A genetic algorithm approach for boundary optimization in converting trimmed NURBS to untrimmed T-spline

For fully exploiting the elegant properties of T-splines like the local refinement and the capacity of representing complicated geometries in industry, this paper intends to solve the problem of the regional distortion and intersection that arise when converting trimmed NURBS into untrimmed T-spline surface, which is usually unstructured T-spline surface including multiple extraordinary points. A genetic algorithm is employed to optimize the fitting error from the trimming curve and the distance between the control polygon of the fitting curve and the trimming curve’s predefined enclosed polygon. Bézier extraction operation for unstructured T-spline is implemented for visualization and isogeometric analysis where Gaussian quadrature rule is used for all integral terms. Several examples are investigated to verify the validity of the proposed method.