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.

We present a novel neural network architecture, termed Decomposer-Composer, for semantic structure-aware 3D shape modeling. Our method utilizes an auto-encoder-based pipeline, and produces a novel factorized shape embedding space, where the semantic structure of the shape collection translates into a data-dependent sub-space factorization, and where shape composition and decomposition become simple linear operations on the embedding coordinates. We further propose to model shape assembly using an explicit learned part deformation module, which utilizes a 3D spatial transformer network to perform an in-network volumetric grid deformation, and which allows us to train the whole system end-to-end. The resulting network allows us to perform part-level shape manipulation, unattainable by existing approaches. Our extensive ablation study, comparison to baseline methods and qualitative analysis demonstrate the improved performance of the proposed method.

This video describes a general framework for computing formulae enumerating polycubes of size n which are proper in n-k dimensions (i.e., spanning all n-k dimensions), for a fixed value of k. (Such formulae are central in the literature of statistical physics in the study of percolation processes and collapse of branched polymers.) The implemented software re-affirmed the already-proven formulae for k <= 3, and proved rigorously, for the first time, the formula enumerating polycubes of size n that are proper in n-4 dimensions.

In this video we show how to enumerate polyominoes on twisted cylinders, and explain how to use them for setting lower bounds on the asymptotic growth rate of polyominoes in the plane.