Blake Courter

Executive summary

• By including differentiable, parametric models in engineering processes, engineering software can better interoperate between human and artificial designers.
• Existing CAD, CAM, and CAE tools can speak this language by adding differential interoperability to their APIs.
• We provide a visually compelling introduction to differential engineering using a cantilevered beam.
• By examining the derivative of a rotation, we briefly unlock some deep math beauty and an application of Unit Gradient Fields (UGFs).
• Differentiable engineering scales to product level systems engineering.

✏️ Math advisory: this post assumes your okay with derivatives, the chain rule from basic calculus, and a little vector math. We will introduce intuitive visual tools to illustrate such concepts in design engineering. While I feel compelled to show the work, you can probably skim and glean the concepts from the illustrations.

👥 Lots of credit: These ideas came from discussions with many people, including:

• Sandilya Kambampati, Intact Solutions
• Luke Church, Gradient Control Laboratories
• Trevor Laughlin, nTop
• Jon Hiller, PTC
• Peter Harman, Infinitive

Introduction

If AI and ML are to participate in the team sport known as “engineering,” they will need not only to produce helpful results, but also fit in with the rest of the team, including human engineers. The situation seems unworkable today, where AI and ML frameworks, emerging computational tools, and even traditional, feature-based CAD appear designed to be used by human operators. For example:

• Generative design for new components via topology optimization typically produces incomplete models that require manual rework.
• The exploding market of simulation tools mostly promises to accelerate simulation but still requires traditional, manual, validation.
• Systems engineers can deploy MDO tools at product or subsystems levels, but such systems typically provide guidance during the concept phase and become reinterpreted by humans for detailed design.

If AI and ML promises to increase the size of the design space that engineers can navigate, how can we bridge these human gaps in the process? As generative design scales to the subsystem and product level, how can we connect all the pieces without the meaning becoming hidden in a nonintuitive latent space? How will we ever achieve the sci-fi dream of synthetic, cyber-physical systems if there must always be humans in the loop?

Abstracting the design engineer

Let’s propose a model for a design engineer, human or automated, which we’ll call “Mechanical Design Automation (MDA)”:

Here’s just the map!

There was a time when I could keep track of all the engineering software companies. We had a few big CAD and CAE vendors, a handful of smaller companies defying VC pressure, and a CAM company for every manufacturing market. 3D printers were things that our resellers lugged around but didn’t really work. Life was simple. I could keep it all in my head.

So far in the series, we’ve defined the basic idea that UGFs generalize SDFs and examined that when representing shapes, UGFs offer design freedom in the shapes’ normal cones. In most of the examples, we’ve shown that this freedom helps recapitulate the kinds of edge treatments we see in engineering software like rolling-ball blends and chamfers. In this post, we’ll take a look at the clearance and midsurface fields that apply to SDFs and the two-body field that applies to all UGFs.

Use the slider to change viewing modes:

The clearance field, \(\ugf{A} + \ugf{B}\,\), the midsurface field, \(\ugf{A} - \ugf{B}\,\), and the two-body field: \(\twobody{\ugf{A}}{\ugf{B}} \equiv \frac{\ugf{A} - \ugf{B}}{\ugf{A} + \ugf{B}}\). The clearance and midsurface fields are overlaid to demonstrate their orthogonality.

With the UGF research entering a public phase, some other collaborations from the background are entering the foreground. In particular, some investigations with some friends have evolved into two new entities: an incubator, Gradient Control Laboratories and its first spinoff, LatticeRobot!

Media coverage from CDFAM ‘23

3DPrint.com: LatticeRobot Launches a Home for Lattices, Metamaterials, and Textures

Develop3D: LatticeRobot announces community for advancing lattices in products

TCT: LatticeRobot launches engineering community for lattice research and knowledge share

Something seemed different about Sarah Frisken and Ron Perry, researchers from MERL who had ventured out to Boston’s Route 128 tech corridor to present their new modeling technology to the top geometry engineers at a leading CAD company. Frisken and Perry demonstrated that their adaptively sampled distance fields (“ADFs”) encoded geometry in a way where the offsets, Booleans, and rounded blends that confounded contemporaneous CAD systems like ours, would always succeed. They demonstrated organic texturing and lattices that would be unthinkable on state-of-the-art boundary representation (B-rep) solids. On the other hand, the modeling operations seemed limited to CSG operations, which had been superseded in mechanical CAD by the more expressive B-reps, and their only practical output was meshed geometry, considered inferior to B-reps. Would it be possible to combine the benefits of B-rep modeling with robust offsets, Booleans, and blends? It was 2001, I’d never seen anything like it, and I was hooked.

Many readers of the last post requested a more formal definition of a UGF. Let’s look a bit more closely at the definition of an SDF and how it compares to UGFs and other useful fields in engineering applications. Some readers may find the visual concepts more intuitive than the nuances, so let’s get a feel for the territory first by examining the field at the intersection of two planes:

For those of us who work in engineering and geometric modeling, “offset” is an everyday operation. We use it in 2D and 3D to produce curves and surfaces at constant distance from other curves and surfaces. With experience, we learn that offset can be failure-prone, especially with precise B-rep solids and meshes. Implicit modeling, in particular, the signed distance field (SDF) representation of shapes, offers robust offsetting, but again, with experience, we learn that the results aren’t always what we expect.

Take these three examples of an offset rectangle, created using three different “line joining” approaches that date back to the early days of 2D graphics and are built into your browser:

1 April 2023 (Fiction)

As mentioned yesterday, hyperbolic space is more spatially dense than Euclidean space, and therefore offers opportunities for higher performance and fidelity in engineering applications. In this case study, we’ll examine how to prepare ordinary Euclidean CAD and mesh geometry for embedding in hyperbolic space and manufacture in QE3D’s quantum entanglement production system.

Triangles in hyperbolic space

The key unit in any structural design, including beam lattices, is a triangle. In Euclidean space, the sum of the angles of set of triangles around a vertex must total 360°. In hyperbolic space, we can increase that total angle to any number we want, even ∞!