three.js/examples/jsm/objects/Sky.js

import {
	BackSide,
	BoxGeometry,
	Mesh,
	ShaderMaterial,
	UniformsUtils,
	Vector3
} from 'three';

/**
 * Represents a skydome for scene backgrounds. Based on [A Practical Analytic Model for Daylight](https://www.researchgate.net/publication/220720443_A_Practical_Analytic_Model_for_Daylight)
 * aka The Preetham Model, the de facto standard for analytical skydomes.
 *
 * Note that this class can only be used with {@link WebGLRenderer}.
 * When using {@link WebGPURenderer}, use {@link SkyMesh}.
 *
 * More references:
 *
 * - {@link http://simonwallner.at/project/atmospheric-scattering/}
 * - {@link http://blenderartists.org/forum/showthread.php?245954-preethams-sky-impementation-HDR}
 *
 *
 * ```js
 * const sky = new Sky();
 * sky.scale.setScalar( 10000 );
 * scene.add( sky );
 * ```
 * 
 * It can be useful to hide the sun disc when generating an environment map to avoid artifacts
 * 
 * ```js
 * // disable before rendering environment map
 * sky.material.uniforms.showSunDisc.value = false;
 * // ...
 * // re-enable before scene sky box rendering
 * sky.material.uniforms.showSunDisc.value = true;
 * ```
 *
 * @augments Mesh
 * @three_import import { Sky } from 'three/addons/objects/Sky.js';
 */
class Sky extends Mesh {

	/**
	 * Constructs a new skydome.
	 */
	constructor() {

		const shader = Sky.SkyShader;

		const material = new ShaderMaterial( {
			name: shader.name,
			uniforms: UniformsUtils.clone( shader.uniforms ),
			vertexShader: shader.vertexShader,
			fragmentShader: shader.fragmentShader,
			side: BackSide,
			depthWrite: false
		} );

		super( new BoxGeometry( 1, 1, 1 ), material );

		/**
		 * This flag can be used for type testing.
		 *
		 * @type {boolean}
		 * @readonly
		 * @default true
		 */
		this.isSky = true;

	}

}

Sky.SkyShader = {

	name: 'SkyShader',

	uniforms: {
		'turbidity': { value: 2 },
		'rayleigh': { value: 1 },
		'mieCoefficient': { value: 0.005 },
		'mieDirectionalG': { value: 0.8 },
		'sunPosition': { value: new Vector3() },
		'up': { value: new Vector3( 0, 1, 0 ) },
		'cloudScale': { value: 0.0002 },
		'cloudSpeed': { value: 0.0001 },
		'cloudCoverage': { value: 0.4 },
		'cloudDensity': { value: 0.4 },
		'cloudElevation': { value: 0.5 },
		'showSunDisc': { value: 1 },
		'time': { value: 0.0 }
	},

	vertexShader: /* glsl */`
		uniform vec3 sunPosition;
		uniform float rayleigh;
		uniform float turbidity;
		uniform float mieCoefficient;
		uniform vec3 up;

		varying vec3 vWorldPosition;
		varying vec3 vSunDirection;
		varying float vSunfade;
		varying vec3 vBetaR;
		varying vec3 vBetaM;
		varying float vSunE;

		// constants for atmospheric scattering
		const float e = 2.71828182845904523536028747135266249775724709369995957;
		const float pi = 3.141592653589793238462643383279502884197169;

		// wavelength of used primaries, according to preetham
		const vec3 lambda = vec3( 680E-9, 550E-9, 450E-9 );
		// this pre-calculation replaces older TotalRayleigh(vec3 lambda) function:
		// (8.0 * pow(pi, 3.0) * pow(pow(n, 2.0) - 1.0, 2.0) * (6.0 + 3.0 * pn)) / (3.0 * N * pow(lambda, vec3(4.0)) * (6.0 - 7.0 * pn))
		const vec3 totalRayleigh = vec3( 5.804542996261093E-6, 1.3562911419845635E-5, 3.0265902468824876E-5 );

		// mie stuff
		// K coefficient for the primaries
		const float v = 4.0;
		const vec3 K = vec3( 0.686, 0.678, 0.666 );
		// MieConst = pi * pow( ( 2.0 * pi ) / lambda, vec3( v - 2.0 ) ) * K
		const vec3 MieConst = vec3( 1.8399918514433978E14, 2.7798023919660528E14, 4.0790479543861094E14 );

		// earth shadow hack
		// cutoffAngle = pi / 1.95;
		const float cutoffAngle = 1.6110731556870734;
		const float steepness = 1.5;
		const float EE = 1000.0;

		float sunIntensity( float zenithAngleCos ) {
			zenithAngleCos = clamp( zenithAngleCos, -1.0, 1.0 );
			return EE * max( 0.0, 1.0 - pow( e, -( ( cutoffAngle - acos( zenithAngleCos ) ) / steepness ) ) );
		}

		vec3 totalMie( float T ) {
			float c = ( 0.2 * T ) * 10E-18;
			return 0.434 * c * MieConst;
		}

		void main() {

			vec4 worldPosition = modelMatrix * vec4( position, 1.0 );
			vWorldPosition = worldPosition.xyz;

			gl_Position = projectionMatrix * modelViewMatrix * vec4( position, 1.0 );
			gl_Position.z = gl_Position.w; // set z to camera.far

			vSunDirection = normalize( sunPosition );

			vSunE = sunIntensity( dot( vSunDirection, up ) );

			vSunfade = 1.0 - clamp( 1.0 - exp( ( sunPosition.y / 450000.0 ) ), 0.0, 1.0 );

			float rayleighCoefficient = rayleigh - ( 1.0 * ( 1.0 - vSunfade ) );

			// extinction (absorption + out scattering)
			// rayleigh coefficients
			vBetaR = totalRayleigh * rayleighCoefficient;

			// mie coefficients
			vBetaM = totalMie( turbidity ) * mieCoefficient;

		}`,

	fragmentShader: /* glsl */`
		varying vec3 vWorldPosition;
		varying vec3 vSunDirection;
		varying vec3 vBetaR;
		varying vec3 vBetaM;
		varying float vSunE;

		uniform float mieDirectionalG;
		uniform vec3 up;
		uniform float cloudScale;
		uniform float cloudSpeed;
		uniform float cloudCoverage;
		uniform float cloudDensity;
		uniform float cloudElevation;
		uniform float showSunDisc;
		uniform float time;

		// gradient at a lattice corner; sinless hash so every GPU produces the same clouds
		vec2 gradient( vec2 i ) {
			vec3 p = fract( i.xyx * vec3( 0.1031, 0.1030, 0.0973 ) );
			p += dot( p, p.yzx + 33.33 );
			return fract( ( p.xx + p.yz ) * p.zy ) * 2.0 - 1.0;
		}

		// 2D gradient noise: isotropic lobes like Perlin at value-noise cost
		float noise( vec2 p ) {
			vec2 i = floor( p );
			vec2 f = fract( p );
			vec2 u = f * f * f * ( f * ( f * 6.0 - 15.0 ) + 10.0 ); // quintic fade
			float a = dot( gradient( i ), f );
			float b = dot( gradient( i + vec2( 1.0, 0.0 ) ), f - vec2( 1.0, 0.0 ) );
			float c = dot( gradient( i + vec2( 0.0, 1.0 ) ), f - vec2( 0.0, 1.0 ) );
			float d = dot( gradient( i + vec2( 1.0, 1.0 ) ), f - vec2( 1.0, 1.0 ) );
			return mix( mix( a, b, u.x ), mix( c, d, u.x ), u.y ) * 1.6; // ~[-1,1]
		}

		// fbm; per-octave drift makes clouds billow instead of scrolling as a rigid stamp
		float fbm( vec2 p, float drift ) {
			float result = 0.0;
			float amplitude = 1.0;
			for ( int i = 0; i < 4; i ++ ) {
				result += amplitude * noise( p );
				amplitude *= 0.5;
				p = p * 2.0 + drift;
			}
			return result;
		}

		// constants for atmospheric scattering
		const float pi = 3.141592653589793238462643383279502884197169;

		const float n = 1.0003; // refractive index of air
		const float N = 2.545E25; // number of molecules per unit volume for air at 288.15K and 1013mb (sea level -45 celsius)

		// optical length at zenith for molecules
		const float rayleighZenithLength = 8.4E3;
		const float mieZenithLength = 1.25E3;
		// 66 arc seconds -> degrees, and the cosine of that
		const float sunAngularDiameterCos = 0.999956676946448443553574619906976478926848692873900859324;

		// 3.0 / ( 16.0 * pi )
		const float THREE_OVER_SIXTEENPI = 0.05968310365946075;
		// 1.0 / ( 4.0 * pi )
		const float ONE_OVER_FOURPI = 0.07957747154594767;

		float rayleighPhase( float cosTheta ) {
			return THREE_OVER_SIXTEENPI * ( 1.0 + pow( cosTheta, 2.0 ) );
		}

		float hgPhase( float cosTheta, float g ) {
			float g2 = pow( g, 2.0 );
			float inverse = 1.0 / pow( 1.0 - 2.0 * g * cosTheta + g2, 1.5 );
			return ONE_OVER_FOURPI * ( ( 1.0 - g2 ) * inverse );
		}

		void main() {

			vec3 direction = normalize( vWorldPosition - cameraPosition );

			// optical length
			// cutoff angle at 90 to avoid singularity in next formula.
			float zenithAngle = acos( max( 0.0, dot( up, direction ) ) );
			float inverse = 1.0 / ( cos( zenithAngle ) + 0.15 * pow( 93.885 - ( ( zenithAngle * 180.0 ) / pi ), -1.253 ) );
			float sR = rayleighZenithLength * inverse;
			float sM = mieZenithLength * inverse;

			// combined extinction factor
			vec3 Fex = exp( -( vBetaR * sR + vBetaM * sM ) );

			// in scattering
			float cosTheta = dot( direction, vSunDirection );

			float rPhase = rayleighPhase( cosTheta * 0.5 + 0.5 );
			vec3 betaRTheta = vBetaR * rPhase;

			float mPhase = hgPhase( cosTheta, mieDirectionalG );
			vec3 betaMTheta = vBetaM * mPhase;

			vec3 Lin = pow( vSunE * ( ( betaRTheta + betaMTheta ) / ( vBetaR + vBetaM ) ) * ( 1.0 - Fex ), vec3( 1.5 ) );
			Lin *= mix( vec3( 1.0 ), pow( vSunE * ( ( betaRTheta + betaMTheta ) / ( vBetaR + vBetaM ) ) * Fex, vec3( 1.0 / 2.0 ) ), clamp( pow( 1.0 - dot( up, vSunDirection ), 5.0 ), 0.0, 1.0 ) );

			// nightsky
			float theta = acos( direction.y ); // elevation --> y-axis, [-pi/2, pi/2]
			float phi = atan( direction.z, direction.x ); // azimuth --> x-axis [-pi/2, pi/2]
			vec2 uv = vec2( phi, theta ) / vec2( 2.0 * pi, pi ) + vec2( 0.5, 0.0 );
			vec3 L0 = vec3( 0.1 ) * Fex;

			// composition + solar disc
			float sundisc = smoothstep( sunAngularDiameterCos, sunAngularDiameterCos + 0.00002, cosTheta ) * showSunDisc;
			L0 += ( vSunE * 19000.0 * Fex ) * sundisc;

			vec3 texColor = ( Lin + L0 ) * 0.04 + vec3( 0.0, 0.0003, 0.00075 );

			// Clouds
			if ( direction.y > 0.0 && cloudCoverage > 0.0 ) {

				// Project to cloud plane (higher elevation = clouds appear lower/closer)
				float elevation = mix( 1.0, 0.1, cloudElevation );
				vec2 cloudUV = direction.xz / ( direction.y * elevation );
				cloudUV *= cloudScale;
				cloudUV += time * cloudSpeed;

				// Cloud density field
				float evolve = time * cloudSpeed * 300.0;
				float cloudNoise = clamp( fbm( cloudUV * 1000.0, evolve ) * 0.7 + 0.5, 0.0, 1.0 );

				// Large-scale coverage variation: clear gaps next to dense banks
				float region = noise( cloudUV * 300.0 ) * 0.37 + 0.5;
				float cov = clamp( cloudCoverage + ( region - 0.5 ) * 0.6, 0.0, 1.0 );

				// Carve clouds where noise rises above the coverage level
				float threshold = 1.0 - cov;
				float cloudMask = smoothstep( threshold, threshold + 0.3, cloudNoise );

				// Fade clouds near horizon (adjusted by elevation)
				float horizonFade = smoothstep( 0.0, 0.03 + 0.06 * cloudElevation, direction.y );
				cloudMask *= horizonFade;

				// Cloud lighting from the sky's own radiance
				float dayFactor = smoothstep( -0.08, 0.3, vSunDirection.y );
				vec3 sunColor = vSunE * Fex * 0.22 * 0.04; // 0.22 ~ albedo/pi, 0.04 = exposure; the aerial composite adds the eye-leg extinction
				vec3 skyAmbient = Lin * 0.04 + vec3( 0.0, 0.0003, 0.00075 );

				// Beer-powder self-shadow from the sampled density
				float depth = max( 0.0, cloudNoise - threshold );
				float beer = exp( depth * -4.0 );
				float powder = 1.0 - beer * beer; // beer*beer == exp(-8*depth)
				float shade = mix( 0.45, 1.0, clamp( beer * powder * 2.6, 0.0, 1.0 ) ); // 2.6 = 1/0.385, normalizes beer*powder peak to 1

				// Henyey-Greenstein forward lobe ( g = 0.7 ): silver lining on rims toward the sun
				float silver = clamp( 0.51 / pow( 1.49 - cosTheta * 1.4, 1.5 ), 0.0, 3.0 ); // 0.51=1-g^2, 1.49=1+g^2, 1.4=2g
				float edge = cloudMask * ( 1.0 - cloudMask ) * 4.0;

				vec3 cloudColor = skyAmbient + sunColor * shade;
				cloudColor += sunColor * silver * edge * 0.6;
				cloudColor *= max( dayFactor, 0.03 );

				// Cloud opacity via Beer's law: density sets how solid the clouds get
				float alpha = ( 1.0 - exp( depth * cloudDensity * -12.0 ) ) * horizonFade;

				// Occlude the sun disc/glow behind opaque cloud
				texColor -= L0 * 0.04 * alpha;

				// Composite through the atmosphere so distant clouds dissolve into haze
				vec3 cloudAerial = mix( texColor, cloudColor, Fex );
				texColor = mix( texColor, cloudAerial, alpha );

			}

			gl_FragColor = vec4( texColor, 1.0 );

			#include <tonemapping_fragment>
			#include <colorspace_fragment>

		}`

};

export { Sky };