nurbspy.nurbs_basis_functions module

nurbspy.nurbs_basis_functions.compute_basis_polynomials(n, p, U, u, return_degree=None)

Evaluate the n-th B-Spline basis polynomials of degree ´p´ for the input u-parametrization

The basis polynomials are computed from their definition by implementing equation 2.5 directly

Parameters:

ninteger

Highest index of the basis polynomials (n+1 basis polynomials)

pinteger

Degree of the basis polynomials

Undarray with shape (r+1=n+p+2,)

Knot vector of the basis polynomials Set the multiplicity of the first and last entries equal to ´p+1´ to obtain a clamped spline

uscalar or ndarray with shape (Nu,)

Parameter used to evaluate the basis polynomials (real or complex!)

return_degreeint

Degree of the returned basis polynomials

Returns:

Nndarray with shape (n+1, Nu)

Array containing the basis polynomials of order ´p´ evaluated at ´u´ The first dimension of ´N´ spans the n-th polynomials The second dimension of ´N´ spans the ´u´ parametrization sample points

nurbspy.nurbs_basis_functions.compute_basis_polynomials_derivatives(n, p, U, u, derivative_order)

Evaluate the derivative of the n-th B-Spline basis polynomials of degree ´p´ for the input u-parametrization

The basis polynomials derivatives are computed recursively by implementing equations 2.7 and 2.9 directly

Parameters:

ninteger

Highest index of the basis polynomials (n+1 basis polynomials)

pinteger

Degree of the original basis polynomials

Undarray with shape (r+1=n+p+2,)

Knot vector of the basis polynomials Set the multiplicity of the first and last entries equal to ´p+1´ to obtain a clamped spline

uscalar or ndarray with shape (Nu,)

Parameter used to evaluate the basis polynomials

derivative_orderscalar

Order of the basis polynomial derivatives

Returns:

N_dersndarray with shape (n+1, Nu)

Array containing the basis spline polynomials derivatives evaluated at ´u´ The first dimension of ´N´ spans the n-th polynomials The second dimension of ´N´ spans the ´u´ parametrization sample points