mindsponge.common.rigids_from_3_points

mindsponge.common.rigids_from_3_points(point_on_neg_x_axis, origin, point_on_xy_plane)[source]

Gram-Schmidt process. Create rigids representation of 3 points local coordination system, point on negative x axis A, origin point O and point on x-y plane P.

First calculate the coordinations of vector $\vec{A} O$ and $\vec{O} P$ . Then use rots_from_two_vecs get the rotation matrix.

Distance between origin point O and the origin point of global coordinate system is the translations of rigid.

Finally return the rotations and translations of rigid.

Reference:: Jumper et al. (2021) Suppl. Alg. 21 ‘Gram-Schmidt process’.

\begin{array}{r} \begin{aligned} {\vec{v}}_{1} = {\vec{x}}_{3} - {\vec{x}}_{2} \\ {\vec{v}}_{2} = {\vec{x}}_{1} - {\vec{x}}_{2} \\ {\vec{e}}_{1} = {\vec{v}}_{1} / | | {\vec{v}}_{1} | | \\ {\vec{u}}_{2} = {\vec{v}}_{2} - {\vec{e}}_{1} ({\vec{e}}_{1}^{T} {\vec{v}}_{2}) \\ {\vec{e}}_{2} = {\vec{u}}_{2} / | | {\vec{u}}_{2} | | \\ {\vec{e}}_{3} = {\vec{e}}_{1} \times {\vec{e}}_{2} \\ r o t a t i o n = ({\vec{e}}_{1}, {\vec{e}}_{2}, {\vec{e}}_{3}) \\ t r a n s l a t i o n = ({\vec{x}}_{2}) \end{aligned} \end{array}

Parameters

point_on_neg_x_axis (tuple) – point on negative x axis A, length is 3. Data type is constant or Tensor with same shape.
origin (tuple) – origin point O, length is 3. Data type is constant or Tensor with same shape.
point_on_xy_plane (tuple) – point on x-y plane P, length is 3. Data type is constant or Tensor with same shape.

Returns

tuple(rots, trans), rigid, length is 2. Include rots $(x x, x y, x z, y x, y y, y z, z x, z y, z z)$: and trans $(x, y, z)$ . Data type is constant or Tensor with same shape.

Supported Platforms:: Ascend GPU

Examples

>>> import mindsponge
>>> A = (1, 2, 3)
>>> O = (4, 6, 8)
>>> P = (5, 8, 11)
>>> ans = mindsponge.common.rigids_from_3_points(A, O, P)
>>> print(ans)
((0.4242640686695021, -0.808290367995452, 0.40824828617045156, 0.5656854248926695,
 -0.1154700520346678, -0.8164965723409039, 0.7071067811158369, 0.5773502639261153,
 0.4082482861704521), (4,6,8))