A tessellation method uses vertex tessellation factors. For a quad patch, the method involves comparing the vertex tessellation factors for each vertex of the quad patch to a threshold value and if none exceed the threshold, the quad is sub-divided into two or four triangles. If at least one of the four vertex tessellation factors exceeds the threshold, a recursive or iterative method is used which considers each vertex of the quad patch and determines how to further tessellate the patch dependent upon the value of the vertex tessellation factor of the selected vertex or dependent upon values of the vertex tessellation factors of the selected vertex and a neighbor vertex. A similar method is described for a triangle patch.