Differential Coordinates for Interactive Mesh Editing

One of the main challenges in editing a mesh is to retainthe visual appearance of the surface after applying variousmodifications. In this paper we advocate the use of lineardifferential coordinates as means to preserve the high-frequencydetail of the surface. The differential coordinatesrepresent the details and are defined by a linear transformationof the mesh vertices. This allows the reconstructionof the edited surface by solving a linear system that satisfiesthe reconstruction of the local details in least squares sense.Since the differential coordinates are defined in a global coordinatesystem they are not rotation-invariant. To compensatefor that, we rotate them to agree with the rotation ofan approximated local frame. We show that the linear leastsquares system can be solved fast enough to guarantee interactiveresponse time thanks to a precomputed factorizationof the coefficient matrix. We demonstrate that our approachenables to edit complex detailed meshes while keepingthe shape of the details in their natural orientation.