Dual spherical spline: A new representation of ruled surface optimization

A ruled surface optimization model is proposed in the paper. It is set up especially to design a blade surface as a ruled surface. In this model, the ruled surface is defined as a dual spherical spline and the control points of the dual spherical spline are served as optimization variables. As points on dual spherical splines correspond to infinite lines in Euclidean space, two directrix curves of a ruled surface are derived by intersecting the ruled surface with the fixed hub and shroud surfaces. In this way, the proposed optimization model can reduce one third number of the variables compared with the conventional ruled surface parametrization methods, such as tensor product surface. Besides, the optimized ruled surface defined as a dual spherical spline has direct link to the manufacturing process.