Mip mapping

A mip-map is a set of images $M = {M_0, ..., M_m}$ , where for all $s$ :

$M_s$ is a resampling of $M_0$ .
$M_s$ has extents $(2^{m - s}, ..., 2^{m - s})$ .

As an overload of terminology, each $M_s$ is also called a mip-map. The meaning of the term should be clear from the context.

Practice

Pastel implements the MipMap class for storing and manipulating mip-maps. It is declared as:

template <typename Type, integer N = 2>
class MipMap;

Memory requirements

Assume an n-dimensional image takes $C$ units of memory. Then the memory requirements for its mipmaps can be bounded by $m(n) = C * (2^n / (2^n - 1))$ . For example:

$m(1) = C * 2$
$m(2) = C * (4 / 3)$
$m(3) = C * (8 / 7)$
$text(lim)_{n -> oo} m(n) = 1$
$\forall n in NN: 1 <= m(n) <= 2$

Example

Here is an example of a mip-map for a 2-dimensional image. The invidual mip-maps have been combined into a single image for visualization. Note: this image was originally 1024 x 1024, which I resampled to 512 x 512 to better fit the webpage.

A mip-map illustrated.

Files

Algorithms for mip-maps

MipMap class

A set of precomputed successive downsamplings of an image

MipMap example

mipmap_example.cpp

Mipmap module

mipmap.h