How is a coordinate system called where values increase to the bottom instead to the top?

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In some computer graphics libraries the coordinate system is almost like the "usual" cartesian coordinate system. The only difference is that the $y$ values increas to the bottom, not to the top.

Does this kind of coordinate system have a name?

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This is simply right-handed vs. left-handed (or right-chiral vs. left-chiral) orientation.