We describe a method for preserving a set of geometric constraints while interactively sculpting a free-form Bspline surface. The surface seeks a fair shape by minimizing an appropriate global energy function. The user controls the surface through the creation and manipulation of geometric constraints such as interpolated points and curves.We represent the free-form surface as a B-spline surface, and formulate a quadratic deformation energy in terms of this basis. Constraints are represented as gradients of quadratic functionals which have a global minimum value when the constraint is satisfied. These constraints are linear in the surface degrees of freedom, and are maintained during surface minimization by transforming the constrained surface equations into an unconstrained system with fewer degrees of freedom.Point, curve, and normal constraints are formulated with reference to a tensor-product B-spline surface. By extension, formulations are applicable to any linearly blended surface.

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.