1. A method for managing texture mapping data in a computer graphics system, the computer graphics system including a host computer, primitive rendering hardware and a primitive data path extending between the host computer and the primitive rendering hardware, the host computer passing primitives to be rendered by the system to the primitive rendering hardware over the primitive data path, the host computer having a main memory that stores texture mapping data corresponding to the primitives to be rendered, the primitive rendering hardware including a local texture memory that locally stores the texture mapping data corresponding to at least one of the primitives to be rendered, the method comprising the steps of: (a) when a primitive passed to the primitive rendering hardware is to be rendered, determining whether its corresponding texture mapping data is in the local texture memory; (b) when the texture mapping data corresponding to the primitive to be rendered is in the local texture memory, rendering the primitive using its corresponding texture mapping data from the local texture memory; and {circle over (c)} when the texture mapping data corresponding to the primitive to be rendered is not in the local texture memory, performing the steps of; downloading the texture mapping data corresponding to the primitive to be rendered from the host computer main memory to the primitive rendering hardware; and rendering the primitive using its corresponding texture mapping data downloaded from the main memory.