A tessellation method uses both vertex tessellation factors and displacement factors defined for each vertex of a patch, which may be a quad, a triangle or an isoline. The method is implemented in a computer graphics system and involves calculating a vertex tessellation factor for each corner vertex in one or more input patches. Tessellation is then performed on the plurality of input patches using the vertex tessellation factors. The tessellation operation involves adding one or more new vertices and calculating a displacement factor for each newly added vertex. A world space parameter for each vertex is subsequently determined by calculating a target world space parameter for each vertex and then modifying the target world space parameter for a vertex using the displacement factor for that vertex.