Procedures

Computes all non-zero basis function of all degrees from $0$ up to $p$.

Spline basis constructor

Computes the nonvanishing basis functions based on Algorithm A2.2 in the NURBS Book ¹.

Returns the number of Bezier segments, integer :: nb, of the basis and the real(wp) :: knots(:) array containing the unique values of the knot vector.

logical function to compare character keys

Computes all nonzero basis functions and their derivatives based on Algorithm A2.3 in the NURBS Book [^1].

Computes a single basis function and its derivatives based on Algorithm A2.5 in the NURBS Book [^1].

Computes the multiplicity of a knot

This procedure is an elemental function and does a binary search and return the integer :: span value, where $u$ lies on. Note that, indexing starts with zero. If $u=u_{m}$, the index is $n (= m - p - 1)$, i.e., $u \in {(u_{n}, u_{nb}]}$, where "nb $(= n+1)$" is number of control points of the univariate spline basis object.

Computes the span and multiplicity of a knot

Return the number of quadrature points for a successive integration

Return the Greville abscissae, $\{u_i\}$, of the knot vector,

Insert knot $\bar{u}$ into ${[u_{k}, u_{k+1})}$ $r$ times.

Computes a single basis function, $N_{i,p}(u)$.

Return the length of the parameter space, i.e., $u_{m}-u_{0}$, where $m$ is the highest index of the knot vector.

This subroutine plots the basis functions or their $d$th order derivatives having index from first to last by computing at interpolation points defined by plotRes, and print the image file into "|cwd|/data/work/fname.ext" if the workspace work is presented, "|cwd|/data/img/fname.ext" if else. Plotting requires GNUPlot installed on your computer. The input parameter terminal set the output terminal of GNUPlot.

logical function to compare real values

Updates all component of the basis according to input knot vector.