Methods, systems, and computer-storage media for efficiently tessellating two dimensional (2-D) curves using a graphics pipeline running on a graphics processing unit (GPU) are provided. A central processing unit (CPU) converts a geometry having one or more 2-D curves into an intermediate tessellation having at least one Bezier fan with a fan origin and four control points. The intermediate tessellation is sent on to the graphics pipeline. A hull shader in the graphics pipeline is configured to approximate the Bezier fan curve by subdividing the curve into a defined number of triangles based on a maximum value of a width or a height of a bounding box containing the four control points of the Bezier fan. A domain shader in the graphics pipeline is configured to determine a vertex position for each of the defined triangles along the curve of the Bezier fan.