Research

⌘R in 3D Space

3D Shape Rule Applicatoin in Computer-Aided Design Systems

University of Kansas
2025

Right after the successful implementation of 3D shape embedding ⌘F, the immediate next milestone is the development of 3D shape rule application, ⌘R. While ⌘F marks a critical breakthrough in enabling machines to perceive and embed three-dimensional shapes, the application of rules through ⌘R is the true engine that drives design processes forward. The ability to apply shape rules directly to embedded geometries transforms abstract computation into tangible design actions, making this module far more impactful for practical workflows. In a recent unedited demonstration video, the performance of ⌘R proved not only efficient but, most importantly, correct. This accuracy is crucial, as it validates the reliability of the algorithms that have been under development since 2019. What this demo confirms is more than functionality—it verifies that the conceptual framework, mathematical rigor, and implementation strategies pursued over the past six years have finally converged into a working system. Achieving this milestone required countless iterations, overcoming challenges of recognition, matching, and transformation in three-dimensional space, a problem long regarded as computationally intractable. The success of ⌘R demonstrates that the system can execute precise rule-based transformations while preserving the integrity of embedded shapes, a key requirement for design applications. It represents the shift from merely recognizing shapes to actively generating new forms in a rule-governed yet flexible way. Seeing the algorithm operate seamlessly in real time, with both speed and accuracy, marks the culmination of years of effort and persistence. Six years of research, trial, and refinement have led to this moment: the realization of 3D shape rule application as a functioning computational design tool. Together, ⌘F and ⌘R lay the foundation for the next era of visual computation, where machines not only see shapes but can also manipulate them creatively in ways directly meaningful to design practice.