Detail-preserving axial deformation using curve pairs

Traditional axial deformation is simple and intuitive for users to modify the shape of objects. However, unexpected twist of the object may be obtained. The use of a curve-pair allows the local coordinate frame to be controlled intuitively. However, some important geometric details may be lost and changed in the deformation process. In this paper, we present a detail-preserving axial deformation algorithm based on Laplacian coordinates. Instead of embedding the absolute coordinates into deformation space in traditional axial deformation, we transform the Laplacian coordinates at each vertex according to the transformation of local frames at the closest points on the axial curve. Then the deformed mesh is reconstructed by solving a linear system that describes the reconstruction of the local details in least squares sense. By associating a complex 3D object to a curve-pair, the object can be stretched, bend, twisted intuitively through manipulating the curve-pair, and can also be edited by means of view-dependent sketching. This method combines the advantages of axial deformation and Laplacian mesh editing. Experimental results are presented to show the effectiveness of the proposed method.