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. Limits Mode 7 can only work on backgrounds, not sprites; therefore, any object that does not rotate or scale with the background must be a sprite, even items that would normally be thought of as part of the background, such as fixed platforms. The game developer must create a sprite with the same appearance as that object. For instance, in Super Castlevania IV, battles in which a large boss such as Koranot rotates have the mobile boss implemented as the background, while the blocks on which the protagonist stands are sprites. With the obvious enhancements, this is similar to how some NES games feature battles against a giant movable boss without the slowdown and flicker inherent in a large sprite set—by making the boss the background, and then moving and animating it. Both systems' examples can only apply to objects in the horizontal plane of the moving object. For instance, a floor, ceiling, or scoreboard can remain part of a background in both the NES and SNES examples as long as they are completely "above" or "below" the field of gameplay. They can also be turned into sprites if the whole screen is needed, but this can cause slowdown. That Mode 7 cannot be used on sprites means that each "size" of an "approaching" sprite for a given distance has to be pre-drawn, meaning that one would see sprites "jump" between a limited number of sizes when "approaching" them. This can be seen in Super Mario Kart and HyperZone whenever an object approaches, or when walking vertically on the Final Fantasy VI map with an airship in view. Similarly, the appearance of sprite rotations must be handled through pre-drawing unless they are done with hardware included in the game cartridge such as the Super FX 2 chip, as with Super Mario World 2: Yoshi's Island. A notable workaround does exist and can be seen in Contra III: The Alien Wars in the second boss battle, and in Super Mario World in the battles against Reznor (platform wall