| he direct control mechanisms described in this dissertation allow the specification of a local or global region of influence to be governed by a single control. Once a specific region has been isolated, on a curve or surface, selected features within the region can be manipulated. These features may include, but are not restricted to, displacement, slope, curvature, points of inflection, discontinuities and smoothness. The free-form parametric curves and surfaces currently available do not often allow the direct control required for the interactive design of precise shapes such as ship hulls and automobile bodies. There are two reasons for this: a single control is unable to isolate an arbitrary local or global region of influence, and the basis functions that are coupled with the controls seldom match the characteristics of a desired feature. New techniques are presented for adding parametric and geometric degrees of freedom to curves and surfaces. For a given curve, the region of influence may span the entire curve or isolate any portion. For a given surface, the region of influence may include the entire surface or any portion defined by a user selected boundary. The boundary shapes used to define regions of influence on a surface include a rectangle, an ellipse and a free-form closed curve. A new set of normalized basis functions for refining the specific characteristics of an isolated region are introduced. The refinements include changes of displacement, adjustments of individual derivatives and the removal of parametric discontinuities. These basis functions are infinitely continuous within their region of influence and provide a boundary continuity that may assume any real value, C... |
