Interactive B-spline Curve Modification by Using Energy Methods

There is an increasing demand in conceptual design for more interactive and intuitive methods for creating and modifying freeform curves and surfaces in CAD modelling systems. The methods should be based not only on the change of the mathematical parameters, but also on the user\´s specified constraints. Energy method is presented to modify a B-spline curve globally. Unlike the traditional internal energy, the new internal energy function will keep the tendency to the shape of original curve other than to produce a "flat" curve while minimizing the internal energy. The curve modifications are carried out by minimizing the total energy: sum of the internal energy and the external energy. Numerical experiments indicate that the curve modification can be interactively and intuitively carried out just by clicking the mouse, the shape of original curve are well preserved, and no local local bump or dent are produced