#spatial direction

mm. i mean the way that louis takes up or occupies space around himself has v v distinctively changed. at the advent of zayn leaving, i made an offhand extremely distraught post about it.

previous to a.z. i have described louis’ spatial occupation as debate based. mostly interactive: he tends to argue with it, push at it, redefine it, work around or with it. now he is notably passive and is letting others take more control - or lead him in his own space. he looks like he feels unsettled and lost. his shoulders are turned in and his legs are together more and his hands are often in his lap. gesture wise, he’s gone smaller and he seems sometimes unsure of how to fill a silence, whereas before, not that he wouldn’t have been unsure sometimes, but that it wouldn’t have occurred to him to let that prohibit him from rushing in and trying to mesh with a space, make it move and adjust to him. louis is, at the core, a very hard worker.

and i look at him, and he is in a lot of pain and has dropped down his spatial interactivity and it’s very obvious.

he’s gone internal i think. as an extroverted, v firmly people oriented person who interacts with space previously in such a way, the dramatic change is both v obvs to me and v v v painful. i think he’s working hard now at keeping a lot of things penned in or minutely expressed and it’s hurting. the space around him feels fragile, which is why people like niall (notably caretaker) or strangers (caretakers of a night) etc are taking it over instead bc louis doesn’t have a lot of energy/spatial care to spare.

his partner in crime is gone. his bus 1 buddy is gone. the warm, interactive, precise relationship that louis has built a spatial foundation to lean on and into is gone. and i think it’s absence has left a lot in it’s place.

In mathematics, any vector used to represent spatial direction is a direction vector. By convention, direction vectors have magnitude = 1. Given that a point vector p = [ x , y ] blends both direction and magnitude into its two numbers, this vector can be teased apart (factored) into two distinct quantities, separating direction from magnitude (length). The length of vector p, p_len, is its distance from the origin, and is obtained using Pythagorean distance:

p_len <-- sqrt ( x*x + y*y )

The direction from the origin to point p, p_dir, is computed by normalizing vector p. Once p_len is established, direction vector p_dir is obtained by scalar multiplying p by 1/p_len to obtain a unit-length vector preserving the direction of p but erasing its length:

p_dir <-- [ x/p_len , y/p_len ]

The factorization of p into direction p_dir and magnitude p_len is quite generally useful. The original vector p can be reconstituted by scalar multiplying its direction by its length:

p <-- p_len * p_dir

Visually and intuitively, 2D direction vectors are equivalent numerically to the set of points on the unit circle, and provide an alternative to using angles for representing directions. 

The appeal of 2D direction vectors (as compared to angles) is that they may be obtained directly from points without appealing to trig functions. Direction vectors may be used to represent any possible spatial direction. Examples are the run direction of a line, the direction perpendicular to a line, and when defining coordinate rotations, specifying the newXaxis you wish to adopt. From an informatics perspective, direction vectors are a more natural way to represent 2D information than angles, since the latter overcompresses 2D directional information into a 1D scalar. Software algorithms benefit from avoiding overcompressed representations, by eschewing singularities and discontinuities as exceptions needing to be handled. For example, slope squeezes the tilt of a line into a single number, but then has to appeal to infinity as a value (for slopes of vertical lines). Direction vectors distribute the information about line tilt more comfortably across two numbers using the finite number range ( -1 .. +1). Vertical lines do not have to be made into a special case, resulting in algorithmic simplification.