Abstract: We present a fast algorithm of texture synthesis on arbitrary surface using “texture extension” and optimal texture coordinates searching.As to those triangles where there is only 1neighbor triangle synthesized,we get their texture coordinates by directly extending the neighbor triangles’texture coordinates, while those triangles with 2 or 3 synthesized neighbors are synthesized by searching their texture coordinates according to their trapezi form borders.Some experimental results are presented which show that synthesis time of our algorithm is about 2/3of that of previous methods.