DAG amendment for inverse control of parametric shapes

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.