Sketch-Based Mesh Model Deformation

3D-model deformation is widely used in such areas as industrious design, model producing, accessory processing and 3D animations. Traditional deformation techniques are too complicated and inefficient to manage. To solve this problem, interactive mesh model deformation based on sketches is studied.In order to control the differential property of the mesh surface in the deformation process, the Laplace operator is introduced and then improved to manipulate the normal and curvature of model surface directly. A system of linear equations founded on discrete Laplace operator is solved in the least squares sense and provide a theoretical proof for the reasonable deformation of mesh model. To implement the deformation method, the silhouette is involved to control the mesh model. Firstly, a silhouette is interpolated on edges of the mesh according to the normal of vertices. Then the serialized silhouette points are projected to a line sketched by the user interactively and the new coordinate of vertices are achieved after solving the linear equations. In addition, when a sketch line is drawn on a specified region of interest, it can create a remarkable feature with the curvature of vertices along the line tuned.The traditional mesh editing techniques always process the form-features approximately. To preserve form-features in a global mesh deformation, this thesis put forward an exact mesh-control method. At first, the local information of form-features is extracted as hard constraints for mesh deformation, and then soft constraints are built using discrete Laplace operator. At last, a system of linear equations established under Lagrange multipliers is solved with the hard constraints exactly satisfied. That produces the global mesh surface deformation with form-features preserved. It's intuitive and easy to control and can be used in the interactive editing.