splinepy.rational_bezier.RationalBezier.composition_derivative#

RationalBezier.composition_derivative(inner, inner_derivative)#

Derivative of composition when given the differentiated inner function with constant outer function. This function differs from compose_sensitivities(), which computes the derivatives concerning the outer function’s control point positions.

Given an outer function \(\mathcal{T}\) and an inner function \(\mathcal{K}\) with its derivative with respect to some design variable \(\alpha\), i.e., \(\frac{\partial \mathcal{K}}{\partial \alpha}\), this function returns the derivative of the composed geometry in the form \(\frac{\partial \mathcal{T}(\mathcal{K})}{\partial\alpha}\) by computing.

\[\frac{\partial\mathcal{T}(\mathcal{K})}{\partial\alpha} = \frac{\partial \mathcal{T}}{\partial u}(\mathcal{K})\cdot \frac{\partial \mathcal{K}}{\partial \alpha}\]

Here \(u\) refers to the parametric coordinates of the deformation function.

Parameters:
Returns:

composition_der

Return type:

BezierBase