If you implement this on the GPU, it's my understanding you can get the 4th-order interpolation quite cheaply exploiting the bilinear texture sampling hardware[

If you implement this on the GPU, it's my understanding you can get the 4th-order interpolation quite cheaply exploiting the bilinear texture sampling hardware[1]. So instead of reading 16 grid values and combining them to get the interpolated sample value, you can fetch 4 bilinearly filtered samples and combine those. And thanks to the hardware filtering, those bilinear samples cost basically the same as reading an unfiltered value. [1]: https://developer.nvidia.com/gpugems/gpugems2/part-iii-high-quality-rendering/chapter-20-fast-third-order-texture-filtering https://developer.nvidia.com/gpugems/gpugems2/part-iii-high-...