Direct Surface Manipulation (DSM) allows a designer to add a raised or indented feature to an existing surface. The user bounds the feature with a closed curve, and defines an influence center that indicates the point or curve of maximum displacement from the original surface. As we move radially outward from the influence center to the boundary curve, the magnitude of displacement is scaled gradually by a one-dimensional polynomial basis function whose values range from 0 to 1. In this paper we present a new technique for assigning parameter values in the radial direction, i.e., u, to points within a DSM feature. The new technique poses parameter distribution as a steady state heat conduction problem and uses a finite element method to solve for $ux,y.$ The new method overcomes some stringent geometric conditions inherited from a fundamentally geometric-based reparameterization scheme and allows us to work with non-star-shaped and multiply connected DSM features. Thus it allows us to apply this surface feature technique to a wider variety of surface applications.

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