Methods and computer-readable media for displaying two-dimensional objects on a display device are disclosed. Rendering requests are received from an application to render two-dimensionally modeled graphics to a display device. Primitive geometries of drawing calls of the rendering requests are tessellated into sequences of triangles. The vertices of the triangles are mapped to a vertex buffer along with an index to identify associated constant data. Batching operations store and communicate calls and mapped data to a graphics processing unit by way of a three-dimensional rendering application program interface. Constant data associated with the mapped data are indexed and appended together in a constant buffer, thereby allowing drawing calls to be coalesced. A staging buffer and a staging texture are provided for batching text anti-aliasing operations. Shader fragments are precompiled and organized by way of a predetermined lookup table.