches" (2D drawings that are coupled with a real time geometric constraint solver) and can be "projected" into sketches, creating new reference lines, that can then be used by the sketch constrain solver, generating a sketch that can be used for more 3D features. This is already complex and fiddly enough. Just having a stable 2D drawing environment that uses a constraint solver but also behaves predictably and doesn't run into numerical instability issues is already an achievement. You don't want a spline blowing up while the user is applying constraints one by one! And yet it's trivial compared to the rest of the problem. Having 3D features analytically (not numerically!) interacting with each other means someone needs to write code that handles the interactions. When I click on a corner and apply a G2 fillet to it, it means that there's now a new 3D surface where every section is a spline with at least 4 control points. When I then intersect that corner with a sphere, the geometric kernel must be able to analytically represent the resulting surface (intersecting that spline-profiled surface with a sphere). If I project that surface into a sketch, the kernel needs to represent its outline from an arbitrary angle — again, analytically. Naturally, there is an explosion of special cases: that sphere might either intersect the fillet, just touch it (with a single contact point), or not touch it at all, maybe after I made some edits to the earlier features. Blender at its core is comparatively trivial. Polygons are just clumps of points, they can be operated on numerically. CAD is hell.
- CoreformGreg 11mo ago
  The other reply is really good. To add to that, the intersection of two bi-cubic Bezier patches (each being but one part of a cubic B-spline surface) is an implicit equation of degree 18^2=324. This simply cannot be implemented exactly in a geometry kernel and thus must be approximated. How do you want to approximate this? If you choose trimming (the industry standard) now you have to handle gaps in your geometry. If you choose remapping into an unstructured watertight spline, you need to solve a constraint system that is NP-hard. If you choose reparameterizing… well, see nVariate’s watertight Boolean technique (disclaimer: I once sponsored a project with nVariate). Now, generally speaking, in a CAD model most surfaces will be “analytic” (plane, torus, conical, arc, line, etc). But whenever some complex surface that joins these surfaces is required, (NUR)B-splines are the principal technique for “covering” the gap.

LoganDark 11mo ago

> Same, but I don't think it's possible without a large and sustained investment into a free geometric modelling kernel, which can probably be only done by a government. Fornjot has been attempting this: https://www.fornjot.app https://www.fornjot.app It's going to be years or decades before it's competitive though. Also, it looks like they switched to keeping progress updates private except to sponsors, which means I don't actually have any easily-accessible information about it anymore which is sad.

dgroshev 11mo ago
I'm very skeptical that one person can make a dent. Paging through the releases, they seem to focus on constructive solid geometry and code-driven shape generation, which I believe is a dead end. The tricky bit is having a G2 (or even G3) fillet that intersects a complex shape built from surface patches and thickened, with both projected into a new sketch, and keeping the workflow sane if I go and adjust the original fillet. I hope one day we'll see a free (as in speech) kernel that can enable that, until then it's just Parasolid, sadly.
- throwrb 11mo ago
  Isn't their project boundary representation? I read a couple of your CAD comments, what an interesting space. It never occurred to me how complex computing 3d geometries is.

deleted 11mo ago

[deleted]

dr_dshiv 11mo ago

> Same, but I don't think it's possible without a large and sustained investment into a free geometric modelling kernel, which can probably be only done by a government. Can you help me understand why this problem is so hard?

dgroshev 11mo ago
The way modern CAD systems work is by having a tree of features/actions that is then used to construct an analytical representation of a 3D object. The features/actions can rely on "sketches" (2D drawings that are coupled with a real time geometric constraint solver) and can be "projected" into sketches, creating new reference lines, that can then be used by the sketch constrain solver, generating a sketch that can be used for more 3D features. This is already complex and fiddly enough. Just having a stable 2D drawing environment that uses a constraint solver but also behaves predictably and doesn't run into numerical instability issues is already an achievement. You don't want a spline blowing up while the user is applying constraints one by one! And yet it's trivial compared to the rest of the problem. Having 3D features analytically (not numerically!) interacting with each other means someone needs to write code that handles the interactions. When I click on a corner and apply a G2 fillet to it, it means that there's now a new 3D surface where every section is a spline with at least 4 control points. When I then intersect that corner with a sphere, the geometric kernel must be able to analytically represent the resulting surface (intersecting that spline-profiled surface with a sphere). If I project that surface into a sketch, the kernel needs to represent its outline from an arbitrary angle — again, analytically. Naturally, there is an explosion of special cases: that sphere might either intersect the fillet, just touch it (with a single contact point), or not touch it at all, maybe after I made some edits to the earlier features. Blender at its core is comparatively trivial. Polygons are just clumps of points, they can be operated on numerically. CAD is hell.
CoreformGreg 11mo ago
The other reply is really good. To add to that, the intersection of two bi-cubic Bezier patches (each being but one part of a cubic B-spline surface) is an implicit equation of degree 18^2=324. This simply cannot be implemented exactly in a geometry kernel and thus must be approximated. How do you want to approximate this? If you choose trimming (the industry standard) now you have to handle gaps in your geometry. If you choose remapping into an unstructured watertight spline, you need to solve a constraint system that is NP-hard. If you choose reparameterizing… well, see nVariate’s watertight Boolean technique (disclaimer: I once sponsored a project with nVariate). Now, generally speaking, in a CAD model most surfaces will be “analytic” (plane, torus, conical, arc, line, etc). But whenever some complex surface that joins these surfaces is required, (NUR)B-splines are the principal technique for “covering” the gap.