  Exploring variations of 3D shapes is a time-consuming process in traditional
3D modeling tools. Deep generative models of 3D shapes often feature continuous
latent spaces that can, in principle, be used to explore potential variations
starting from a set of input shapes. In practice, doing so can be problematic:
latent spaces are high dimensional and hard to visualize, contain shapes that
are not relevant to the input shapes, and linear paths through them often lead
to sub-optimal shape transitions. Furthermore, one would ideally be able to
explore variations in the original high-quality meshes used to train the
generative model, not its lower-quality output geometry. In this paper, we
present a method to explore variations among a given set of landmark shapes by
constructing a mapping from an easily-navigable 2D exploration space to a
subspace of a pre-trained generative model. We first describe how to find a
mapping that spans the set of input landmark shapes and exhibits smooth
variations between them. We then show how to turn the variations in this
subspace into deformation fields, to transfer those variations to high-quality
meshes for the landmark shapes. Our results show that our method can produce
visually-pleasing and easily-navigable 2D exploration spaces for several
different shape categories, especially as compared to prior work on learning
deformation spaces for 3D shapes.
