Modeling and Exploring Co‐variations in the Geometry and Configuration of Man‐made 3D Shape Families

We introduce co‐variation analysis as a tool for modeling the way part geometries and configurations co‐vary across a family of man‐made 3D shapes. While man‐made 3D objects exhibit large geometric and structural variations, the geometry, structure, and configuration of their individual components usually do not vary independently from each other but in a correlated fashion. The size of the body of an airplane, for example, constrains the range of deformations its wings can undergo to ensure that the entire object remains a functionally‐valid airplane. These co‐variation constraints, which are often non‐linear, can be either physical, and thus they can be explicitly enumerated, or implicit to the design and style of the shape family. In this article, we propose a data‐driven approach, which takes pre‐segmented 3D shapes with known component‐wise correspondences and learns how various geometric and structural properties of their components co‐vary across the set. We demonstrate, using a variety of 3D shape families, the utility of the proposed co‐variation analysis in various applications including 3D shape repositories exploration and shape editing where the propagation of deformations is guided by the co‐variation analysis. We also show that the framework can be used for context‐guided orientation of objects in 3D scenes.