  In this paper, we give several simple methods for drawing a whole rational
surface (without base points) as several Bezier patches. The first two methods
apply to surfaces specified by triangular control nets and partition the real
projective plane RP2 into four and six triangles respectively. The third method
applies to surfaces specified by rectangular control nets and partitions the
torus RP1 X RP1 into four rectangular regions. In all cases, the new control
nets are obtained by sign flipping and permutation of indices from the original
control net. The proofs that these formulae are correct involve very little
computations and instead exploit the geometry of the parameter space (RP2 or
RP1 X RP1). We illustrate our method on some classical examples. We also
propose a new method for resolving base points using a simple ``blowing up''
technique involving the computation of ``resolved'' control nets.
