The constraint elevation for parametric continuity order of NURBS curve and surface

For the NURBS curve that hold the arbitrary degrees and generally structured knots, under the assumption of unchanging the knot vector and the degree of NURBS curve, we present the constraint conditions for elevating the parametric continuity order of NURBS curve at the interior knots by modifying their control points and weights. Meanwhile, we obtain the freedom degree of the control points and the weights when the parametric continuity order of NURBS curve elevates by one. Furthermore, we obtain the conditions for elevating the parametric continuity order of NURBS surface along its isoparametric line by modifying their control points and weights. Meanwhile, the freedom degree of the control points and the weights when the parametric continuity order of NURBS surface elevates by one is presented at the end.