No abstract

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.

The potential performance benefits of simple, low power active elements in the lateral secondary, between the truck and carbody is investigated analytically by parametric studies utilizing a fifteen degree of freedom lateral dynamic model subject to alignment and cross-level inputs. It is shown that significant improvements in ride quality can be obtained at current operating speeds by using less than 3 kw per truck by sensing lateral carbody accelerations and utilizing lateral force actuators between the truck and carbody. It is also shown that in order to improve the truck critical speed and/or to improve the ride quality at very high speeds requires control of the truck kinematic mode. This can be achieved, at the expense of increased power requirements, by sensing absolute truck lateral and yaw velocities and utilizing combined lateral force actuators to exert a yaw moment on the truck. It is concluded that significant ride quality improvements can be achieved by low power, small bandwidth actuators while stabilty improvements requires increased power and larger bandwidth systems.

A parametric description of an elastic surface is used as the basis for a free-form shape design package. The energy functional of shape deformation are used to develop the equations of motion for the surface. The user, interacting with the model during a time simulation of its motion, is capable of guiding the surface into desirable configurations. The dynamic nature of these models cause them to seek shapes with desirable properties which can free the user from having to control every aspect of the surface while achieving design goals. The strong analogy between these models and physical systems allows the user to control the shape in intuitive fashions. This approach gives the user considerable control of the global aspects of the shape while retaining control of small scale local shape.