polyhedra

This post will pose more questions than answers, since it seems we’re still in the “wild west” early days of popular adoption of a plethora of AI offerings, and I am hardly keeping up with all the developments in so many sectors as “everyone and their uncle” jumps on the proverbial AI bandwagon!

(I’m also in the midst of moving from Arizona back to Oregon, so this will be a quick commentary! I hope to have much more useful information, helpful resources, and examples in a future post!)

In prior posts, I’ve dabbled with some AI-generated geometric imagery:

• Digital dabbling with Dall-E (early primitive experiments)
• AI generated geometry – revisited a few months later (a little further along, but still nascent)

Here is an example from the more recent post:

Here is an example from the earlier post:

While the geometric imagery generated by artificial intelligence is often stunning, I typically notice that the images frequently don’t provide accurate models of precise geometric archetypes, being more oriented toward popular art and illustration than images for science, engineering, or renderings with CAD accuracy. If one looks closely, there are inconsistencies and “wonkiness” that don’t hold up to zoomed-in scrutiny if one wants the photorealism that ray-tracing software can achieve.

Do you know of websites, software, AI apps running on various platforms, browsers, devices, etc., that address this seeming void in AI functionality? I’m hoping that soon we’ll find mechanisms that assist in generating imagery with the same accuracy as ray-tracing software using precise geometric coordinates for the vertices of polyhedra, for example. If so, let me know via our contact form.

I found this web page of “AI Geometric Art Examples” by Open Art that looks promising, but when I click on the “… create …” buttons, I arrive at a more generic-looking interface. I’ll explore further when I have more time, but I’m eager to hear from readers if you’ve found good AI for geometry. Here’s a nice image from the page noted above:

I posed this query: “geometric image generation for science, engineering, renderings with CAD precision” to my browser (Brave) and got this response:

“Geometric Image Generation for Science
Recent advancements in geometric image generation for science, engineering, and high-precision renderings are increasingly focused on bridging the gap between visual data and parametric Computer-Aided Design (CAD) models. A significant development is the CADCrafter framework, which generates parametric CAD models directly from unconstrained real-world images, such as those captured by users with standard cameras.
This approach leverages a latent diffusion model conditioned on geometric features like depth and normal maps, which are invariant to texture and help mitigate the domain gap between synthetic training data and real-world images.
To ensure the generated CAD command sequences are geometrically valid, the model employs direct preference optimization (DPO) fine-tuning using feedback from an automatic CAD compiler, which acts as a code checker to categorize outputs as valid or invalid.

This method addresses the limitations of traditional generative models that produce 3D shapes with rough surfaces and indistinct edges, which lack the precision required for manufacturing and simulation.
By training solely on synthetic textureless CAD data and testing on real-world images, CADCrafter demonstrates robustness and generalization to unseen objects, even when processing single-view images.
The framework’s ability to distill knowledge from multi-view to single-view inputs enhances its accuracy and practicality for everyday applications.

Further, geometric deep learning (GDL) techniques are being applied to analyze and generate CAD data directly from complex representations like Boundary Representation (B-Rep), which encodes high-level parametric details.
GDL methods, including Graph Neural Networks (GNNs) and Transformers, are used for tasks such as similarity analysis, retrieval, synthesis, and autocompletion of CAD models, aiming to automate repetitive design tasks and facilitate design reuse.
These methods can learn intricate geometric features from B-Rep data without converting it to formats like meshes or point clouds, thus avoiding computational expense and information loss.

For applications involving imaging data, such as microtomographic scans, fast, realistic simulations on GPUs are used to generate synthetic CT images that include realistic artefacts like beam hardening and photon noise.
These simulations are crucial for creating accurate CAD models from data affected by strong imaging artefacts, enabling precise geometric analysis of materials and structures.
The gVirtualXray (gVXR) framework exemplifies this, simulating X-ray projections and CT volumes in milliseconds on a GPU, which is orders of magnitude faster than Monte Carlo simulations, while maintaining high accuracy.
This speed enables the use of repetitive simulations for tasks like image registration and training deep-learning algorithms.

These integrated approaches—combining image-to-CAD generation, geometric deep learning, and high-fidelity simulation—represent a transformative shift towards creating precise, editable, and manufacturable digital twins from diverse data sources, significantly enhancing workflows in science, engineering, and design.

AI-generated answer. Please verify critical facts.”

(Note the now familiar disclaimer in the last line.)

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