A method and apparatus thereof for generating a computer graphics image using quadrangle-shaped primitives formed by combining connected triangle-shaped primitives. In a computer graphics rendering process, a first triangle-shaped primitive and a second triangle-shaped primitive that are connected (that is, they share vertices and a side) are optionally combined to form a quadrangle-shaped primitive. When the first and second triangle-shaped primitives are combined, the resultant quadrangle-shaped primitive is forwarded to a quad-based rasterization process (e.g., a rasterizer or rasterizer subsystem). Otherwise, the first triangle-shaped primitive is forwarded to the rasterization process. The second triangle-shaped primitive may also be forwarded to the rasterization process separate from the first, or it may be used to form a quadrangle in combination with another triangle primitive connected to it. A graphics subsystem could effectively double its throughput of connected triangle primitives by going from three vertices and three edges per primitive to four vertices and four edges per primitive.