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Wii VC Round-to-Zero: Difference between revisions
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The example given above is taken from the code controlling the oscillation of the platforms at the beginning of [[Bowser in the Fire Sea]]. Using the N64's rounding mode, the <code>y</code> variable, which represents the platform's height, will repeatedly return to its original value and continue oscillating with fixed maximum height. Even though each double to single conversion produces a small amount of error, this error balances out over the course of the platform's cycle. On the Wii VC, however, the error always accumulates in the same direction (upward if the platform is below ''y'' = 0, and downward if the platform is above ''y'' = 0), and so the platform slowly drifts in the vertical direction. This is known as '''Wii VC platform drift'''. | The example given above is taken from the code controlling the oscillation of the platforms at the beginning of [[Bowser in the Fire Sea]]. Using the N64's rounding mode, the <code>y</code> variable, which represents the platform's height, will repeatedly return to its original value and continue oscillating with fixed maximum height. Even though each double to single conversion produces a small amount of error, this error balances out over the course of the platform's cycle. On the Wii VC, however, the error always accumulates in the same direction (upward if the platform is below ''y'' = 0, and downward if the platform is above ''y'' = 0), and so the platform slowly drifts in the vertical direction. This is known as '''Wii VC platform drift'''. | ||
From its starting position of y=-3065 til it reaches y=-2048, this platform rises 254 times by 1/4096th of a unit for each 256 frame cycle, 127 times as it goes up, 127 times as it goes down (at the peak and bottom of the oscillation cycle, the platform stays still so no rounding occurs). So doing the math, 127/128*1/4096units*30frames*60seconds*60minutes, we get that the platform drifts by ~13. | From its starting position of y=-3065 til it reaches y=-2048, this platform rises 254 times by 1/4096th of a unit for each 256 frame cycle, 127 times as it goes up, 127 times as it goes down (at the peak and bottom of the oscillation cycle, the platform stays still so no rounding occurs). So doing the math, 127/128*1/4096units*30frames*60seconds*60minutes, we get that the platform drifts by ~13.0806 units/h. | ||
Once it passes y=-2048, the platform halves in rising speed: ~6. | Once it passes y=-2048, the platform halves in rising speed: ~6.5403 units/h. The platform continues to halve in speed as it passes through y=-1024, y=-512, y=-256, and all other 2^n boundaries til it comes to a halt near y=0. | ||
As it passes through a 2^n boundary, its behavior becomes complex. Throughout its up-down oscillation cycle, the platform is sometimes past the 2^n boundary and sometimes not. The overall speed decrease as the platform's average height passes through the 2^n boundary is represented by a differential equation of <code>[velocity of y]=dy/dt=arccos(y)</code>: the platform suddenly slows down quickly, then at a slower rate before it decelerates faster again, and finally, suddenly the platform's acceleration completely stops, the speed settling at a constant, half of what it started with. | As it passes through a 2^n boundary, its behavior becomes complex. Throughout its up-down oscillation cycle, the platform is sometimes past the 2^n boundary and sometimes not. The overall speed decrease as the platform's average height passes through the 2^n boundary is represented by a differential equation of <code>[velocity of y]=dy/dt=arccos(y)</code>: the platform suddenly slows down quickly, then at a slower rate before it decelerates faster again, and finally, suddenly the platform's acceleration completely stops, the speed settling at a constant, half of what it started with. | ||