Analyzing the Spatial Construction of Super C

Taxonomy of Virtual Spaces Part II

The Super Mario Bros. World 1-1 replica is working well in my project, but the original game doesn't have much of a sense of depth into screen space. There are some hills, clouds, bushes, castles, fences, and horsehair plants in the background, but it is difficult to get a sense of how far these objects are from the player's path. I am able to infer some implied depth from objects like warp pipes, but the game's orthographic projection makes everything appear very flat.

For my second game world, I turn to another NES classic, Super C (Konami, 1988), the sequel to the original Contra and a port of Konami's arcade game Super Contra (1988). [Why did Konami name this game Super C instead of Super Contra in the USA? It is assumed that it was to avoid comparison to Ronald Reagan's Iran-Contra scandal that had recently been exposed.] I have written about Super C before as an example of a game with elevation oblique projection. The game actually has a wide variety of visuo-spatial configurations with different styles of gameplay in different levels, but I want to concentrate on Area 1, Fort Firestorm.

Super C Area 1, Fort Firestorm

What is Oblique Projection?

With an oblique projection, the front face of an object that is parallel to the picture plane (in this case, the dark wall below the ground plane) is represented in its true shape, just like an orthographic projection. However, unlike orthographic projections where the projectors are perpendicular to the picture plane, oblique projectors are at an oblique angle to the picture plane (remember that this uses the Primary Geometry projection model). Therefore, two other sides of the object are also visible, but their shapes are distorted (read my other posts for more on the historic confusion between axonometric and oblique terminology).

The receding lines of the object are foreshortened (or not) by a certain amount depending on the angle of the projectors from the picture plane. Cavalier Projection is when the projectors are at 45° and the foreshortening ratio is 1:1 (in other words, no foreshortening). Cabinet Projection is when the projectors are at arccot(1/2) (about 64°) and the foreshortening ratio is 1:2 (receding lines are drawn at 1/2 normal length. These are older methods of creating technical drawings for the military (cavalier) or furniture industry (cabinet) and are designed for preserving object measurements, not for their aesthetic qualities. For a less distorted image, a foreshortening ratio of 2/3 or 3/4 would be more pleasing to the eye ("Planar Geometric Projections and Viewing Transformations" by Ingrid Carlbom and Joseph Paciorek, Computing Surveys, vol. 10, no. 4 (1978) pg. 482).

What Kind of Oblique Projection is Fort Firestorm?

What would these floor sections look like from an overhead view?

The game's imagery must be analyzed before I can determine how to recreate the world with 3-D models. How wide is the player's path? Characters are about the same size on the screen as in Super Mario Bros. so I can keep the general scale the same (measured in 16 x 16 pixel "blocks" that translate to Unity square meters).

In the image above, the large gray rhombus shapes on the player path look like they are obliquely distorted square shapes to me, reminiscent of the square slabs of a sidewalk. The long edge of each rhombus (the non-foreshortened edge) is exactly 64 pixels. The short edge (the foreshortened edge) is almost exactly 32 pixels. This gives a 1:2 foreshortening ratio, which is a Cabinet Projection. The exact type of oblique projection is not important, but this gives me a ratio to determine the size of the "gutters" and projections along the edge of the player path. On the right of the above image, I show what an overhead view of the player path would look like if seen from directly overhead.

With these measurements, I can easily recreate the main player path of the level in 3-D.