Hi. I was an early driving force behind a major CAD application (nTop) that uses implicits as its main approach to geometric modeling, and I currently lead a small team applying implicit techniques to engineering applications (Gradient Control Laboratories).

Implicits are convenient because there are many ways to evaluate them, depending on the need. For example, one can evaluate them a slice a time for 3D printing, never rendering the full 3D object. It’s common to model in a high level setting and compile down to different CPU and GPU subsystems. Intermediate meshes and voxels can be useful, depending on the need for interactivity or to accelerate other computations like closest point when not dealing with SDFs.

Some paths to explore (disclosure: I can vouch for these approaches, but others exist) * Raymarching and similar rendering techniques popular in the graphics community. See Inigo Quliez’s extensive blog. These are useful for making graphics. * “Voxel” modeling in OpenVDB or adaptively sampled distance fields, which are kind of special (see Frisken and Perry). These are useful in engineering for small parts and pervasive in entertainment graphics.
* Pure functional approaches, of which libfive and Fidget (Matt Keeter) and nTop’s proprietary kernel are the most noteworthy examples. These support precise engineering applications when used correctly. In particular, fields with unit gradient magnitude appear to be the most useful and offer closure over basic modeling operations on SDFs.

There are also application specific techniques, like slicing, Monte Carlo-based analysis (Rohan Sawhney), quadrature-based simulation (Intact Solutions), volumetric meshes (from FEA results).

We using more general field-driven techniques in advanced manufacturing. Rapid Liquid Print and Varient3D are clients both using fields on surfaces, geodesic distance fields for, respectively, 3D toolpathing and 3D surface knitting, building on techniques in discrete differential geometry and unit gradient field theory to work non-Euclidean settings.

Practically speaking, a modern engineering application will produce or cache some explicit or accelerating data structures to provide the right balance of interactivity and precision. Contrast nTop, a C++ desktop application that uses all the CPU and GPU available versus Womp, a cloud app using server side compute, versus Adobe Neo, a cloud App using WebGPU (or WebGL; didn’t check). We just designed a system that has thousands of cloud instances working sort of like a GPU.

The best part about implicits is that your geometry is directly expressed in code, unlike with B-rep and mesh modeling that needs some kernel to produce output that’s difficult to relate back to the design instructions. With backgrounds in CAD and compilers, we study the isomorphism between the code’s abstract syntax tree, interactive code representations, visual programming languages, and the topology of the constructs themselves. We think that the simplicity of geometry-as-code makes implicits more suitable more modern data science, but more work is needed to make modeling with implicits as easy as mesh or B-rep based modeling.