1. A method for smoothing a three-dimensional (3D) mesh, the method comprising: identifying a set of vertices within an area of the 3D mesh that is operated on by a volume-preserving mesh smoothing brush that is configured to smooth the 3D mesh; for each vertex in the set of vertices, computing a modified position; estimating a change in volume of the 3D mesh based on the modified positions computed for the vertices in the set of vertices; and for each vertex in the set of vertices, computing an updated position of the vertex based on the modified position computed for the vertex and the estimated change in volume of the 3D mesh.