The Interpolation And Conformal Smooth Stitching Of NURBS Curves And Surfaces

Along with the rapid improvement of modern industry Sci-Tech, modeling technology of curve and surface are becoming more and more maturity. Non-uniform Rational B-spline (NURBS) is becoming the most outlooks modeling technology. It has been specified as a standard of industrial products geometry description method and has been widely used and recommended.On the NURBS curve and surface interpolation is an basic problem in CAGD, which is also a common topic in industry design and manufacture. In this paper, researching on NURBS curve and surface interpolation mainly consists of the following four parts.(1) Integrated the current NURBS curve interpolation scheme, and improved the curve interpolation method with end derivative constraint, then discussed the influence on the shape of the interpolation curve with the first or second derivative constraints in the end data points by large numbers of numerical examples.(2) Proposed a new NURBS curve interpolation scheme when multiple data points having mixed derivative constraints at the same time, such as the first derivative and the second derivative constraints. And proposed the algorithm to compute knot vectors and construct interpolation liner equations in this case.(3) Based on the curve interpolation, further studied the NURBS surface interpolation method when a plurality of selected data points having mixed derivative constraints in a selected direction.(4) The numerical examples demonstrate the effectiveness of the algorithm and method, and confirmed the constraints of mixed derivatives play a significant role in the control of interpolation curve. Therefore, engineering designers provided a better NURBS curves and surfaces interpolation method with high fidelity.Then converted NURBS curve into piecewise rational Bezier curves by knot insertion algorithm, and studied the G1continuous stitching method of NURBS curves through the corresponding continuous stitching method in the category of rational Bezier method. And on this basis put forward the method of conformal and G1continuous stitching of NURBS curves.Finally, by designed a side view and body surface of SUV car, demonstrates the value of the proposed interpolation method when a plurality of selected data points having mixed derivative constraints, as well as the G1continuous stitching method.