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Following is the equation of Writhe matrix from the article Topology based Representation(page no. 6). enter image description here

What is the meaning of 'sign' in the second part of this equation? I am not sure if this is some typo in that article as the other article of Hierarchical Motion Planning(page no. 3), compleletely neglects the term 'sign[...]' enter image description here

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Sign is a function that returns +1 whenever the operand is anything positive, -1 if it's anything negative, and 0 if it's zero. I'm not sure if it's mathematically correct for your equation as I'm not familiar with it, but it's not an uncommon function, especially in the realm of robotics.

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    $\begingroup$ Plus the sign of a vector is generally returned as a vector where each element is the sign as @Chuck describes for the corresponding element of its argument. $\endgroup$ – SteveO Mar 31 '16 at 0:00
  • $\begingroup$ @SteveO is correct; there's no definition for multiple elements (what would it be if a11 were positive and a21 were negative?) so any multidimensional inputs yield multidimensional outputs. $\endgroup$ – Chuck Mar 31 '16 at 0:05

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