Deformable object modelling and its exploitation for engineering design - Fang, Li Xing (2008)
Design of functional shapes in mechanical engineering requires accuracy. Existing techniques for shape deformation used in computer graphics and animation are not suitable for mechanical design because their freeform nature do not cater to the accuracy essential in such design. This thesis presents a new method for shape deformation: applying non-linear transformations to freeform NURBS surfaces, producing a result that closely approximates the desire result. A transformation is specified as a function of the spatial variables, mapping points in Euclidean three space, E , into E . The result is achieved first by performing the transformation on the control points, and then adjusting the result. This result is approximate, but can be improved by increasing the number of control points, by adopting a procedure for automatically inserting control points. A recursive algorithm for adaptive knot refinement has been developed to determine where and by how much to refine the surfaces for a target tolerance through the transformation. This helps in reducing the number of control points required for the target tolerance. In the transformation, the original and deformed surfaces retain the same representation: NURBS. This is important because it means that a system needs only to deal with only one surface type, and not a range of them.