A multi-resolution texture mapping system suitable for large scale terrain rendering using commodity graphics processing units (GPU). The GPU vertex and fragment shaders are used to implement the clip-mapping functionality. The terrain texture is represented by a combination of a mip-map and a multi-level clip-map having independent origins and off-set values. The independent clip-map levels may be independently updated. The offset values allow the origins to be associated with a reference point in a scene to be rendered. The desired clip-map level to be used to render a particular fragment may be determined using the base 2 logarithm of the maximum screen-space derivative of the source texture required by the terrain geometry to be drawn. If the desired clip-map level is non-integer and lies between two clip-map levels, appropriate texel data is created by interpolating between the bounding clip-map levels. This interpolation allows a multi-resolution texture mapping to be displayed.