Approximate lofting by B-spline curve fitting based on energy minimization

Hyungjun Park and Kwangsoo Kim

Abstract

Presented in this paper is a method for approximately lofting a given set of curves within a specified tolerance. It is based on refitting input curves simultaneously on a common knot vector and interpolating them to get a resultant NURBS surface. A concept of reducing the number of interior knots of the common knot vector is well adopted to acquire more compact representation for the resultant surface. Energy minimization is newly introduced in curve refitting process to stabilize the solution of the fitting problem and to get more fair curves. The proposed approximate lofting provides more smooth surface models and realizes more efficient data reduction especially when the parameterization and compatibility of input curves are not good enough. The method has been successfully implemented in a new CAD/CAM software VX Vision of Varimetrix Corporation.

Keywords:B-spline curve fitting, energy minimization, constrained quadratic functional optimization, approximate lofting

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