Real-time editing of man-made mesh models under geometric constraints

Abstract

Editing man-made mesh models under multiple geometric constraints is a crucial need for product design to facilitate design exploration and iterative optimization. However, the presence of multiple geometric constraints (e.g. the radius of a cylindrical shape, distance from a point to a plane) as well as the high dimensionality of the discrete mesh representation of man-made models make it difficult to solve this constraint system in real-time. In this paper, we propose an approach based on subspace decomposition to achieve this goal. When a set of variables are edited by the user, the proposed method minimizes the residual of the constraint system in a least square sense to derive a new shape. The resulting shape shall comply with the assigned (extrinsic) constraints while maintaining the original (intrinsic) constraints analyzed from the given mesh model. In particular, we extract a meaningful subspace of the entire solution space based on the user’s edits to reduce the order of the problem, and solve the constraint system globally in real-time. Finally, we project the approximate solution back to the original solution space to obtain the editing result.