Stepping panel to panel throughout a chart is essentially traveling without moving. One aspect of difficulty that we can measure is the total distance traveled as the player hits the arrows. To do this we must understand the possible methods that a foot can move from one arrow to the next. Let us examine the following pattern's possibilities, starting with the left foot.
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If we ask where the left foot could go after the right foot hits the down arrow, we immediate know of two locations. Let's start with the more difficult move, hitting the right arrow with the left foot. If the arrow the foot is coming from is located directly across linearly to the arrow the foot is going to, this is called a lateral-transfer. These tend to be the least found in step chart design because many of them change the player's viewfield from standard to limited quickly. This is also the farthest the foot can normally travel on the game stage. These two elements make these transfers the hardest to perform both in orientation and distance. To determine the distance traveled, there are two variables we need to speak about; panelLength and footApex.
panelLength & footApex
You'll notice that both of these terms are displayed using camelCase, which is a popular formatting style for programming. We differentiate these terms from the others because they are variables and depend on other factors we cannot control but must account for. The first is panelLength which is simply the size of the panel. For the purposes of this study, we assume that the panels are all equal in terms of size and shape. These squares are arranged in a 3 by 3 pattern where the corner and center squares are not used for gameplay while the edge squares are the targets. Since these are squares, the length and width are equal; this distance is the panelLength variable. In the case of a lateral-transfer, the foot will move across two panelLengths; center of the first panel to the next according to stage rules. But we can make this distance more accurate using the footApex.
The footApex is a player variable which accounts for the need to lift the foot off of a panel to move to the next one. We assume the player lifts their foot the highest in the middle of the transfer At first, this seems trivial to account for as this should be a relatively small number in comparison to the panel-to-panel distance. Indeed, a player will maximize efficiency keeping this variable small. However, we will see that this number is critical to account for all of the transfer types.
Returning back to the lateral-transfer measurement, we've explained that the distance is two panelLengths; center of the first to center of the next. Using the footApex variable we can estimate the distance traveled for this player's lateral-transfer using the Pythagorean Theorem.
As you can see in the image above, we first need to get the hypotenuse using half of the distance from panel-to-panel, which in this case is simply one panelLength, and the footApex. Then using the theorem we double the result to get the panel distance traveled. This example is simple because the panelLength of a lateral-transfer is easy to calculate. The next is not as easy.
In our example, we can also move the left foot to the up arrow. When the foot moves from a panel to a panel located diagonally across from it, it is called a diagonal-transfer. Diagonal-transfers are more popular than lateral-transfers because a step-artist always has the option of inserting one no matter the player's current foot assignment. In terms of measuring the distance traveled, things get a bit more complicated because we need the Pythagorean Theorem just to calculate this distance. The panel-to-panel distance of a diagonal-transfer is the square root of 2 panelLengths. Then using the Pythagorean Theorem again and including the footApex, we can determine the distance traveled for a diagonal-transfer just as we did with the lateral-transfer previously by halving the panel-to-panel distance and doubling the result from the theorem. Also note all double-steps performed for the purpose of viewfield are diagonal-transfers.
One last type of transfer the player could perform next is called the zero-transfer. As the name implies, the foot doesn't move to a different arrow but instead hits the same arrow again; in this case the left arrow. However, we must account for this movement of up and down to activate the panel again, especially in the case of jacks and jackhammers as they will add up in distance traveled. As you can tell, measuring a zero-transfer distances is as easy as doubling the footApex variable; one distance going up and one going down. These types of transfers are also popular because the arrow a foot came from is always an option for that foot as the arrow is now recently available. Let's look at one more possibility in movement, here's the pattern:
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This possibility here is the final arrow we haven't attempted to hit, the one currently occupied by the right foot. Initially we will assume that it is more efficient to merely perform the jack and not continue to alternate feet. However, future discussions will examine the possibility of alternating feet with this pattern as it is a complex battle between step-artist intent and a player's playstyle. For now, we will merely identify that this move will require at least the diagonal-transfer of the left foot to the down arrow. We would need more information to determine the placement of the right foot as two feet should not occupy the same arrow.
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