Fairing wireframes in industrial surface design

Wireframe is a modeling tool widely used in industrial geometric design. The term wireframe refers to two sets of curves, with the property that each curve from one set intersects with each curve from the other set. Akin to the mu-, v-isocurves in a tensor-product surface, the two sets of curves in a wireframe span an underlying surface. In many industrial design activities, wireframes are usually set up and adjusted by the designers before the whole surfaces are reconstructed. For adjustment, the fairness of wireframe has a direct influence on the quality of the underlying surface. Wireframe fairing is significantly different from fairing individual curves in that intersections should be preserved and kept in the same order. In this paper, we first present a technique for wireframe fairing by fixing the parameters during fairing. The limitation of fixed parameters is further released by an iterative gradient descent optimization method with step-size control. Experimental results show that our solution is efficient, and produces reasonably fairing results of the wireframes.