| The main goal of this research project is to compute a Non-Uniform Rational B-Spline (NURBS) surface S(u, v) that interpolates NURBS curves C(u) and that is as smooth as possible, as compact as possible in terms of memory, and whose parameterization is ideally in terms of arc length, i.e. the derivatives are constant in magnitude. The curves, designed at General Electric, partially describe an hydraulic turbine component whose complete surface must be computed. These curves are represented by piecewise planar NURBS curves of degree 2 containing C0/G0 or C0/G1 continuous breaking points, at the jonction of curves segments. With classical skinning approaches, each curve breaking point causes a surface crease---the line along the junction of two surface patches---of C 0 continuity. This results in surfaces that oscillate in the area of the original curve's breaking points. To address this problem, the concept of constraint is introduced. A constraint groups breaking points from different curves into one crease, which then corresponds to a feature in the surface and reflects the designer's intent. The algorithm that computes the constraints and incorporates them in the skinning process is detailed, and its results are compared with those of classical skinning algorithm on a set of industrial test cases. The proposed algorithm improves resulting surface shape and reduces the number of surface control points by a factor 10, but at the expense of overall surface parameterization quality. Also, the thesis suggests choosing interpolation parameters by a logarithmic function of distance between data points---the average distance between curves in the case of skinning. This variant of the more common methods, uniform, arc length, and centripetal, produces slightly smoother surfaces for the current industrial application. |
