In this paper, based on the idea of profit and loss modification, we presentthe iterative non-uniform B-spline curve and surface to settle a key problem in computeraided geometric design and reverse engineering, that ...In this paper, based on the idea of profit and loss modification, we presentthe iterative non-uniform B-spline curve and surface to settle a key problem in computeraided geometric design and reverse engineering, that is, constructing the curve (surface)fitting (interpolating) a given ordered point set without solving a linear system. We startwith a piece of initial non-uniform B-spline curve (surface) which takes the given point setas its control point set. Then by adjusting its control points gradually with iterative formula,we can get a group of non-uniform B-spline curves (surfaces) with gradually higherprecision. In this paper, using modern matrix theory, we strictly prove that the limit curve(surface) of the iteration interpolates the given point set. The non-uniform B-spline curves(surfaces) generated with the iteration have many advantages, such as satisfying theNURBS standard, having explicit expression, gaining locality, and convexity preserving,etc展开更多
文摘In this paper, based on the idea of profit and loss modification, we presentthe iterative non-uniform B-spline curve and surface to settle a key problem in computeraided geometric design and reverse engineering, that is, constructing the curve (surface)fitting (interpolating) a given ordered point set without solving a linear system. We startwith a piece of initial non-uniform B-spline curve (surface) which takes the given point setas its control point set. Then by adjusting its control points gradually with iterative formula,we can get a group of non-uniform B-spline curves (surfaces) with gradually higherprecision. In this paper, using modern matrix theory, we strictly prove that the limit curve(surface) of the iteration interpolates the given point set. The non-uniform B-spline curves(surfaces) generated with the iteration have many advantages, such as satisfying theNURBS standard, having explicit expression, gaining locality, and convexity preserving,etc
