So since each level of a mipmap is a quarter of the size where we take half the height and half the width of the previous level, I believe the storage overhead can be calculated as follows: We start with a size WxH image and as we create new mipmaps we get the series WH + (W/2 * H/2) + (W/4 * H/4) + ... + (1 * 1). Total Overhead = WH (1 + 1/2 + 1/4 + ...). And the sum of the series (1 + 1/2 + 1/4 + ...) converges to 1/(1 - 1/4) = 4/3. So the total storage = WH*4/3
DestinyLuong
Why does mipmapping split the image up into RGB? Does this affect the way that they are stored at all?
sylviacx
For the RGB layout, my understanding is that an image is represented by its R, G, and B channels. So for a 10x10 pixel image, we need to store 10x10 R, 10x10 G, and 10x10 B values. Those values are represented by the largest R, G, and B squares. Since each layer is downsampled by half, the effective "area" or storage of the subsequent layers are decreased by 1/4, which is why the next R, G, and B squares are 1/4 the size of the originals. Effectively, the total "area" taken by the higher levels of the mipmap can all fit into the fourth quadrant.
stephanie-fu
Is there any optimization on the GPU level to get these pyramids to fit and be processed most efficiently?
So since each level of a mipmap is a quarter of the size where we take half the height and half the width of the previous level, I believe the storage overhead can be calculated as follows: We start with a size WxH image and as we create new mipmaps we get the series WH + (W/2 * H/2) + (W/4 * H/4) + ... + (1 * 1). Total Overhead = WH (1 + 1/2 + 1/4 + ...). And the sum of the series (1 + 1/2 + 1/4 + ...) converges to 1/(1 - 1/4) = 4/3. So the total storage = WH*4/3
Why does mipmapping split the image up into RGB? Does this affect the way that they are stored at all?
For the RGB layout, my understanding is that an image is represented by its R, G, and B channels. So for a 10x10 pixel image, we need to store 10x10 R, 10x10 G, and 10x10 B values. Those values are represented by the largest R, G, and B squares. Since each layer is downsampled by half, the effective "area" or storage of the subsequent layers are decreased by 1/4, which is why the next R, G, and B squares are 1/4 the size of the originals. Effectively, the total "area" taken by the higher levels of the mipmap can all fit into the fourth quadrant.
Is there any optimization on the GPU level to get these pyramids to fit and be processed most efficiently?