Abstract: We present an approach to define shape deformations by constructing and interactively modifying C¹ continuous time-dependent divergence-free vector fields. The deformation is obtained by a path line integration of the mesh vertices. This way, the deformation is volume-preserving, free of (local and global) self-intersections, feature preserving, smoothness preserving, and local. Different modeling metaphors support the approach which is able to modify the vector field on-the-fly according to the user input. The approach works at interactive frame rates for moderate mesh sizes, and the numerical integration preserves the volume with a high accuracy.