Autostereoscopy is usually perceived at finite viewpoints that result from the separated pixel array of a display system. With directionally illuminated autostereoscopy, the separation of the illumination channel from the image channel provides extra flexibility in optimizing the performance of autostereoscopy. This work demonstrates that by taking advantage of illumination freedom, seamless viewpoints in the sweet viewing region, where the ghosting does not cause significant discomfort, are realized. This realization is based on illuminating the screen with a polyline array of light emitting diodes (LEDs), and continuous viewpoints are generated through independent variation in the radiance of each individual LED column. This new method is implemented in the directionally illuminated display for both single and multiple viewers, proving its effectiveness as a valuable technique for achieving a high-quality and high-resolution autostereoscopic display with seamless viewpoints.