任意NUBS曲线的小波分析和造型技术

Multi-resolution NUBS Curves with Arbitrary Number of Control Points

为了对任意 NU BS曲线进行精确的分解和重构 ,提出了半正交 B样条小波分解和重构的新算法 ,同时给出了处理非均匀 B样条曲线的非整数阶分辨率的小波分解和重构算法 ,并实现了任意非均匀 B样条曲线的多分辨率表示 ,对于任意非均匀 B样条或 NU BS曲线 ,无论它有多少个控制点 ,均可以对它进行半正交分解和重构 ,而不受控制点数必须等于 2 i +3的限制 ,从这个意义上讲 ,该方法不仅可以实现连续分辨率水平 (continuous- resolution-level)的非均匀 B样条曲线造型 ,还可以对非均匀 B样条和 NU RBS曲线进行精确的分解和重构 .这对于 B样条曲线曲面的多分辨率造型与显示具有重大应用价值 .

B-spline wavelets have been widely used in multi-resolution modeling for curves and surfaces, but there are some defects in such modeling using semi-orthogonal B-spline wavelets. First, some existing algorithms for multi-resolution curves use uniform B-spline curves to approximate non-uniform B-spline(NUBS) curves. This will result in an error between the new curve and the original one. Second, the constraints in the existing algorithms specify the shape at a continuous-resolution level by interpolating those at integer-resolution levels. If the control point number of a B-spline curve does not match that of a curve at an integer-resolution, that is, 2 i+3<n<2 i+1 +3 where i is an integer, it is impossible to exactly reconstruct the curve with n control points from the decomposition. In this paper, new algorithms for decomposition and reconstruction of arbitrary non-uniform B-spline curves are proposed at continuous-resolution levels. Practical examples for multi-resolution modeling of arbitrary non-uniform B-spline curves are given using semi-orthogonal B-spline wavelets.