There have been attempts to go that route from both the hardware (eg Nvidia NV1, 1995) and software side (eg Quake 3 Area, 1999) and many attempts to render cur

There have been attempts to go that route from both the hardware (eg Nvidia NV1, 1995) and software side (eg Quake 3 Area, 1999) and many attempts to render curved surfaces since. Generally triangles have remained dominant because they are easier to model, easier to manipulate and are rendered extremely optimally on hardware. The approximation to polygons when rendering is a non trivial task. Individual curved patches can be easily approximated to triangles but once you connect those patches together you have to ensure that the tessellated triangle edges match between neighboring patches. For the most part it is just easier and more performant to model with triangles and brute-force render them. One day curved surfaces may be a better choice but currently triangles are dominant.