whats being said in this thread is sufficient for DI in Brawl but not entirely complete...
From Magus (
source):
This is the control stick, obviously. For purposes of SDI, the blue zone is considered 'neutral', while moving the control stick from inside the blue zone to inside the orange zone is considered one input. When rotating the stick clockwise, the placement of the stick on the first frame after it passes a pink arrow is the next DI input (likewise for blue arrows and counterclockwise). This is why going from a diagonal to a cardinal direction (the '36' in '23698') is ignored - because you don't pass an arrow.
The c-stick is considered a macro of 'control stick + attack' by the game, overriding the control stick's direction for one frame. More c-stick inputs are ignored until after the c-stick has been returned to the blue zone. This explains why 'hold 7, c-stick 9' provides 3 inputs - the game considers the upper pink arrow crossed on the frame the c-stick is pressed and the upper blue arrow on the frame afterward.
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In Melee, the control stick was looked at as a circle. That is, the most you could move in any direction via SDI was a total of 1 space per input. You could go 1 space directly horizontal, directly vertical, diagonally, at a 20 degree angle, etc. As an example, if you divided an up-right SDI into its components, you would see that you move 1/sqrt(2) spaces up and 1/sqrt(2) right (see: pythagorean theorem), for a total movement of 1 space. Thus, 'ideal' SDI, getting the most possible movement in one cardinal direction, would involve deviating from that direction by 10 degrees on either side to move as directly as possible while still crossing its blue and pink arrows.
On the other hand, Brawl looks at the control stick a little differently. The maximum movable distance during SDI is not right at the edge of the control stick but somewhat inward. This means that if you move the control stick all the way in a cardinal direction in Brawl, you have a 1-space movement, but if you move off the cardinal towards the diagonal, you still get that full 1 space in that direction
in addition to whatever the component of the other direction is! Right at the diagonal, your movement is a full space in both components. That means you move a total of sqrt(2) spaces in the diagnoal direction, as opposed to Melee's 1 space. Think of Brawl's control stick like a square rather than a circle - you can go completely in one direction and completely in a perpendicular direction at the same time, rather than only being able to go partially in both. Thus, you get no benefit from sticking within 10 degrees of the cardinal as opposed to going to diagonals (unless it's faster for you), as you'll get the maximum amount of SDI in whatever particular cardinal direction both ways.
tl;dr: Melee ideal DI in a cardinal direction is hold control stick 10 degrees off the cardinal and smash the c-stick 10 degrees off the cardinal the other way, while Brawl ideal SDI works with any number of degrees 10 to 45 off the cardinal, and gives a slightly larger boost in whatever direction than Melee does.
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This applies to trajectory DI as well, using the same concepts (Melee maximum anywhere is 1 space, Brawl maximum on cardinals is 1 space but on diagonals is sqrt(2) spaces (by 'Project:M', the pictures mean 'Melee and Project:M'):
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This also applies to escaping grabs and breaking stun, ex. holding the control stick on 7 while moving the c-stick from 9 to 1 and back (game reads the stick as 797179717...) is significantly faster than not holding the control stick (read as 9191...), and moving the control stick from 7 to 3 while moving the c-stick from 9 to 1 (alternating so that one stick is moving while the other stick is still) is significantly faster than both (797313797313...). Note how all of those notations have two 9's and two 1's but vastly different amounts of control stick inputs.
