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.

翻译：探索三维形状的变体是传统三维建模工具中耗时的一个过程。三维形状的深度生成模型通常具有连续的潜在空间，原则上可用于从一组输入形状开始探索可能的变体。然而，在实践中，这样做可能存在问题：潜在空间维度高且难以可视化，包含与输入形状无关的形状，且通过潜在空间的线性路径常导致次优的形状转换。此外，理想情况下，人们希望能够在用于训练生成模型的原始高质量网格（而非其低质量输出几何体）上探索变体。在本文中，我们提出了一种方法，通过构建从易于导航的二维探索空间到预训练生成模型子空间的映射，来探索一组给定标志形状之间的变体。我们首先描述了如何找到一种映射，该映射覆盖输入标志形状集合并展示其间的平滑变化。然后，我们展示了如何将子空间中的变体转化为变形场，以将这些变体转移到标志形状的高质量网格上。我们的结果表明，我们的方法可以为多个不同形状类别生成视觉上令人愉悦且易于导航的二维探索空间，特别是与之前关于学习三维形状变形空间的工作相比。