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 \(\vec AO\) and \(\vec OP\). 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.
\[\begin{split}\begin{split} &\vec v_1 = \vec x_3 - \vec x_2 \\ &\vec v_2 = \vec x_1 - \vec x_2 \\ &\vec e_1 = \vec v_1 / ||\vec v_1|| \\ &\vec u_2 = \vec v_2 - \vec e_1(\vec e_1^T\vec v_2) \\ &\vec e_2 = \vec u_2 / ||\vec u_2|| \\ &\vec e_3 = \vec e_1 \times \vec e_2 \\ &rotation = (\vec e_1, \vec e_2, \vec e_3) \\ &translation = (\vec x_2) \\ \end{split}\end{split}\]- 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 \((xx, xy, xz, yx, yy, yz, zx, zy, zz)\)
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))