Knot removal for B-spline curves

With a transformation matrix of B-spline bases (abbreviated to BSBT matrix), a B-spline basis can be represented by another B-spline basis. In this paper, we first give the existence conditions and some useful properties of BSBT matrices. Then we ...

The modification of a knot of a B-spline curve of order k generates a family of B-spline curves. We show that an envelope of this family is a B-spline curve defined by the same control polygon, and its order is k - m, where m is the multiplicity of the ...

Euler spirals have linear varying curvature with respect to arc length and can be applied in fields such as aesthetics pleasing shape design, curve completion or highway design, etc. However, evaluation and interpolation of Euler spirals to ...

• A class of Bézier curves and B-spline curves are defined by discrete Euler spiral-like control polygons.
• The defined curves are called Euler Bézier spirals and Euler B-spline spirals when the curvature plots are monotone.
• Euler ...