A battle royale on the inside of a hollow world

The sky is the other half of the map

The map is the inside surface of a sphere or an ellipsoid. A field holds you to the shell and fades with altitude, so the middle of the world is a weightless void with a glowing core, the Heart. Everything you see overhead is playable ground. Gates fold the surface together: walk through one and you come out somewhere else, still moving, and the world turns to put your feet down again.

What the prototype above already does

• Three worlds you can switch between: Hollow (sphere), Lens (two facing plates joined by a rim) and Rama (a tube with domed caps). Each can be scaled from 0.4× to 1.4× in the pause menu, so the Hollow runs from a 60 m sphere to a 210 m one.
• Skin gravity, lift beams up launch spires (one column the deck's width, so nothing overhangs), sling pads, and drifters: floating rocks with their own small gravity wells.
• The camera re-levels by rolling about your view axis when "down" flips mid-flight.
• Three live see-through gate pairs: Antipode, Sling and Drift. You can walk, shoot and throw through them.
• A first-person gun with recoil, spread, a 24-round magazine and reloads, plus an under-barrel launcher whose skyshells arc along the field. It is the classic black rifle the bunnies hold, in black metal that takes its shape from the sky it reflects (the holes don't shine), and drawn as a projection like them: a mint rim and the red and cyan fringe. Its bore runs parallel to your view, so it points at the reticle at any range. Your own chunky plush paws hold it, the left one pumping the launcher (Paws in the pause menu turns them off). A reload is a little show: the gun cants to show its magazine well, the left paw strips the old magazine and flicks it away (it glitches out as it falls, being a projection), a new one prints into the paw on the way up, clasped round its body, rocks in front lip first and seats with a slap, then the paw lets go and boops it from below; from empty it goes from the magazine straight up to slap the bolt catch instead. The rounds go in at the seat (1.15 s, or 1.45 s from empty) and firing skips the rest; a skyshell launch cuts a reload short. A fall-arc preview shows where you will land.
• The Skylance, a long-range launcher on key 2, an RPG's lines in the rifle's black metal. Its round sits in the mouth, a fat warhead whose belly band glows as the lock builds; two lamps on the back of the front sight show the rounds left. A shot kicks the round out of the mouth and its motor lights a beat later, then it tears off along the path you aimed; the next round prints in half a second on, and after the last the left paw loads a new one and boops its nose. In flight the round shows its motor and four fins. Hold right mouse and its whole flight is solved ahead of time, with the same step the round will fly with. The path, the landing ring and the flight time show in your view, through gates too, and the map becomes a to-scale side view of the shot. It fires only after a short steady lock. Everyone near the landing point sees a warning ring with a countdown, and bots run from it, more slowly when they are mid-fight. Inside the ring's inner 6 m nobody survives; from there to its 9 m rim the blast falls from 90 to 30 damage and shoves people away. A building between you and the blast stops it. Rocks and the Heart pull its rounds three times harder, over twice their usual reach, so a shot aimed just past a rock curves around it and can land on someone hiding behind it. A faint vermilion rim marks that reach while you aim, and the pause menu has a dial for it (1× gives rounds the same field as you).
• The grapple on key 3: a speargun-shaped grapple gun in the rifle's black metal, its hook's three claws folded back round the mouth and its reel hung under the barrel. The hook bites anything built or floating within 56 m (a mint ring marks where), and aiming low on a wall hands it up to the roof edge, or a spire's deck. Hold the trigger to ride the line in; on a roof edge it aims over the edge and, once your feet are over, flings you on the way you look with most of your speed plus a bonus for the line you reeled in. On a drifter or the Heart it holds you on a rope so you whip round. Let go any time to fly on. Two hooks, 3 s each to come back, with a lamp on the gun for each. The design and its measured flights are on The grapple.
• Hit feedback: damage numbers that add up over each target (amber for the head, vermilion for blasts), a distinct headshot sound, a kill banner that counts your kills this life with a rising chime, a line on where each Skylance round landed and what it did, and a combat report of damage dealt and taken when you go down.
• Bots that move with the same physics and fire the same gun, dressed as bunnies. A dash on the ground is one long bound, sized to how far the burst carries them. They react after a delay, aim off at first and settle, fire in bursts, strafe and dodge, and cross the void on pads and lifts. Their number, skill and skin (bunny or the old capsule) are set in the pause menu.
• A map centred on you whose rim is your antipode, and sound that arrives late across the void.
• The field, haze and camera comfort settings are all tunable from the pause menu.

Not in it yet: other people, loot, the zone, netcode. It exists to answer one question: does moving, seeing and fighting in this world feel good?

Shape and size

Inside a convex shell, the straight line between any two points on the surface stays inside. So in principle everybody can see everybody, and anything you throw hard enough lands somewhere on the map. Both facts are the point of the game, and both need managing.

How big

Battle royales are sized by area per player. For a sphere, R = √(N · a / 4π), where N is the player count and a is the area per player. The void adds playable volume on top of the surface area, so the target sits between Warzone's small Rebirth Island and Apex.

Three shapes, three games

• Hollow (sphere). Every point is equivalent and every point has a true antipode. It gives the cleanest map (§6) and the purest version of the idea. Start here.
• Lens (oblate). Two nearly flat worlds face each other 190 m apart, like the film Upside Down, joined by a tight rim (radius of curvature about 49 m). The rim is a half-pipe that carries you from floor to ceiling without leaving the ground. It suits team modes: your plate against theirs.
• Rama (prolate). A tube with domed caps. Across the waist is close (220 m) and along the axis is far (460 m), which makes natural lanes. The long sightline down the axis needs cover.

On an ellipsoid, "down" is the gradient of the ellipsoidal radius ρ = |(x/a, y/b, z/c)|. That gradient is exactly normal to the shell, so buildings stand upright everywhere and the same code serves all three shapes.

Gravity that fades with height

A real hollow planet would be weightless inside. Newton's shell theorem says a uniform shell pulls on nothing it contains, so something else has to hold players to the ground. I compared three candidates.

The Gaussian puts almost all of the climb into the first 40 metres. Near the ground the game plays like a normal shooter at about twice Earth gravity, which is typical for snappy games. A rooftop is floaty. Above the void line you drift, and whichever side you drift toward wins you. The small linear drift term means nobody can park at the centre forever.

Measured in the prototype

How size changes it

Players, buildings, gates and weapons stay human-sized at every scale. What changes is the world around them. Smaller worlds get smaller towns below 0.7×, and from 1× a hamlet joins at the middle of each of the twenty faces. The towns sit on a frame shared by every size: the spawn plaza at the north pole, the Antipode at the south, and ten towns in two rings either side of a band round the middle (see Landscape). Where the ground curves tightly, a block that would lean into its neighbour is cut down. The gravity falloff height and the spires scale with the radius. Haze is rescaled so the far side fades by the same amount. Rocks only spawn where the void has room for them, with their wells clear of the ground and the spire decks.

Crossing time grows roughly with the radius. Small worlds cross in 4–7 seconds, a good fit for duels and 2v2. The player counts use the battle royale density from §1; an arena mode would pack players tighter. At 0.4× the scripted deck jump comes down on the Heart, because the void is small enough that the Heart and the rocks sit on the obvious lines.

A crossing of 7–12 seconds is long enough to read as an event and short enough to stay fast. At 1.4×, close to the 200 m match world, crossings take 9–18 seconds, so that world will need a stronger air dash or a void boost to keep them under ten. Pads aim themselves. Each one tries eight headings 16–18° off vertical and keeps the one that lands farthest around without hitting a drifter or the Heart. Launching straight up was a bug: everything aimed at the centre got caught by the Heart's well.

What this does to level design

• Verticals converge. Every "up" points at the centre, so two 60 m towers 10 m apart at the ground are 6 m apart at the top of a 150 m world. The first lift beams leaned into their own spire's deck. Beams now run parallel to the spire, and bridges between rooftops get shorter the higher they are.
• Spires are launch towers. A glowing lift beam carries you up. From the deck, a jump plus an air dash crosses the void, and a sling pad crosses it for you.
• Landings are fast. Crossing lands you at 35–50 m/s, so there is no fall damage. Landing is a slam instead: a shock ring and screen shake now, an area-damage ability later. The cost is exposure: while you cross, you are a slow meteor that the whole world can see.
• Drifters and the Heart add wells to the field, like Super Mario Galaxy's planetoids. Paths bend around them, so a near miss of the Heart is a slingshot.
• Fast rounds get their own wells. How much a well bends a shot and how hard it is to climb out of it are the same quantity: the bend goes with the square of the well's escape speed over the shot's speed. A rock already takes 12–14 m/s to leave, more than a jump. A skyshell (30 m/s) skimming one bends 10–17°; a Skylance round (85 m/s) bends 2°. Pulling hard enough to bend the round 13° would take 34 m/s to leave, so nobody who landed on a rock would get off. Skylance rounds therefore feel the rock and Heart wells three times stronger and twice as wide, and bodies keep theirs. A round passing within about 6 m of a rock bends 5–10° and lands 10–20 m from where it would have, and the landing still moves smoothly as you sweep the aim. Shots that pass nowhere near a well are untouched: in 1,500 random shots from the ground at 0.65×, the median moved 0 m and 92% moved less than 5 m. Near the Heart the change is small, under 8 m, because rounds cross the centre at about 78 m/s.
• The math is analytic and deterministic. Client prediction of the field is exact, arcs can be previewed (the fall arc in the prototype), and a server can evaluate it cheaply.

Which way is up

"Up" is wherever the field says it is. The camera has to follow that without making people sick or making them lose their aim. The prototype uses five rules.

1. Small changes carry the camera along. Walking over curved ground, the camera turns by the same minimal rotation as "up" (parallel transport, the idea behind rotation-minimising frames). Without this your pitch drifts by the curvature: 11.5° after 30 m on a 150 m sphere.
2. Big changes are flips, and a flip is a roll about the view axis only. Your view direction never moves, so your aim stays on target. The world turns around the crosshair at a capped speed (4.5 rad/s by default, adjustable). Rotation about one axis is measurably less sickening than combined pitch and roll.
3. Look where you are going and the flip happens around your target. Crossing the void you usually look at the far side, which starts as "up" and becomes "down". The re-level then spins the image gently around the crosshair, and your aim never leaves the spot you are falling toward. Looking dead on, there is nothing to rotate at all.
4. Controls follow the camera, never the world. Super Mario Galaxy's first game reversed left and right when Mario walked upside down, and players got lost. The sequel kept his head up. Here W is always "forward on screen".
5. In the void, controls go fully 3D. When gravity is weak, mouse yaw turns about the camera's own axis, WASD thrusts along the view, and re-levelling slows to a third of its speed.

Seeing across the void

In a concave world everyone has a line of sight to everyone. Unmanaged, the best spot is any rooftop with a long rifle. The prototype uses haze; the full game adds four more tools.

1. A haze core. Haze density is Gaussian around the Heart, and the optical depth along any sight line has a closed form (an erf), so it costs a few instructions per pixel. Short lines along the ground stay clear. Lines that pass near the centre fade. Across the Hollow, a target 90° away keeps about 73% of its contrast, 120° keeps 54%, and your antipode keeps about 19%.
2. The Heart itself only blocks near-exact antipodes: beyond 175° for a 7 m core in a 150 m world. A core of R/2 would hide everything beyond 120°. Core size is the main knob between an open world and a private one.
3. Canopy architecture. Roofs, awnings, arcades and trees give cover from above. Open plazas are the risky ground. Rooftops are high ground and also exposed to a whole hemisphere, so height is never free.
4. Ballistics. Rifles stay hitscan inside about 150 m. Long weapons get travel time. Skyshells arc along the field and through gates, which makes artillery across the sky a skill with a visible preview.
5. Sound travels at 343 m/s. A shot from the far side arrives about 0.9 s after its flash, like thunder. It gives information and it gives the world a sense of size. The prototype delays and muffles every sound by distance.

Haze also hides level-of-detail changes on the far side, and that matters for rendering, because there is no horizon to hide anything behind (§9).

Gates

A gate is a rectangle that shows, and leads to, another rectangle somewhere else. One rule covers everything: crossing gate A applies the transform M = B · R_y(π) · A⁻¹ to your position, velocity and camera, and then §3 re-levels you to the local field. The same transform carries bullets, skyshells, sound and the virtual camera that draws the view.

Gate kinds in the prototype

• Antipode gate (cyan). A fixed pair joining the spawn plaza to the point directly overhead. It is a fast way across with no flight and no exposure.
• Sling gate (pink). The exit floats 63 m up, faces just past the Heart, and gives you a minimum exit speed of about 27 m/s. Walk in at a jog and 8 seconds later you land about 120° around the world.
• Drift gate (gold). The exit stands on the underside of a drifter. You arrive standing on a rock in the sky, with your old plaza hanging overhead.

Ideas for the full game

• Folds: a player-placed pair. Drop an anchor, move, then open a 12-second two-way gate between the anchor and you. It works as a periscope, an ambush and an escape.
• Phase gates that move each zone phase, so routes have to be re-learned within a match.
• A gate inside the Heart. Outer Wilds sends you through Brittle Hollow's black hole to the White Hole. Here, diving into the core could send you to the drift field or the next safe zone.

The research suggests some rules. Most gate pairs should keep local "up" the same on both sides. Rotating gates should be rare and memorable. Every exit view should include a landmark. Each pair gets a colour, and the map shows pairs as dashed links.

How the prototype draws and runs them

• Each visible gate renders the scene from a virtual camera M · C into a texture. The surface samples that texture in screen space. The virtual camera's near plane is replaced by the exit gate's plane (Lengyel's oblique clipping), so nothing behind B leaks in.
• The gate surface is a thin box behind the plane, so the view doesn't tear while your eye passes through it. Gates seen inside gates show a tint instead of recursing. The budget is three live gates per frame at 0.6× resolution.
• Hitscan and skyshells split their rays at gates and continue from the exit. Valve's Portal team used the same approach, plus duplicate models for anything halfway through. We will need those duplicates for players.

Finding your way

A normal minimap shows a flat patch around you. Here the whole world is around you, and the most important place is the one straight overhead. So the map is an azimuthal equidistant projection centred on you. Distance from the centre is distance along the ground. The 90° ring is where the floor becomes the wall. The rim is your antipode: everything on it is directly over your head.

• On non-spheres the same map is the logarithmic map of the surface. The Vector Heat Method computes it, along with geodesic distances, on any mesh in milliseconds (Sharp, Soliman & Crane 2019; Crane et al. 2013). Karney's algorithms give exact geodesics on ellipsoids, including triaxial ones.
• Landmarks you can steer by: the Heart (always roughly "up"), the launch spires and their glowing lifts, gate colours, the band round the middle, and each region's own flowers, cooler toward the north and warmer toward the south. Manifold Garden's playtesters got lost in its wraparound gravity. Strong regional identity is the cheap fix.

The match

The match is 40 players in a world about 200 m in radius, aiming for 12 to 15 minutes. The geometry gives the battle royale shape three moments no flat map can have.

1. The drop. Pods ring the Heart. Everyone starts weightless at the centre, sees the whole world at once, and pushes off toward any point of it. There is no flight path, because every landing spot is equally far away.
2. The Eclipse. The safe zone is a spherical cap that shrinks (area 2πR²(1 − cos θ)). The storm grows from the opposite point, so the threat is literally overhead, and everyone can watch the zone close on the far side while they fight.
3. The Heart finale. In the last phase the storm covers the whole shell, and the safe zone becomes a sphere of void around the Heart, shrinking inward. The final fight is weightless and fully 3D among the drifters, like Descent, Shattered Horizon or Echo VR's arena.

Loot and abilities that use the geometry

• Mobility: jump jets, the grapple (a hook on a cable that bites buildings and wells and reels you in, designed on its own page), Fold charges (§5), and a sling grenade that drops a temporary pad.
• Field tools: a gravity grenade that flips the field locally for four seconds, and a plumb scanner that marks who is directly above you.
• Weapons: a hitscan rifle for the floor fight, skyshell launchers for artillery across the sky, and a chord rifle (slow, high velocity) for long sightlines through the haze.
• Slam: landing after a crossing does area damage, so arriving fast is a threat as well as a risk.

What has been tried

How to build it

Keep the world math in one small library

The shell, the field, the gate transforms and the ray casts are a few hundred lines of closed-form math. They live in one library that the client, the server, the bots and the tools all call: sim.js, which runs the whole match (every body, weapon and bot) from inputs at a fixed 120 Hz, with no screen and no clock. The same seed and inputs give the same match in a browser or in Node. That is the best defence against prediction drift between client and server. A port to C++ or Rust (with WASM for the browser) stays open if a full server needs it; in Node a step with 100 bodies takes about 1.2 ms.

Engine

My recommendation: keep iterating on feel in the browser (three.js now, Rapier next) until the 2v2 test in §11 is fun. Then choose the engine. Unreal is the default for a 40-player server-authoritative shooter; Godot makes sense if the team stays small.

Rendering a world with no horizon

• From almost anywhere you can see half the world or more. That calls for hierarchical LOD and impostors for the far hemisphere, plus GPU-driven instancing in the style of Manifold Garden. The haze hides the LOD transitions.
• The Heart is a single point light at the centre, so one cube shadow map covers the entire world. Shadows fall straight "down" everywhere. Rotating shades around the Heart, like Ringworld's shadow squares, could add a moving day and night.
• Gates are the expensive part: each live gate is another scene render. The budget is capped, with distance falloff, tinted recursion and low-resolution views far away.

Netcode

• Server-authoritative, with client prediction and lag-compensated hits (Bernier 2001; Overwatch, GDC 2017). The analytic field makes prediction of free flight exact.
• Teleports need a flag so remote players don't visibly slide across the world. Source does this with an interpolation counter that increments on teleport. Better still, interpolate in the gate's frame while someone is halfway through.
• Lag-compensated rays have to split at gates, using each gate's position at the rewound time. I found no public write-up of this, so it is ours to design and test early.
• Send orientation as a full quaternion, never yaw and pitch alone. Players on the ceiling are upside down for you.

Bots and audio

• Navmesh per surface patch, plus off-mesh links for gates, lifts, slings and precomputed void jumps. The arcs are cheap to sample, so jump links can be generated offline.
• Audio needs propagation delay, distance filtering, and emitters at the exit gate for sounds that pass through. Wwise rooms and portals are a starting point, though teleport gates need custom virtual emitters.

Risks

Plan

1. Feel prototype (this page). Movement, field, camera, gates, haze. Tune until crossing the void is fun on its own.
2. Combat sandbox. Damage, three weapons, simple bots, a slam ability. Measure kill distances and sickness.
3. 2v2 networked arena in a small Hollow (R 60–80 m). Prediction, lag compensation and gate netcode. This is the go or no-go on fun.
4. Squads at 24 players in the Lens. The Eclipse zone, loot, Folds.
5. 40-player battle royale slice at R 200 m with the drop and the Heart finale.

Open decisions

• Field events. A director that reshapes gravity for a few seconds, starting with a band of push that sweeps through the sphere. The brainstorm, with a live slice of the world and measured effects, is on its own page: Field events.
• The grapple. A third gun that fires a hook on a cable: it bites anything built or floating, reels you in while you hold, and flings you on when you let go; round a drifter or the Heart it whips you round. With it, the towns become anchors: heights tied to the void line, a crown in each town and waypoint towers along half the routes. Flights measured in the game, the rules and the townscape proposal are on The grapple.
• World size doesn't read. Changing the size in the pause menu barely changes how far away the far side looks. From inside a sphere, the far side fills the same angles at any radius, so only things with a fixed real size give the scale away, and the prototype hides two of them. The haze is normalised so the whole diameter fades the same at every size, and buildings shrink with the world between 0.55× and 1×. The options are a physical haze with a fixed density per metre (a 120 m world looks crisp, a 420 m one hazy), a partial one that scales with √size, or full-height buildings at every size. The risk is too much haze in the big worlds, so decide after playtesting both.

References

I checked each of these against its source. Where only an abstract or a secondary source was available, the entry says so.