3D graphics hardware relies on a simple idea – break up the task of producing a picture into lots and lots and lots of very simple tasks, and farm out those tasks to lots and lots of very simple computer processors.
This means that they break up the image into lots and lots of tiny triangles, and farm the rendering of each of those triangles out to the many processors in the graphics chips.
With an actual curve, you have one very large complex object. Rendering that is going to be one very complex task, which graphics hardware isn’t set up for. Dividing the task up, on the fly, into many little tasks is also going to be complex and time consuming. Doing that in the 1/60th of a second you have between frames is just too much. So instead, when the program or game is created, we break up that curve into as many tiny triangles as our hardware can manage, and hide the roughness with a blur filter.
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