3.5.9. CREATE-BASIS function

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This function is used to create a basis of spatial vectors on the model. Currently, the only method available to create a basis is the CARTESIAN method. This method expects you to provide 2 non collinear vectors. The basis is then computed according to the following procedure.

If you provide $\underline{u_{c_1}}$ and $\underline{u_{c_2}}$, the basis computed is $(\underline{u_1}, \underline{u_2}, \underline{u_3})$ such as:

• $\underline{u_1} = \frac{\underline{u_{c_1}}}{\|\underline{u_{c_1}}\|}$
• $\underline{u_2} = \underline{u_{c_2}} - (\underline{u_{c_2}} \cdot \underline{u_1})\underline{u_1}$ and then $\underline{u_2} = \frac{\underline{u_2}}{\|\underline{u_2}\|}$
• $\underline{u_3} = \underline{u_1} \times \underline{u_2}$

If you provide $\underline{u_{c_1}}$ and $\underline{u_{c_3}}$, the basis computed is $(\underline{u_1}, \underline{u_2}, \underline{u_3})$ such as:

• $\underline{u_1} = \frac{\underline{u_{c_1}}}{\|\underline{u_{c_1}}\|}$
• $\underline{u_3} = \underline{u_{c_3}} - (\underline{u_{c_3}} \cdot \underline{u_1})\underline{u_1}$ and then $\underline{u_3} = \frac{\underline{u_3}}{\|\underline{u_3}\|}$
• $\underline{u_2} = \underline{u_3} \times \underline{u_1}$

If you provide $\underline{u_{c_2}}$ and $\underline{u_{c_3}}$, the basis computed is $(\underline{u_1}, \underline{u_2}, \underline{u_3})$ such as:

• $\underline{u_2} = \frac{\underline{u_{c_2}}}{\|\underline{u_{c_2}}\|}$
• $\underline{u_3} = \underline{u_{c_3}} - (\underline{u_{c_3}} \cdot \underline{u_2})\underline{u_2}$ and then $\underline{u_3} = \frac{\underline{u_3}}{\|\underline{u_3}\|}$
• $\underline{u_1} = \underline{u_2} \times \underline{u_3}$

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In this example we are defining 2 basis (BASIS_A and BASIS_B).

CREATE-BASIS  
  MODEL: MY_MODEL
  NAME: BASIS_A
  CARTESIAN
    U1: 1.,0.,0  
    U2: 1.,1.,0.
 
CREATE-BASIS  
  MODEL: MY_MODEL
  NAME: BASIS_B
  CARTESIAN
    U3: 1.,0.,1.  
    U2: 1.,1.,0.

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