  Mapping high-fidelity 3D geometry to a representation that allows for
intuitive edits remains an elusive goal in computer vision and graphics. The
key challenge is the need to model both continuous and discrete shape
variations. Current approaches, such as implicit shape representation, lack
straightforward interpretable encoding, while others that employ procedural
methods output coarse geometry. We present GeoCode, a technique for 3D shape
synthesis using an intuitively editable parameter space. We build a novel
program that enforces a complex set of rules and enables users to perform
intuitive and controlled high-level edits that procedurally propagate at a low
level to the entire shape. Our program produces high-quality mesh outputs by
construction. We use a neural network to map a given point cloud or sketch to
our interpretable parameter space. Once produced by our procedural program,
shapes can be easily modified. Empirically, we show that GeoCode can infer and
recover 3D shapes more accurately compared to existing techniques and we
demonstrate its ability to perform controlled local and global shape
manipulations.
