# Proper name for Inverted Cartesian coordinate system?

In most 2D computer graphic rendering applications (HTML Canvas, Flash, etc...), the coordinate system used is like this:

My question is, what is the mathematical/technical name for this kind of coordinate system? Inverted Cartesian?

• The way these axes are oriented is negative that of the "standard" orientation. I guess you could call this the "left-handed" plane, since the cross product here obeys the left-hand rule. Jan 22, 2013 at 6:05
• @ABlumenthal What does cross product mean here? There is no $z$ axis. Jan 22, 2013 at 6:07
• Math can't really tell us what a coordinate system "is", just how to change from one to another. Because you are considering two systems related by a reflection, you could call one of them "reflected Cartesian coordinates" (which one of the two is "reflected" is just a matter of convention.) Jan 22, 2013 at 6:10

You've tapped into a major incompatability between the standard Math convention taught in Math class, and some CS graphics programming systems (but not all).

I use the term "upside-down y-coordinates" to highlight the problem from a math educator's perspective.

The depth of the problem increases as one delves into more complex spatial problem-solving where vector geometry is advantageous. Here, you want to have strong conventions for representing spatial directions. Standard direction-angles increase CCW, but the designers of "upside-down y-coordinate" graphics toolboxes face a dilemma where they are nudged toward having their direction angles increase CW (so that the trig. functions don't need to be redefined).

Over many years of working in the scientific software area, I have noticed that the "native 2D graphics libraries" are shallow in function when starting off on the wrong foot with inverted ys. This is partly because the early departure from convention cuts off the graphics library developer from advanced, geometric theory.

Khan Academy teaches standard coordinates (y-up) in its Math lectures, and upside-down coordinates (y-down) in its Computer Science graphics lessons (based on JavaScript). That's a confusing approach to be taking.

• Yeah, in most professional, industry-standard 3D software/animation programs, y-up is the norm. But in traditional math classes, z-up is commonly taught. HTML Canvas (as you pointed out using JavaScript) is based on y-down since the origin of the canvas is in the top left corner. Aug 16, 2017 at 13:26
• I try to separate the discussion of conventions for 2D VS. 3D Cartesian axes. There are many more choices for "standard axes" orientations in 3D. However, if you look at STEM apps in design, CAD, chemistry, applied math, the convention in 3D is for z-up, and x-y in the level plane. x generally points to the right, and y -points back away from the viewer. I've also seen x pointing toward the viewer, and y-pointing to the right, or something in between. Aug 16, 2017 at 22:18
• Even outside of computer graphics, the inverted vertical axis occurs (sort of) in the way we normally index matrices in mathematics, with row 1 being the top row, etc.
– Ned
May 29, 2019 at 23:55