Kamui and the Kamui Dimension

Obito's Mangekyo carries Kamui, the power to slip through space and into another dimension.

Two Use-only Techniques

Kamui is two techniques, both use-only: you select them on the loadout and use them with right click.

Listed stats: Kamui is rank A, 3,100 chakra, 27 second cooldown, 6 hand signs. Kamui: Warp is rank S, 5,800 chakra, 45 second cooldown, 6 hand signs. The right-click uses below have their own costs.
Each belongs to one eye. Kamui (your own intangibility and self-warp) belongs to the RIGHT eye. Kamui: Warp (the snap and taking others) belongs to the LEFT eye.
Without that eye in its socket, or with it blind, the technique is refused ("needs the right eye" or "needs the left eye").

Kamui: Intangibility

Hold right click (without sneaking: a sneaking press is the self-warp). It costs 80 chakra a second while held and keeps you "in Kamui": every hostile hit (any hit with an attacking or direct entity, or any jutsu damage) is cancelled and passes through you, with dark smoke particles.
Holding adds 8 strain a second (0.06% right-eye blindness a second).
Smoke ripples spiral round your body, and the body is drawn with a slow twist round the eye.
When you let go, your body slides back over a moment (the phasing lingers about half a second). Out of chakra, it ends.

Kamui: Self-warp

Sneak and press right click, looking anywhere (straight down at your feet works too).
Cost: 150 chakra (free in creative) and 120 strain (0.9% right-eye blindness).
Your body twists into a swirl over 1.2 seconds (bound in place and intangible), then is drawn through into the Kamui dimension, or back out if you are already there.
On arrival you come out of a swirl on the far side, with Slow Falling for 2 seconds.

Kamui: Warp

Select it and hold right click on a target: the one you aim at within 32 blocks, or the first in a 12-degree cone. Looking away to another target (or none) starts the hold over.
A soft whine plays at 1 second to show the snap is ready.
The snap: hold at least 1 second and let go before 3 seconds. Costs 90 chakra and 160 strain (1.2% left-eye blindness). Space twists round the target: it is bound for 0.6 seconds, then half a second later takes 26 "erase" damage, and every enemy jutsu projectile within 4 blocks of it is swallowed.
The take: hold for 3 seconds. Costs 300 chakra and 180 strain (1.35% left-eye blindness). The target is bound for 1.4 seconds while it twists into the swirl, then is sent into the Kamui dimension. Players go too, and see their own body spiral away.
How long they stay: someone taken in is held there for one minute, then the swirl brings them back out to the Overworld (with a moment of Slow Falling). Taking them again restarts the minute.
Anyone stuck in the Kamui dimension with no Obito eye of their own (for example, a player who logged out while held) is let out by the swirl after a moment.

NPC and Cast Versions

When cast rather than held (as NPCs do), Kamui makes the caster intangible for 0.6 seconds with a vortex, and Kamui: Warp snaps the nearest target (bound 0.6 seconds, 26 erase damage, swallows projectiles, 160 strain).

The Kamui Dimension

An endless city of square stone pillars packed side by side, with no gaps to fall through. The tops are flat, pale blue-grey and lit; the sides are dark slate, shading darker further down, with pale highlighted edges down every corner.
Pillars come in sizes from 16x16 down to 4x4. Small ones stand taller and more varied. The land rolls gently around height 96, with tops up to 136.
Each 128x128 region holds one great pale 28x28 platform.
The layout is fixed by position, so it is the same every time and goes on forever.

The Kamui Sky and Rules

There is no sky: a black void with no sun, stars or clouds, and dark fog that fades distant pillars to black.
It is always night, with only a faint ambient light and no skylight.
No mobs spawn there, beds and respawn anchors don't work, and there are no raids.

Travelling in and Out

One block in Kamui equals sixteen blocks outside.
Going in, you arrive at your Overworld position divided by 16, on top of the pillar there, or at the centre of the region's great platform if it's within 48 blocks.
Coming out always returns you to the Overworld at 16 times your Kamui coordinates, on the surface.

How the Swirl Looks

Space twists into a tight spiral centred on the right (Sharingan) eye. First the head is wrung round into it, then the whole body, every part blurring and stretching along the spiral's arms and darkening as it's drawn into the point and gone. A vortex of dark streaks turns round the eye; when the body is through, it closes, leaves a twisted ripple ring in the air, and space snaps back. Coming out is the same, in reverse.