# tangent_vector¶

Tangent vector calculation for 2+ noded elements.

Calculates the tangent vector interpolating every dimension separately. It uses a (n_nodes - 1) degree polynomial, and the differentiation is analytical.

Calculation method:

1. A n_nodes-1 polynomial is fitted through the nodes per dimension.

2. Those polynomials are analytically differentiated with respect to the node index

3. The tangent vector is given by:

$\vec{t} = \frac{s_x'\vec{i} + s_y'\vec{j} + s_z'\vec{k}}{\left| s_x'\vec{i} + s_y'\vec{j} + s_z'\vec{k}\right|}$

where $$'$$ notes the differentiation with respect to the index number

param in_coord

array of coordinates of the nodes. Dimensions = [n_nodes, ndim]

type in_coord

np.ndarray

Notes

Dimensions are treated independent from each other, interpolating polynomials are computed individually.