Mode 7

Mode 7 graphics are generated for each pixel by mapping screen coordinate ${\displaystyle \mathbf {r} }$ to background coordinate ${\displaystyle \mathbf {r} ^{\prime }}$using an affine transformation and sampling the corresponding background color. The 2D affine transformation is specified for each scanline by 6 parameters; ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$, and ${\displaystyle d}$ define the matrix ${\displaystyle \mathbf {M} }$, while ${\displaystyle x_{0}}$ and ${\displaystyle y_{0}}$ define the vector ${\displaystyle \mathbf {r} _{0}}$ locates the origin of the matrix transformation and is related to a translation vector. Specifically, screen coordinate ${\displaystyle \mathbf {r} }$ is translated to the origin coordinate system, the matrix is applied, and the result is translated back to the original coordinate system to obtain ${\displaystyle \mathbf {r} ^{\prime }}$. In 2D matrix notation, this is written as

${\displaystyle \mathbf {r} ^{\prime }=\mathbf {M} (\mathbf {r} -\mathbf {r} _{0})+\mathbf {r} _{0}}$

${\displaystyle {\begin{bmatrix}x'\\y'\end{bmatrix}}={\begin{bmatrix}a&b\\c&d\end{bmatrix}}\left({\begin{bmatrix}x\\y\end{bmatrix}}-{\begin{bmatrix}x_{0}\\y_{0}\end{bmatrix}}\right)+{\begin{bmatrix}x_{0}\\y_{0}\end{bmatrix}}}$.

All arithmetic is carried out on 16-bit signed fixed point numbers, while all offsets are limited to 13 bits. The radix point is between bits 7 and 8.

Two-dimensional affine transformations can produce any combination of translation, scaling, reflection, rotation, and shearing—and nothing else. However, many games create additional effects by setting a different transformation matrix for each scanline. In this way, pseudo-perspective, curved surface, and distortion effects can be achieved.