DAG amendment for inverse control of parametric shapes

Abstract

Parametric shapes model objects as programs producing a geometry based on a few semantic degrees of freedom, called hyper-parameters. These shapes are the typical output of non-destructive modeling, CAD modeling or rigging. However they suffer from the core issue of being manipulated only indirectly, through a series of values rather than the geometry itself. In this paper, we introduce an amendment process of the underlying direct acyclic graph (DAG) of a parametric shape. This amendment enables a local differentiation of the shape w.r.t. its hyper-parameters that we leverage to provide interactive direct manipulation of the output. By acting on the shape synthesis process itself, our method is agnostic to the variations of the connectivity and topology that may occur in its output while changing the input hyper-parameters. Furthermore, our method is oblivious to the internal logic of the DAG nodes. We illustrate our approach on a collection of examples combining the typical nodes found in modern parametric modeling packages - such as deformation, booleans and surfacing operators - for which our method provides the user with inverse control over the hyper-parameters through a brush stroke metaphor.

Differentiable 3D CAD Programs for Bidirectional Editing

“…The primary limitation of our approach is that while topological changes can be achieved by editing the program, our synchronization step by definition always preserves mesh topology; as it requires the function generating the mesh to be continuous, as well differentiable on most of its domain for the technique to work well. Michel et al [MB21] illustrate another path forward where the gradient is not evaluated throughout the optimization and topologi-cal changes can be supported as long as UV coordinates are maintained. We see potential to merge such methods and accommodate a greater class of operators with higher performance, and note that the question of optimizing edits across topological change is unsolved in general.…”

“…Of particular note is the DAG Amendment method described by Michel et al [MB21], which also allows inverse control of procedural models generated by a DAG of operations, using a brush interaction to address edit ambiguity. This work handles operations that can change the output mesh topology as long as an unambiguous mapping from output to input UV coordinates is maintained.…”

Automatic Differentiable Procedural Modeling

“…His system expresses the manipulations as differential equations, solved using a technique similar to auto differentiation. A work close to ours has been recently presented by Michel and Boubekeur [MB21]. Their method allows for interactive direct manipulation of a parametric shape defined by a procedural graph.…”

“…A regularization term is usually used during optimization to address the problem of multiple solutions when solving the inverse problem with a non‐injective forward operator (i.e., an under‐determined edit), but this strategy privileges one solution over others [Gle94, MB21]. Instead, we explore the optimality region and present the user with various configurations to choose from.…”

“…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.…”