bworld/common/worldgen/terrain.ts

// the shape of the overworld, built the way minecraft 1.18+ (and terralith on top of it) does it:
// large noises for continentalness, erosion and weirdness feed nested splines that give each column a target height,
// how jagged its peaks are and how rough its ground is. a 3d density around that height decides what's solid,
// and caves are cut out of it. terralith's flavor comes from the extra shapes: terraced plateaus with cliffs,
// shattered hills full of overhangs, deep river valleys and gorges, jagged peaks and rare sky islands
import { CHUNK_HEIGHT, SEA_LEVEL } from "$/common/constants.ts";
import { clamp, lerp, OctaveNoise2D, OctaveNoise3D, Quantiles, smoothstep } from "./noise.ts";
import { Spline, spline, SplineInputs } from "./spline.ts";

// measured with tools/noise_quantiles.ts
const QUANTILES_6 = new Quantiles([
	-0.833,
	-0.386,
	-0.311,
	-0.256,
	-0.21,
	-0.17,
	-0.133,
	-0.098,
	-0.065,
	-0.032,
	0,
	0.032,
	0.065,
	0.098,
	0.133,
	0.17,
	0.21,
	0.256,
	0.311,
	0.386,
	0.833,
]);
const QUANTILES_4 = new Quantiles([
	-0.917,
	-0.48,
	-0.393,
	-0.328,
	-0.273,
	-0.222,
	-0.174,
	-0.13,
	-0.086,
	-0.042,
	0,
	0.042,
	0.086,
	0.13,
	0.174,
	0.222,
	0.273,
	0.328,
	0.393,
	0.48,
	0.917,
]);
const QUANTILES_3 = new Quantiles([
	-0.91,
	-0.468,
	-0.377,
	-0.308,
	-0.249,
	-0.199,
	-0.154,
	-0.113,
	-0.073,
	-0.036,
	0,
	0.036,
	0.073,
	0.113,
	0.154,
	0.199,
	0.249,
	0.308,
	0.377,
	0.468,
	0.91,
]);
const QUANTILES_2 = new Quantiles([
	-0.962,
	-0.536,
	-0.439,
	-0.368,
	-0.306,
	-0.248,
	-0.195,
	-0.146,
	-0.096,
	-0.046,
	0,
	0.046,
	0.096,
	0.146,
	0.195,
	0.248,
	0.306,
	0.368,
	0.439,
	0.536,
	0.962,
]);
const QUANTILES_TEMPERATURE = new Quantiles([
	-0.973,
	-0.6,
	-0.509,
	-0.44,
	-0.379,
	-0.319,
	-0.254,
	-0.19,
	-0.127,
	-0.063,
	0,
	0.063,
	0.127,
	0.19,
	0.254,
	0.319,
	0.379,
	0.44,
	0.509,
	0.6,
	0.973,
]);

// blocks of height per unit of density, how soft the ground's surface is
const THICKNESS = 20;
// solid ground always ends here, and nothing reaches past the top of the world
const TOP_SLIDE_START = CHUNK_HEIGHT - 24;
const TOP_SLIDE_END = CHUNK_HEIGHT - 4;
const MIN_CAVE_Y = 5;

// the climate at a column, every value spread evenly from -1 to 1
export interface Climate {
	// ocean far below 0, coast around -0.2, further inland higher
	continentalness: number;
	// low is mountains, high is flat land
	erosion: number;
	// picks between variants, and its folded form pv
	weirdness: number;
	// peaks and valleys: -1 in a valley (rivers), 1 on a peak
	pv: number;
	temperature: number;
	humidity: number;
}

// everything 2d about a column that the density needs, worked out once per column
export interface TerrainColumn {
	climate: Climate;
	// where the ground's surface is before 3d noise, in blocks
	height: number;
	// how much 3d noise moves the ground, in units of density
	roughness: number;
	// 0 to 1, how much of it are terraced plateaus and shattered hills
	plateau: number;
	shattered: number;
	// 0 to 1, how pointy its peaks are
	jaggedness: number;
	// a sky island above it, when there is one
	island?: { top: number; bottom: number };
}

// minecraft's peaks and valleys: weirdness folded so both its ends are peaks and its middle a valley
export function peaks_and_valleys(weirdness: number) {
	return 1 - Math.abs(3 * Math.abs(weirdness) - 2);
}

// the valley value holds until -0.85, so rivers have a flat bottom and some width
const PV_POINTS = [-1, -0.85, -0.65, -0.35, 0, 0.45, 0.8, 1];
const EROSION_POINTS = [-1, -0.6, -0.3, 0, 0.3, 0.6, 1];

// the heights over land at one level of continentalness, relative to sea level. base lifts everything, mountains
// scales how tall they get. each erosion gets a spline over peaks and valleys: a valley value, then how far above
// base the ground rises towards the peaks
function land(base: number, mountains: number): Spline {
	const row = (valley: number, rises: number[]) =>
		spline("pv", PV_POINTS, [valley, valley, ...rises.map((rise) => base + rise * mountains)]);
	return spline("erosion", EROSION_POINTS, [
		// barely eroded: huge mountains, their valleys are gorges high above the sea
		row(base + 14 * mountains, [22, 44, 66, 88, 104, 110]),
		row(base + 8 * mountains, [14, 28, 42, 54, 62, 66]),
		// hills and highlands, their valleys carry rivers
		row(-4, [8, 20, 28, 36, 42, 44]),
		row(-5, [4, 10, 15, 20, 23, 24]),
		row(-5, [2, 6, 9, 12, 13, 14]),
		// worn flat: plains and wetlands
		row(-4, [1, 3, 5, 7, 8, 8]),
		row(-3, [0, 1, 2, 3, 3, 3]),
	]);
}

// target height above sea level
const OFFSET = spline(
	"continentalness",
	[-1, -0.55, -0.3, -0.18, -0.12, -0.04, 0.2, 0.5, 1],
	[-46, -32, -18, -8, -2, land(1, 0.3), land(3, 0.65), land(8, 1), land(14, 1.15)],
);

// how pointy peaks get, 0 to 1. only tall, barely eroded mountains have them
const JAGGEDNESS = spline("erosion", [-1, -0.6, -0.3, 0], [
	spline("pv", [-0.2, 0.3, 1], [0, 0.6, 1]),
	spline("pv", [0, 0.5, 1], [0, 0.4, 0.7]),
	spline("pv", [0.3, 0.8, 1], [0, 0.2, 0.3]),
	0,
]);

// 3d noise strength: mountains are rougher than plains
const ROUGHNESS = spline("erosion", [-1, -0.5, 0, 0.5, 1], [0.32, 0.22, 0.14, 0.1, 0.06]);

export class OverworldTerrain {
	#continentalness: OctaveNoise2D;
	#erosion: OctaveNoise2D;
	#weirdness: OctaveNoise2D;
	#temperature: OctaveNoise2D;
	#humidity: OctaveNoise2D;
	#warp_x: OctaveNoise2D;
	#warp_z: OctaveNoise2D;
	#jagged: OctaveNoise2D;
	#plateau: OctaveNoise2D;
	#shattered: OctaveNoise2D;
	#sky: OctaveNoise2D;
	#island_shape: OctaveNoise2D;
	#island_height: OctaveNoise2D;
	#ground: OctaveNoise3D;
	#island_noise: OctaveNoise3D;
	#cheese: OctaveNoise3D;
	#spaghetti_a: OctaveNoise3D;
	#spaghetti_b: OctaveNoise3D;
	#entrances: OctaveNoise2D;

	constructor(seed: string) {
		this.#continentalness = new OctaveNoise2D(seed, "continentalness", 1024, [1, 1, 2, 2, 1, 1]);
		this.#erosion = new OctaveNoise2D(seed, "erosion", 768, [1, 1, 0, 1, 1]);
		this.#weirdness = new OctaveNoise2D(seed, "weirdness", 256, [1, 2, 1]);
		this.#temperature = new OctaveNoise2D(seed, "temperature", 1536, [1.5, 0, 1]);
		this.#humidity = new OctaveNoise2D(seed, "humidity", 512, [1, 1]);
		this.#warp_x = new OctaveNoise2D(seed, "warp_x", 200, [1, 1]);
		this.#warp_z = new OctaveNoise2D(seed, "warp_z", 200, [1, 1]);
		this.#jagged = new OctaveNoise2D(seed, "jagged", 48, [1, 1]);
		this.#plateau = new OctaveNoise2D(seed, "plateau", 640, [1, 1]);
		this.#shattered = new OctaveNoise2D(seed, "shattered", 512, [1, 1]);
		this.#sky = new OctaveNoise2D(seed, "sky", 900, [1, 1]);
		this.#island_shape = new OctaveNoise2D(seed, "island_shape", 56, [1, 1]);
		this.#island_height = new OctaveNoise2D(seed, "island_height", 300, [1, 1]);
		this.#ground = new OctaveNoise3D(seed, "ground", 64, [1, 1, 0.5], 1.2);
		this.#island_noise = new OctaveNoise3D(seed, "island_noise", 24, [1, 1]);
		this.#cheese = new OctaveNoise3D(seed, "cheese", 80, [1, 0.5], 0.6);
		this.#spaghetti_a = new OctaveNoise3D(seed, "spaghetti_a", 64, [1], 0.8);
		this.#spaghetti_b = new OctaveNoise3D(seed, "spaghetti_b", 64, [1], 0.8);
		this.#entrances = new OctaveNoise2D(seed, "entrances", 90, [1, 1]);
	}

	climate(x: number, z: number): Climate {
		// a small warp, so coasts and biome edges aren't the noise's smooth blobs
		const wx = x + this.#warp_x.sample(x, z) * 24;
		const wz = z + this.#warp_z.sample(x, z) * 24;
		const weirdness = QUANTILES_3.even(this.#weirdness.sample(wx, wz));
		return {
			continentalness: QUANTILES_6.even(this.#continentalness.sample(wx, wz)),
			erosion: QUANTILES_4.even(this.#erosion.sample(wx, wz)),
			weirdness,
			pv: peaks_and_valleys(weirdness),
			temperature: QUANTILES_TEMPERATURE.even(this.#temperature.sample(wx, wz)),
			humidity: QUANTILES_2.even(this.#humidity.sample(wx, wz)),
		};
	}

	column(x: number, z: number): TerrainColumn {
		const climate = this.climate(x, z);
		const { continentalness: c, erosion: e } = climate;
		const inputs: SplineInputs = climate;
		const inland = smoothstep(-0.1, 0.3, c);

		let height = OFFSET.get(inputs);

		// jagged peaks: sharp ridges pushed up from the tallest mountains
		const jaggedness = clamp(JAGGEDNESS.get(inputs), 0, 1) * inland;
		if (jaggedness > 0) {
			const ridge = 1 - Math.abs(this.#jagged.sample(x, z));
			height += jaggedness * 26 * ridge * ridge;
		}

		// terraced plateaus: raised land cut into flat benches and cliffs, like terralith's
		// yosemite cliffs and painted mountains
		const plateau = smoothstep(0.35, 0.55, QUANTILES_2.even(this.#plateau.sample(x, z))) *
			smoothstep(-0.75, -0.45, e) * (1 - smoothstep(0.1, 0.4, e)) * smoothstep(-0.05, 0.1, c);
		if (plateau > 0 && climate.pv > -0.8) {
			const raised = height + 20 * plateau;
			height = lerp(plateau, height, terrace(raised, 16));
		}

		// shattered hills: ground broken up by strong 3d noise into overhangs, arches and spires
		const shattered = smoothstep(0.55, 0.75, QUANTILES_2.even(this.#shattered.sample(x, z))) *
			smoothstep(-0.6, -0.3, e) * (1 - smoothstep(0.3, 0.5, e)) * smoothstep(-0.05, 0.1, c);

		const roughness = ROUGHNESS.get(inputs) + shattered * 0.9;

		return {
			climate,
			height: SEA_LEVEL + height,
			roughness,
			plateau,
			shattered,
			jaggedness,
			island: this.#island(x, z),
		};
	}

	// skylands: rare regions of floating islands, flat topped with long hanging undersides
	#island(x: number, z: number): TerrainColumn["island"] {
		const region = smoothstep(0.9, 0.97, QUANTILES_2.even(this.#sky.sample(x, z)));
		if (region <= 0) {
			return undefined;
		}
		const shape = region * smoothstep(0.05, 0.35, this.#island_shape.sample(x, z));
		if (shape <= 0) {
			return undefined;
		}
		const center = 178 + this.#island_height.sample(x, z) * 24;
		return { top: center + 2 + 6 * shape, bottom: center - 4 - 34 * shape * Math.sqrt(shape) };
	}

	// positive is solid, before caves
	density(column: TerrainColumn, x: number, y: number, z: number) {
		let density = (column.height - y) / THICKNESS + column.roughness * this.#ground.sample(x, y, z);

		const island = column.island;
		if (island && y > island.bottom - 4 && y < island.top + 4) {
			const solid = Math.min((island.top - y) / 3, (y - island.bottom) / 6) +
				0.4 * this.#island_noise.sample(x, y, z);
			density = Math.max(density, solid);
		}

		if (y > TOP_SLIDE_START) {
			density -= smoothstep(TOP_SLIDE_START, TOP_SLIDE_END, y) * 4;
		}
		if (y < 1) {
			density = Math.max(density, 1);
		}
		return density;
	}

	// negative where a cave is. caves stay under the ground's skin except at entrances, and never break
	// the floor of oceans and rivers
	cave(column: TerrainColumn, x: number, y: number, z: number) {
		if (y < MIN_CAVE_Y) {
			return 1;
		}
		const depth = column.height - y;
		if (column.height < SEA_LEVEL + 3 && depth < 14) {
			return 1;
		}
		if (depth < 7 && this.#entrances.sample(x, z) < 0.5) {
			return 1;
		}

		// cheese caves: big open caverns
		const cheese = (0.52 - this.#cheese.sample(x, y, z)) * 4;
		// spaghetti caves: long winding tunnels where two noises are both near zero
		const a = Math.abs(this.#spaghetti_a.sample(x, y, z));
		const b = Math.abs(this.#spaghetti_b.sample(x, y, z));
		const spaghetti = (Math.max(a, b) - 0.07) * 8;
		return Math.min(cheese, spaghetti);
	}
}

// flat benches every step blocks, joined by steep cliffs
function terrace(height: number, step: number) {
	const k = height / step;
	const floor = Math.floor(k);
	return (floor + smoothstep(0.4, 0.6, k - floor)) * step;
}