Megalomaniak It is trigonometry, just using less data more intelligently. Think of a normal bezier curve, even a curve drawn in the Godot menu is a good example:
In this case you have 3 points you can move around in the editor, and between them you see a line. This line is smooth, not a straight line: You obtain this hump automatically just by defining the 3 points, each pixel on the line knows where it should be located based on its position in 2D space. Therefore you can only add 3 points to get a round bump, instead of needing to have say 16 points with straight lines between them to manually simulate the curve yourself and do so at a lower accuracy for more cost.
My idea was what it would have been like if the GPU and OpenGL could do this in 3D space with vertices / surfaces in meshes: Instead of drawing straight triangles between vertices, treat each vertice as a curve point and draw 2D bezier curves between them. Just as for a 2D curve you know where a pixel is supposed to be between vertices by calculating the X + Y coordinates against them, in 3D you'd do the same based on X + Y + Z coordinates.
Like I said I'm aware there's likely a good reason why this never happened, and whatever the reason it's likely too late now unless GPU manufacturers invent a new 3D technology (and we just got Vulkan). Godot like other engines is limited by the capabilities of the rendering technology it works with so it can't do this at hardware level even if it tried... which I guess makes me thinking about this a bit bizarre since it's pointless, didn't want this to get side-tracked from parallax but it's a concept from the same book of magic tricks that could have been used to better allow the illusion of infinite detail.