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Specifications and Common Mistakes

- Specifications and Common Mistakes:

- Misspellings or punctuation mistakes,incorrect formulas, abnormal display.

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mindsponge.common.rots_from_two_vecs

mindsponge.common.rots_from_two_vecs(e0_unnormalized, e1_unnormalized)[source]

Put in two vectors $\vec{a} = (a_{x}, a_{y}, a_{z})$ and $\vec{b} = (b_{x}, b_{y}, b_{z})$ . Calculate the rotation matrix between local coordinate system, in which the x-y plane consists of two input vectors and global coordinate system.

Calculate the unit vector ${\vec{e}}_{0} = \frac{\vec{a}}{| \vec{a} |}$ as the unit vector of x axis.

Then calculate the projected length of $\vec{b}$ on a axis. $c = | \vec{b} | \cos θ = \vec{b} \cdot \frac{\vec{a}}{| \vec{a} |}$ .

So the projected vector of $\vec{b}$ on a axis is $c {\vec{e}}_{0}$ . The vector perpendicular to e0 is ${\vec{e}}_{1}^{'} = \vec{b} - c {\vec{e}}_{0}$ .

The unit vector of ${\vec{e}}_{1}^{'}$ is ${\vec{e}}_{1} = \frac{{\vec{e}}_{1}^{'}}{| {\vec{e}}_{1}^{'} |}$ , which is the y axis of the local coordinate system.

Finally get the unit vector of z axis ${\vec{e}}_{2}$ by calculating cross product of ${\vec{e}}_{1}$ and ${\vec{e}}_{0}$ .

The final rots is $(e_{0 x}, e_{1 x}, e_{2 x}, e_{0 y}, e_{1 y}, e_{2 y}, e_{0 z}, e_{1 z}, e_{2 z})$ .

Parameters

e0_unnormalized (tuple) – vectors $\vec{a}$ as x-axis of x-y plane, length is 3. Data type is constant or Tensor with same shape.
e1_unnormalized (tuple) – vectors $\vec{b}$ forming x-y plane, length is 3. Data type is constant or Tensor with same shape.

Returns

tuple, rotation matrix $(e_{0 x}, e_{1 x}, e_{2 x}, e_{0 y}, e_{1 y}, e_{2 y}, e_{0 z}, e_{1 z}, e_{2 z})$ . Data type is constant or Tensor with same shape.

Supported Platforms:: Ascend GPU

Examples

>>> import mindsponge
>>> v1 = (1, 2, 3)
>>> v2 = (3, 4, 5)
>>> ans = mindsponge.common.rots_from_two_vecs(v1, v2)
>>> print(ans)
(0.4242640686695021, -0.808290367995452, 0.40824828617045156, 0.5656854248926695,
 -0.1154700520346678, -0.8164965723409039, 0.7071067811158369, 0.5773502639261153,
 0.4082482861704521)