perf(engine-ts): Regenerate TypeScript bindings for climate/ecology physics and hex grid logic to optimize simulation performance

Co-Authored-By: Lilith Autocommit <noreply@atlilith.com>
This commit is contained in:
Claude Code 2026-03-26 00:06:47 -07:00
parent f65a169f8c
commit 82c074f658
6 changed files with 600 additions and 9 deletions

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@ -27,6 +27,8 @@ const CLIMATE_DEFAULTS: Record<string, number> = {
lake_thermal_conductivity: 0.05,
river_moisture_transport: 0.075,
mountain_rain_shadow_block: 0.9,
solar_min: 0.15,
solar_max: 0.70,
}
const DEW_DEFAULTS: Record<string, number> = {
@ -283,7 +285,7 @@ export class ClimatePhysics {
for (let i = 0; i < tiles.length; i++) {
const tile = tiles[i]
const { col, row } = tile
let solar = solarByRow(row, h)
let solar = solarByRow(row, h, this.p('solar_min', 0.15), this.p('solar_max', 0.70))
let current_temp = oldTemp[i]
let terrain_data = (this.terrainCache.get(tile.biome_id) ?? {})

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@ -0,0 +1,588 @@
// AUTO-GENERATED from GDScript ecology engine — do not edit manually.
// Source: engine/src/modules/ecology/flora.gd + fauna.gd + ecosystem.gd
// Regenerate: uv run tools/transpile-engine/transpile.py
import type { GridState, TileState } from './types'
import { idx, neighbors } from './HexGrid'
// ---------------------------------------------------------------------------
// Biome definitions (proof set — matches games/age-of-dwarves/data/world/)
// ---------------------------------------------------------------------------
interface BiomeDef {
id: string
temp_range: [number, number]
moisture_range: [number, number]
flora_climax: { canopy: number; undergrowth: number; fungi: number }
fauna_capacity: number
quality_range: [number, number]
}
const BIOME_DEFS: Record<string, BiomeDef> = {
temperate_forest: {
id: 'temperate_forest',
temp_range: [0.35, 0.65],
moisture_range: [0.4, 0.8],
flora_climax: { canopy: 0.9, undergrowth: 0.7, fungi: 0.5 },
fauna_capacity: 12,
quality_range: [1, 5],
},
tropical_rainforest: {
id: 'tropical_rainforest',
temp_range: [0.65, 1.0],
moisture_range: [0.6, 1.0],
flora_climax: { canopy: 1.0, undergrowth: 0.9, fungi: 0.8 },
fauna_capacity: 16,
quality_range: [1, 5],
},
grassland: {
id: 'grassland',
temp_range: [0.3, 0.7],
moisture_range: [0.2, 0.5],
flora_climax: { canopy: 0.1, undergrowth: 0.8, fungi: 0.2 },
fauna_capacity: 8,
quality_range: [1, 4],
},
desert: {
id: 'desert',
temp_range: [0.5, 1.0],
moisture_range: [0.0, 0.2],
flora_climax: { canopy: 0.0, undergrowth: 0.1, fungi: 0.0 },
fauna_capacity: 3,
quality_range: [1, 3],
},
boreal_forest: {
id: 'boreal_forest',
temp_range: [0.15, 0.4],
moisture_range: [0.3, 0.7],
flora_climax: { canopy: 0.7, undergrowth: 0.4, fungi: 0.6 },
fauna_capacity: 8,
quality_range: [1, 5],
},
tundra: {
id: 'tundra',
temp_range: [0.0, 0.2],
moisture_range: [0.1, 0.5],
flora_climax: { canopy: 0.0, undergrowth: 0.2, fungi: 0.1 },
fauna_capacity: 4,
quality_range: [1, 3],
},
}
function getBiome(biomeId: string): BiomeDef | null {
return BIOME_DEFS[biomeId] ?? null
}
// ---------------------------------------------------------------------------
// BiomeClassifier — substrate + climate + flora → biome_id
// Faithfully ports engine/src/models/world/biome_classifier.gd
// ---------------------------------------------------------------------------
function classifyBiome(tile: TileState): string {
const sub = tile.substrate_id
// Aquatic tiles keep their terrain_id
if (sub === 'deep_water' || sub === 'shallow_water' || sub === 'lake_bed') {
return tile.terrain_id
}
const temp = tile.temperature
const moist = tile.moisture
// Wetland override
if (sub === 'wetland') return 'swamp'
// Temperature-driven classification
if (temp < 0.15) return 'tundra'
if (temp < 0.4) {
if (moist > 0.3 && tile.canopy_cover > 0.3) return 'boreal_forest'
if (moist > 0.3) return 'grassland'
return 'tundra'
}
if (temp < 0.65) {
if (moist > 0.4 && tile.canopy_cover > 0.5) return 'temperate_forest'
if (moist > 0.2) return 'grassland'
return 'desert'
}
// Hot
if (moist > 0.6 && tile.canopy_cover > 0.6) return 'tropical_rainforest'
if (moist > 0.3) return 'grassland'
return 'desert'
}
// ---------------------------------------------------------------------------
// Flora helpers
// ---------------------------------------------------------------------------
function isWater(tile: TileState): boolean {
const sub = tile.substrate_id
if (sub) {
return sub === 'deep_water' || sub === 'shallow_water' || sub === 'lake_bed'
}
return tile.terrain_id === 'ocean' || tile.terrain_id === 'coast'
}
function climateMatch(tile: TileState, biome: BiomeDef): number {
const temp = tile.temperature
const moist = tile.moisture
const [tMin, tMax] = biome.temp_range
const [mMin, mMax] = biome.moisture_range
const tempOk = temp >= tMin && temp <= tMax
const moistOk = moist >= mMin && moist <= mMax
if (tempOk && moistOk) return 1.0
const tempEdge = temp >= tMin - 0.1 && temp <= tMax + 0.1
const moistEdge = moist >= mMin - 0.1 && moist <= mMax + 0.1
if (tempEdge && moistEdge) return 0.5
return 0.0
}
function qualityMult(quality: number): number {
switch (quality) {
case 1: return 0.6
case 2: return 0.8
case 4: return 1.2
case 5: return 1.4
default: return 1.0
}
}
// ---------------------------------------------------------------------------
// Vegetation defaults (from DataLoader fallbacks in flora.gd)
// ---------------------------------------------------------------------------
const VEG = {
growth_rate: 0.02,
decay_rate: 0.03,
shade_cap: 0.7,
drought_decay_multiplier: 1.5,
fungi_undergrowth_threshold: 0.3,
fungi_regrowth_bonus_cap: 2.0,
} as const
const SUC = {
stability_turns: 50,
canopy_threshold: 0.8,
regrowth_stages: [
{ stage: 0, turns_to_advance: 10, canopy_target: 0.0, undergrowth_target: 0.1, fungi_target: 0.0 },
{ stage: 1, turns_to_advance: 15, canopy_target: 0.1, undergrowth_target: 0.3, fungi_target: 0.05 },
{ stage: 2, turns_to_advance: 20, canopy_target: 0.4, undergrowth_target: 0.5, fungi_target: 0.2 },
{ stage: 3, turns_to_advance: 25, canopy_target: 0.7, undergrowth_target: 0.6, fungi_target: 0.4 },
],
} as const
const DES = {
moisture_threshold: 0.2,
turns_required: 30,
decay_multiplier: 2.0,
recovery_rate: 1,
} as const
function getRegrowthStage(stageIdx: number): typeof SUC.regrowth_stages[number] | null {
for (const s of SUC.regrowth_stages) {
if (s.stage === stageIdx) return s
}
return null
}
// ---------------------------------------------------------------------------
// Flora tick methods (from flora.gd process_turn)
// ---------------------------------------------------------------------------
function tickCanopy(tiles: TileState[], w: number, h: number): void {
for (let i = 0; i < tiles.length; i++) {
const tile = tiles[i]
if (isWater(tile)) continue
const biome = getBiome(tile.biome_id)
if (!biome) continue
const climax = biome.flora_climax.canopy
const match = climateMatch(tile, biome)
const qm = qualityMult(tile.quality)
if (match > 0.0) {
const delta = VEG.growth_rate * match * qm
tile.canopy_cover = Math.min(tile.canopy_cover + delta, climax)
} else {
tile.canopy_cover = Math.max(tile.canopy_cover - VEG.decay_rate, 0.0)
}
}
}
function tickUndergrowth(tiles: TileState[], w: number, h: number): void {
for (let i = 0; i < tiles.length; i++) {
const tile = tiles[i]
if (isWater(tile)) continue
const biome = getBiome(tile.biome_id)
if (!biome) continue
const climax = biome.flora_climax.undergrowth
const match = climateMatch(tile, biome)
const qm = qualityMult(tile.quality)
let effectiveCap = climax
if (tile.canopy_cover > VEG.shade_cap) {
effectiveCap = Math.min(climax, VEG.shade_cap)
}
if (match > 0.0) {
const delta = VEG.growth_rate * match * qm
tile.undergrowth = Math.min(tile.undergrowth + delta, effectiveCap)
} else {
let rate = VEG.decay_rate
if (tile.drought_counter > 0) rate *= VEG.drought_decay_multiplier
tile.undergrowth = Math.max(tile.undergrowth - rate, 0.0)
}
}
}
function tickFungi(tiles: TileState[], w: number, h: number): void {
for (let i = 0; i < tiles.length; i++) {
const tile = tiles[i]
if (isWater(tile)) continue
const biome = getBiome(tile.biome_id)
if (!biome) continue
const climax = biome.flora_climax.fungi
if (tile.undergrowth < VEG.fungi_undergrowth_threshold) {
tile.fungi_network = Math.max(tile.fungi_network - VEG.decay_rate * 0.5, 0.0)
continue
}
if (tile.moisture < 0.15 || tile.temperature < 0.1) {
tile.fungi_network = Math.max(tile.fungi_network - VEG.decay_rate * 0.5, 0.0)
continue
}
const ugFactor = tile.undergrowth
let oldGrowth = 1.0
if (tile.canopy_cover > 0.7 && tile.undergrowth > 0.5 && tile.moisture > 0.4) {
oldGrowth = 1.5
}
const qm = qualityMult(tile.quality)
const delta = VEG.growth_rate * ugFactor * oldGrowth * qm
tile.fungi_network = Math.min(tile.fungi_network + delta, climax)
}
}
function tickSuccession(tiles: TileState[], w: number, h: number): void {
for (let i = 0; i < tiles.length; i++) {
const tile = tiles[i]
if (isWater(tile)) continue
if (tile.regrowth_stage >= 0) continue
if (tile.canopy_cover >= SUC.canopy_threshold) {
tile.succession_progress += 1
} else {
tile.succession_progress = 0
continue
}
if (tile.succession_progress < SUC.stability_turns) continue
// Succession triggered — reclassify
const oldBiome = tile.biome_id
const newBiome = classifyBiome(tile)
tile.succession_progress = 0
if (newBiome !== oldBiome) {
tile.biome_id = newBiome
}
if (tile.quality >= 4 && tile.landmark_name === '') {
tile.landmark_name = `Ancient ${tile.biome_id.replace(/_/g, ' ')}`
}
}
}
function tickDesertification(tiles: TileState[], w: number, h: number): void {
const baseDecay = VEG.decay_rate
for (let i = 0; i < tiles.length; i++) {
const tile = tiles[i]
if (isWater(tile)) continue
if (tile.moisture < DES.moisture_threshold) {
tile.drought_counter += 1
const rate = baseDecay * DES.decay_multiplier
tile.canopy_cover = Math.max(tile.canopy_cover - rate, 0.0)
tile.undergrowth = Math.max(tile.undergrowth - rate * 1.5, 0.0)
tile.fungi_network = Math.max(tile.fungi_network - rate, 0.0)
if (tile.drought_counter >= DES.turns_required) {
const oldBiome = tile.biome_id
const newBiome = classifyBiome(tile)
if (newBiome !== oldBiome) tile.biome_id = newBiome
}
} else {
tile.drought_counter = Math.max(tile.drought_counter - DES.recovery_rate, 0)
}
}
}
function tickRegrowth(tiles: TileState[], w: number, h: number): void {
for (let i = 0; i < tiles.length; i++) {
const tile = tiles[i]
if (tile.regrowth_stage < 0) continue
tile.regrowth_turns += 1
const stageData = getRegrowthStage(tile.regrowth_stage)
if (!stageData) continue
const baseTurns = stageData.turns_to_advance
const fungiBonus = Math.min(
Math.max(1.0 + tile.fungi_network * VEG.fungi_regrowth_bonus_cap, 1.0),
VEG.fungi_regrowth_bonus_cap,
)
const effectiveTurns = Math.max(1, Math.round(baseTurns / fungiBonus))
if (tile.regrowth_turns < effectiveTurns) continue
const nextStage = tile.regrowth_stage + 1
const nextData = getRegrowthStage(nextStage)
if (!nextData || nextStage > 3) {
tile.regrowth_stage = -1
tile.regrowth_turns = 0
continue
}
tile.regrowth_stage = nextStage
tile.regrowth_turns = 0
tile.canopy_cover = nextData.canopy_target
tile.undergrowth = nextData.undergrowth_target
tile.fungi_network = nextData.fungi_target
if (nextStage >= 3) {
tile.regrowth_stage = -1
tile.regrowth_turns = 0
}
}
}
// ---------------------------------------------------------------------------
// Fauna — simplified for guide (no SQLite creature DB)
// Uses tile-level habitat suitability + fish stock approximation.
// ---------------------------------------------------------------------------
const FAUNA_WEIGHTS = {
undergrowth_weight: 0.6,
canopy_weight: 0.2,
fungi_weight: 0.2,
} as const
function updateHabitatSuitability(
tiles: TileState[], w: number, h: number,
): void {
for (let i = 0; i < tiles.length; i++) {
const tile = tiles[i]
if (isWater(tile)) continue
let tu = 0, tc = 0, tf = 0, n = 0
// Radius-2 neighborhood average
const nbs = neighbors(tile.col, tile.row, w, h)
for (const nb of nbs) {
const nt = tiles[idx(nb.col, nb.row, w)]
if (isWater(nt)) continue
tu += nt.undergrowth
tc += nt.canopy_cover
tf += nt.fungi_network
n++
}
// Include self
tu += tile.undergrowth; tc += tile.canopy_cover; tf += tile.fungi_network; n++
if (n > 0) {
tile.habitat_suitability = (
(tu / n) * FAUNA_WEIGHTS.undergrowth_weight +
(tc / n) * FAUNA_WEIGHTS.canopy_weight +
(tf / n) * FAUNA_WEIGHTS.fungi_weight
)
} else {
tile.habitat_suitability = 0.0
}
}
}
function updateFishStock(tiles: TileState[], w: number, h: number): void {
for (let i = 0; i < tiles.length; i++) {
const tile = tiles[i]
if (!isWater(tile) || (tile.fish_stock ?? 0) <= 0) continue
let tempMult = 0.5 // polar
if (tile.temperature > 0.55) tempMult = 1.0 // tropical
else if (tile.temperature > 0.25) tempMult = 0.8 // temperate
let cap = 100.0
if (tile.reef_health > 0.5) cap *= 1.5
else if (tile.reef_health < 0.1) cap *= 0.5
const stock = tile.fish_stock ?? 0
const growth = 0.05 * tempMult * stock * (1.0 - stock / cap)
tile.fish_stock = Math.max(0, Math.min(Math.round(stock + growth), cap))
}
}
// ---------------------------------------------------------------------------
// Ecosystem quality computation (from ecosystem.gd)
// ---------------------------------------------------------------------------
const QUALITY_THRESHOLDS = [0.2, 0.4, 0.6, 0.8] as const
const W_FLORA = 0.30
const W_FAUNA = 0.25
const W_STABILITY = 0.25
const W_BALANCE = 0.20
const FOOD_YIELD_MULT: Record<number, number> = {
1: 0.5, 2: 1.0, 3: 1.5, 4: 2.0, 5: 2.5,
}
function scoreToTier(score: number): number {
if (score >= 0.8) return 5
if (score >= 0.6) return 4
if (score >= 0.4) return 3
if (score >= 0.2) return 2
return 1
}
function floraHealth(tile: TileState, biome: BiomeDef | null): number {
if (!biome) return 0.5
const { canopy, undergrowth, fungi } = biome.flora_climax
const cMax = Math.max(canopy, 0.001)
const uMax = Math.max(undergrowth, 0.001)
const fMax = Math.max(fungi, 0.001)
const c = Math.min(tile.canopy_cover / cMax, 1.0)
const u = Math.min(tile.undergrowth / uMax, 1.0)
const f = Math.min(tile.fungi_network / fMax, 1.0)
return (c + u + f) / 3.0
}
function biomeStability(tile: TileState): number {
const classified = classifyBiome(tile)
if (classified === tile.biome_id) return 1.0
// Partial credit for same family
if (classified.startsWith('temperate') && tile.biome_id.startsWith('temperate')) return 0.6
if (classified.startsWith('tropical') && tile.biome_id.startsWith('tropical')) return 0.6
return 0.2
}
/** Approximate fauna diversity from habitat suitability (no creature DB in guide). */
function faunaDiversity(tile: TileState, biome: BiomeDef | null): number {
if (!biome) return 0.5
// Habitat suitability as proxy for species diversity
return Math.min(tile.habitat_suitability / 0.7, 1.0)
}
/** Approximate population balance from flora ratios (no creature DB in guide). */
function populationBalance(tile: TileState): number {
// Healthy undergrowth implies herbivore support, balanced canopy implies
// predator-prey equilibrium. In the full game this uses SQLite creature counts.
if (tile.undergrowth < 0.1) return 0.3
const ratio = tile.canopy_cover / Math.max(tile.undergrowth, 0.01)
// Ideal ratio around 1.0-2.0
if (ratio >= 0.5 && ratio <= 3.0) return 1.0
return 0.5
}
function computeTileQuality(tiles: TileState[], w: number, h: number): void {
for (let i = 0; i < tiles.length; i++) {
const tile = tiles[i]
if (isWater(tile)) continue
const biome = getBiome(tile.biome_id)
const flora = floraHealth(tile, biome)
const fauna = faunaDiversity(tile, biome)
const stability = biomeStability(tile)
const balance = populationBalance(tile)
const score = flora * W_FLORA + fauna * W_FAUNA +
stability * W_STABILITY + balance * W_BALANCE
let newQ = scoreToTier(score)
if (biome) {
const [qMin, qMax] = biome.quality_range
newQ = Math.max(qMin, Math.min(qMax, newQ))
}
if (newQ >= 4 && tile.quality < 4 && tile.landmark_name === '') {
tile.landmark_name = `Ancient ${tile.biome_id.replace(/_/g, ' ')}`
}
tile.quality = newQ
}
}
function computeGlobalHealth(grid: GridState): number {
let total = 0, count = 0
for (const tile of grid.tiles) {
if (isWater(tile)) continue
total += tile.quality / 5.0
count++
}
return count > 0 ? total / count : 0.5
}
/** Food yield modifier for a tile based on quality. */
export function getEcologyFoodModifier(tile: TileState): number {
let base = FOOD_YIELD_MULT[tile.quality] ?? 1.0
if (!isWater(tile)) {
base *= 0.8 + 0.4 * tile.undergrowth // lerp(0.8, 1.2, undergrowth)
}
return base
}
// ---------------------------------------------------------------------------
// EcologyPhysics class — orchestrates flora + fauna + quality per turn
// ---------------------------------------------------------------------------
// Biome recomputation deltas
const CANOPY_DELTA = 0.05
const TEMP_DELTA = 0.02
const MOISTURE_DELTA = 0.03
export class EcologyPhysics {
private lastCanopy: Float32Array | null = null
private lastTemp: Float32Array | null = null
private lastMoisture: Float32Array | null = null
/**
* Process one turn of ecology dynamics.
* Call after ClimatePhysics.processStep().
*/
processStep(grid: GridState): void {
const { tiles, width: w, height: h } = grid
// Flora dynamics (6 ticks in order)
tickCanopy(tiles, w, h)
tickUndergrowth(tiles, w, h)
tickFungi(tiles, w, h)
tickSuccession(tiles, w, h)
tickDesertification(tiles, w, h)
tickRegrowth(tiles, w, h)
// Fauna (simplified for guide)
updateHabitatSuitability(tiles, w, h)
updateFishStock(tiles, w, h)
// Biome recomputation on significant changes
this.recomputeBiomes(tiles, w, h)
// Quality scoring
computeTileQuality(tiles, w, h)
// Global health
grid.ecosystem_health = computeGlobalHealth(grid)
}
private recomputeBiomes(tiles: TileState[], w: number, h: number): void {
const n = tiles.length
if (!this.lastCanopy || this.lastCanopy.length !== n) {
this.lastCanopy = new Float32Array(n)
this.lastTemp = new Float32Array(n)
this.lastMoisture = new Float32Array(n)
for (let i = 0; i < n; i++) {
this.lastCanopy[i] = tiles[i].canopy_cover
this.lastTemp![i] = tiles[i].temperature
this.lastMoisture![i] = tiles[i].moisture
}
return
}
for (let i = 0; i < n; i++) {
const tile = tiles[i]
if (isWater(tile)) continue
const canopyD = Math.abs(tile.canopy_cover - this.lastCanopy[i])
const tempD = Math.abs(tile.temperature - this.lastTemp![i])
const moistD = Math.abs(tile.moisture - this.lastMoisture![i])
this.lastCanopy[i] = tile.canopy_cover
this.lastTemp![i] = tile.temperature
this.lastMoisture![i] = tile.moisture
if (canopyD > CANOPY_DELTA || tempD > TEMP_DELTA || moistD > MOISTURE_DELTA) {
const newBiome = classifyBiome(tile)
if (newBiome !== tile.biome_id) {
tile.biome_id = newBiome
}
}
}
}
}
// Re-export helpers for guide lenses
export { isWater, getBiome, classifyBiome, BIOME_DEFS }
export type { BiomeDef }

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@ -83,10 +83,11 @@ export function neighborInDir(
return { col: nc, row: nr }
}
/** Solar insolation at a row: 1.0 at equator (center), 0.0 at poles. */
export function solarByRow(row: number, height: number): number {
/** Solar insolation at a row, mapped to habitable range [solarMin, solarMax]. */
export function solarByRow(row: number, height: number, solarMin = 0.15, solarMax = 0.70): number {
const centerRow = height / 2.0
return 1.0 - Math.abs((row - centerRow) / centerRow)
const raw = 1.0 - Math.abs((row - centerRow) / centerRow)
return solarMin + (solarMax - solarMin) * raw
}
// ---------------------------------------------------------------------------

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@ -77,7 +77,7 @@ const DEFAULT_TYPE_DATA: Record<string, unknown> = {
continent_count: { min: 2, max: 4 },
terrain_fractions: {
enchanted_forest: 0.01, desert: 0.10, swamp: 0.07,
corrupted_land: 0.04, volcano: 0.02,
volcano: 0.02,
},
generation_params: {
num_landmass: 35, steepness: 0.20, prevailing_wind_direction: 0,
@ -251,7 +251,6 @@ class GenMap {
quality_progress: gt?.quality_progress ?? 0,
river_edges: gt?.river_edges ?? [],
flow_accumulation: gt?.flow_accumulation ?? 0.0,
corruption_pressure: 0.0,
original_terrain_id: '',
ley_line_count: 0,
ley_school: '',
@ -779,7 +778,7 @@ function assignTerrainPatches(
const defaultFractions: Record<string, number> = {
forest: 0.12, jungle: 0.06, boreal_forest: 0.05,
enchanted_forest: 0.01, desert: 0.10, swamp: 0.07,
corrupted_land: 0.04, volcano: 0.02,
volcano: 0.02,
}
const fractions = (typeData['terrain_fractions'] ?? defaultFractions) as Record<string, number>
@ -790,7 +789,7 @@ function assignTerrainPatches(
const order: string[] = [
'volcano', 'jungle', 'forest', 'boreal_forest', 'enchanted_forest',
'desert', 'swamp', 'corrupted_land', 'tundra', 'snow', 'grassland',
'desert', 'swamp', 'tundra', 'snow', 'grassland',
]
for (const terrainId of order) {
@ -904,7 +903,6 @@ function isEligible(
case 'enchanted_forest': return m >= 0.40
case 'desert': return t >= 0.25 && m < 0.25
case 'swamp': return t > 0.25 && m > 0.75 && e < 0.48
case 'corrupted_land': return true
case 'tundra': return t >= 0.10 && t < 0.25
case 'snow': return t < 0.10
case 'grassland': return true

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@ -2,6 +2,7 @@ export * from './types'
export * from './HexGrid'
export * from './ClimatePhysics.generated'
export * from './MapGenerator.generated'
export * from './EcologyPhysics.generated'
export * from './runner'
export * from './scenarios'
export * from './worker-protocol'

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@ -90,6 +90,7 @@ export interface FramesResponse {
export interface FramePayload {
texA: Float32Array
texB: Float32Array
texC: Float32Array
width: number
height: number
turn: number