Parallel Universe: Difference between revisions
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[[File:ParallelUniverseViews.jpg|thumb|A diagram of Parallel Universe movement in [[Hazy Maze Cave]], after [[Mario]] has returned to the main map.]] | [[File:ParallelUniverseViews.jpg|thumb|A diagram of Parallel Universe movement in [[Hazy Maze Cave]], after [[Mario]] has returned to the main map.]] | ||
A '''Parallel Universe''', or '''PU''', is a region of space located far outside the intended map boundaries that reflects certain aspects, especially the floors and/or ceilings, of the main map. When the game looks for floors below (or ceilings above) a given object, it first "truncates" the object's position from a floating point value to a 16-bit integer value. While the range of a floating point value is infinite, the range of a 16-bit integer value is -2<sup>15</sup> = -32,768 to 2<sup>15</sup> - 1 = 32,767. If a coordinate of the object's position falls outside this range, it "wraps around". For example, if one of these floating point values is 40,000, then 40,000 - 65,536 = -25,536 will be used when determining if the object is aligned with a floor or ceiling. This gives the illusion that the floors and ceilings of the main level map are "copied" repeatedly in a uniform 3D grid, at a spacing of 65,536 units. | |||
[[File:Visible PU.png|thumb|184x184px|Frame of [[Peter Fedak|Peter Fedak's]] video where he turns Parallel Universes visible using hacks; notice the lack of [[objects]]|left]] | |||
The | The truncation responsible for the existence of parallel universes is only performed when determining alignment with floors and ceilings. This means that walls and objects, both of which use floating point arithmetic to determine collision, do not "exist" in PUs, unless they are brought there. | ||
== Vertical parallel universes == | == Vertical parallel universes == | ||
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==Travel and movement== | ==Travel and movement== | ||
[[File:Mario looking from a PU.png|thumb|251x251px|Mario looking to the original map from a PU]] | [[File:Mario looking from a PU.png|thumb|251x251px|Mario looking to the original map from a PU]] | ||
Parallel universes have found uses in both speed TASes and the [[A Button Challenge]] since they allow greater control of movement through a level. PU routing is comparable to movement through a five-dimensional space, as Mario can be modelled as travelling along five axes: three "relative" axes describing his position within the map, and two integers to specify which PU he is currently in. Mario can adjust his [[speed]] and [[angle]] to move relatively around the stage regardless of how many PUs he moves in the ''x'' or ''z'' dimensions. | Parallel universes have found uses in both speed TASes and the [[A Button Challenge]] since they allow greater control of movement through a level. PU routing is comparable to movement through a five-dimensional space, as Mario can be modelled as travelling along five axes: three "relative" axes describing his position within the map, and two integers to specify which PU he is currently in. Mario can adjust his [[speed]] and [[angle]] to move relatively around the stage regardless of how many PUs he moves in the ''x'' or ''z'' dimensions. | ||
Mario's movement is split up into four [[Movement Steps|quarter steps]], and if any of these quarter steps attempts to place Mario out of bounds, his movement is cancelled. Therefore in order to move to a PU, Mario's speed must be a multiple of four times the distance between PUs. If Mario takes all four quarter steps, then he will move four PUs in a single frame. This distance is called the '''Quadruple Parallel Universe''', or '''QPU''', distance. | |||
If one of Mario's quarter steps (other than the first one) ends out of bounds, the game will cut his movement short. In this case, Mario does not travel the full QPU distance, and instead ends at whichever PU he made it to before his intended quarter step became out of bounds. This is referred to as a '''misaligned QPU'''. | |||
As travelling to PUs involves moving very far from the origin, floating point imprecision can begin to have a significant affect on Mario's position, angle, and collision. | As travelling to PUs involves moving very far from the origin, floating point imprecision can begin to have a significant affect on Mario's position, angle, and collision. | ||
== Floating point truncation crash == | == Floating point truncation crash == | ||
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* Mario's quarter step gets cancelled while on the ground | * Mario's quarter step gets cancelled while on the ground | ||
* Mario collides with a wall head-on with PU speed | * Mario collides with a wall head-on with PU speed | ||
== Miscellaneous behavior == | |||
Certain objects and graphics behave interestingly while in parallel universes. For example: | |||
* Shadows and coin twinkle effects are glitchy | |||
* Spawning a 100 coin star will [[Softlock|softlock]] the game |