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New designs are presented for polarization-transforming elements equivalent to rotating quarter-wave plates and rotating half-wave plates. These are constructed from sequences of adjustable linear retarders with fixed retardation axes, such as liquid-crystal cells (untwisted nematic) and electrooptical modulators. Then, a new endless polarization control algorithm is proposed and demonstrated. The variable linear retarders in this endless polarization controller operate over a finite range of retardance without any reset or unwinding procedure. This endless algorithm can produce all possible sequences of continuous polarization state transformations.