Research

⌘F in 3D Space

3D Shape Embedding in Computer-Aided Design Systems

University of Kansas
2025

Waiting has been far too long, but at last, it is here—3D Shape Embedding, ⌘F in 3D space! Since the proposal of shape grammar formalism in 1972, the shape grammar community has faced one of its most enduring challenges: building a true shape grammar interpreter in a digital environment (Dr. James Gips called this project as a dream for a Big Enchilada in 1999). Central to this challenge is shape embedding, the ability to recognize, match, and manipulate shapes directly as they are seen, rather than through symbolic descriptions or numerical abstractions. For decades, researchers across architecture, engineering, and computer science wrestled with this problem, and even the possibility of a fully functional 2D shape rewriting system seemed far beyond reach. That impasse held until 2018, when Shape Machine was introduced as the first working 2D shape rewriting system, finally demonstrating that direct computation with shapes was achievable. The success of this system marked a decisive turning point in the field and opened new directions for design computation. Since then, shape embedding has remained the central focus of my research, and the excitement within the shape grammar community at witnessing its 2D implementation was tremendous. Yet despite this critical breakthrough, the ultimate aspiration—to extend shape embedding into three dimensions—remained unfulfilled for decades, viewed as nearly impossible given the complexity of embedding in volumetric space. Today, that aspiration has finally materialized. With the introduction of the 3D Shape Embedding engine, we are no longer confined to planar interpretations but can now rigorously compute with three-dimensional shapes directly, preserving their visual integrity while enabling rule-based transformation and generation. This achievement represents not only the culmination of fifty years of vision and persistence but also the beginning of a new chapter in shape grammar research, one where machines can truly see and act with shapes in three dimensions.