The present disclosure relates to a rendering system that that accurately and efficiently renders regions bounded by cubic Bezier splines. For example, in some embodiments, the rendering system generates control triangles, interior triangles, and anti-aliasing triangles from cubic Bezier spline segments of a vector-based convex object. Based on the generated triangles, the rendering system renders anti-aliased cubic Bezier splines as well as the geometry within the cubic Bezier splines. In one or more embodiments, the rendering system efficiently allocates computations between a central processing unit (CPU) and graphics processing unit (GPU) of a computing device in a manner that significantly reduces computational and memory resources.