Differentiable 3D CAD Programs for Bidirectional Editing

Abstract

Modern CAD tools represent 3D designs not only as geometry, but also as a program composed of geometric operations, each of which depends on a set of parameters. Program representations enable meaningful and controlled shape variations via parameter changes. However, achieving desired modifications solely through parameter editing is challenging when CAD models have not been explicitly authored to expose select degrees of freedom in advance. We introduce a novel bidirectional editing system for 3D CAD programs. In addition to editing the CAD program, users can directly manipulate 3D geometry and our system infers parameter updates to keep both representations in sync. We formulate inverse edits as a set of constrained optimization objectives, returning plausible updates to program parameters that both match user intent and maintain program validity. Our approach implements an automatically differentiable domain‐specific language for CAD programs, providing derivatives for this optimization to be performed quickly on any expressed program. Our system enables rapid, interactive exploration of a constrained 3D design space by allowing users to manipulate the program and geometry interchangeably during design iteration. While our approach is not designed to optimize across changes in geometric topology, we show it is expressive and performant enough for users to produce a diverse set of design variants, even when the CAD program contains a relatively large number of parameters.

Automatic Differentiable Procedural Modeling

“…However, one major limitation of their approach is that they use finite‐differences, which is slower and can cause numerical problems, whereas we use auto‐differentiation. Cascaval et al [CSQ ∗ 22] present another method close to ours. Their differentiable procedural model is expressed as a CAD program, which is conceptually equivalent to our graph‐based representation.…”

“…Our work is inspired by recent work on the differentiability of rendering [KBM ∗ 20], physics systems [dABPSA ∗ 18, HKUT20], and inverse control of parametric shapes [MB21, CSQ ∗ 22]. We build a proxy differentiable representation of the procedural model that allows for efficient computation of the derivatives of the output with respect to the model's parameters.…”

Certifiable Robot Design Optimization using Differentiable Programming

“…Of course, this is a deliberately narrow view of engineering design, since it focuses on parameter optimization and ignores important steps like problem formulation and system architecture selection. Our focus on parameter optimization is intentional, as it allows the designer to focus her creative abilities and engineering judgment on the architecture problem, using computational aids as interactive tools in a larger design process [10,11]. This focus is common in design optimization (e.g.…”

“…This focus is common in design optimization (e.g. aircraft design in [11] and 3D CAD optimization in [10]).…”

“…We can then use automatic differentiation to derive gradients connecting these parameters to the system's behavior and optimize accordingly. This view is inspired by recent work in 3D design optimization [10], aircraft design [11], and machine learning [12,13].…”