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

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