Rendering for light field displays (LFDs) requires rendering of dozens or hundreds of views, which must then be combined into a single image on the display, making real-time LFD rendering extremely difficult. We introduce light field display point rendering (LFDPR), which meets these challenges by improving eye-based point rendering [Gavane and Watson 2023] with texture-based splatting, which avoids oversampling of triangles mapped to only a few texels; and with LFD-biased sampling, which adjusts horizontal and vertical triangle sampling to match the sampling of the LFD itself. To improve image quality, we introduce multiview mipmapping, which reduces texture aliasing even though compute shaders do not support hardware mipmapping. We also introduce angular supersampling and reconstruction to combat LFD view aliasing and crosstalk. The resulting LFDPR is 2-8x times faster than multiview rendering, with similar comparable quality.