Mode7 transformations

Question

I've been studying mode7 from the SNES, and looking how to build it myself in C++.

I've found plenty of examples in SDL for rendering stuff like Mariokart levels, where the mode7 effect is applied by 'hovering' over a picture.

What I'm wondering is, is how difficult it would be to apply transformations like shown in this gif from 7th Saga: starting with a normal, top-down view on a image and then rotating, zooming and ending up in the 'mariokart-like' perspective.

Is this worthwile to build manually in pixel-by-pixel transformations, or should I be making this in a true 3D environment like OpenGL?

Or Maybe some kind of in-between solution, where I use SDL to transform/rotate textures, and then use manual pixel manipulation?

For reference, this is a project I've been studying for Mode7: https://github.com/jmermar/Mode7-SDL

Answer 1

Using full 3D, it's pretty easy. You're simply moving & rotating the camera relative to a textured quad or flat mesh.

Using pixels only, it's more challenging. The mapping formula is available on Wikipedia:

Mode 7 graphics are generated for each pixel by mapping screen coordinate \$r\$ to background coordinate \$r'\$ using an affine transformation and sampling the corresponding background color. The 2D affine transformation is specified for each scanline by 6 parameters; \$a,b,c, d\$ define the matrix \$M\$, while \$x_0\$ and \$y_0\$ define the vector \$r_0\$ locates the origin of the matrix transformation and is related to a translation vector. Specifically, screen coordinate \$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 \$r'\$. In 2D matrix notation, this is written as: $$r'=M(r-r_0)+r_0 \\ \begin{bmatrix} x' \\ y' \end{bmatrix} = \begin{bmatrix} a & b \\ c & d \end{bmatrix} ( \begin{bmatrix} x \\ y \end{bmatrix} - \begin{bmatrix} x_0 \\ y_0 \end{bmatrix}) + \begin{bmatrix} x_0 \\ y_0 \end{bmatrix} $$ 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.

If you're looking at the historical, pixel manipulation method, it's worth mentioning that the original implementation had some rounding errors that resulted in visual artifacts - the output looked somewhat blocky & had visual artifacts:

The above was taken from this video clip.

As to which approach you should use - only you can answer that. That depends on your time, interest, skills, constraints and other things not covered in the question & beyond the scope of GDSE recommendations. My advice would be to consider the pros & cons of those factors & choose accordingly.