BB-spline scale-space of spline curves and surfaces

We present iterative algorithms for BB-spline scale-space smoothing of geometric data and recovery of high frequency information in the smoothing process. The scale-space representation is based on a directional smoothing process using BB-splines. If the geometric data are approximated or modelled by uniform BB-splines or box-splines then the scale-space smoothing produces BB-spline curves or box-spline surfaces. The method is applicable to geometric data processing and geometric modelling of free-form curves and surfaces from quadrilateral polyhedra with extraordinary vertices.

► BB-spline scale-space of uniform spline curves at rational scales are splines.
► BB-spline scale-space of uniform spline surfaces at rational scales are box-splines.
► Simple iterative algorithms are derived to compute the new control points.
► The algorithms consist of taking moving averages and repeating control points.
► Applications to geometric data processing and geometric modelling.