# In the GJK algorithm, when is a point ever closer to the origin than a line?

The GJK algorithm depends upon a function in its loop that updates the simplex and search direction for the next iteration (which is often called something like `DoSimplex()` or `ProcessSimplex()`). In order to find the next simplex, the algorithm divides the current simplex into regions, and determines which region contains the origin.

Here is an example of the regions for a 1-simplex (i.e. a line). In this example, the simplex previously only contained point B, and then point A was added in the direction of the origin.

Now it makes sense to me why the origin can't be in region 4, since we just came from there. However, I can't think of any case where the origin would be in region 1 either. We just traveled from B to the origin, and if we didn't reach the origin, then we know there was no collision. So won't the origin always be in 2 or 3? Why does every algorithm always check whether the origin is in region 1?

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