tangent_vectorΒΆ
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:
- A n_nodes-1 polynomial is fitted through the nodes per dimension.
- Those polynomials are analytically differentiated with respect to the node index
- 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] |
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type in_coord: | np.ndarray |
Notes
Dimensions are treated independent from each other, interpolating polynomials are computed individually.