Merge pull request #16187 from WestLangley/dev-sh3

Added spherical harmonics class

src/math/SphericalHarmonics3.js

@@ -0,0 +1,211 @@
+import { Vector3 } from './Vector3.js';
+
+/**
+ * @author bhouston / http://clara.io
+ * @author WestLangley / http://github.com/WestLangley
+ *
+ * Primary reference:
+ *   https://graphics.stanford.edu/papers/envmap/envmap.pdf
+ *
+ * Secondary reference:
+ *   https://www.ppsloan.org/publications/StupidSH36.pdf
+ */
+
+// 3-band SH defined by 9 coefficients
+
+function SphericalHarmonics3() {
+
+	this.coefficients = [];
+
+	for ( var i = 0; i < 9; i ++ ) {
+
+		this.coefficients.push( new Vector3() );
+
+	}
+
+}
+
+Object.assign( SphericalHarmonics3.prototype, {
+
+	isSphericalHarmonics3: true,
+
+	set: function ( coefficients ) {
+
+		for ( var i = 0; i < 9; i ++ ) {
+
+			this.coefficients[ i ].copy( coefficients[ i ] );
+
+		}
+
+		return this;
+
+	},
+
+	zero: function () {
+
+		for ( var i = 0; i < 9; i ++ ) {
+
+			this.coefficients[ i ].set( 0, 0, 0 );
+
+		}
+
+		return this;
+
+	},
+
+	// get the radiance in the direction of the normal
+	// target is a Vector3
+	getAt: function ( normal, target ) {
+
+		// normal is assumed to be unit length
+
+		var x = normal.x, y = normal.y, z = normal.z;
+
+		var coeff = this.coefficients;
+
+		// band 0
+		target = coeff[ 0 ] * 0.282095;
+
+		// band 1
+		target += coeff[ 1 ] * 0.488603 * y;
+		target += coeff[ 2 ] * 0.488603 * z;
+		target += coeff[ 3 ] * 0.488603 * x;
+
+		// band 2
+		target += coeff[ 4 ] * 1.092548 * ( x * y );
+		target += coeff[ 5 ] * 1.092548 * ( y * z );
+		target += coeff[ 6 ] * 0.315392 * ( 3.0 * z * z - 1.0 );
+		target += coeff[ 7 ] * 1.092548 * ( x * z );
+		target += coeff[ 8 ] * 0.546274 * ( x * x - y * y );
+
+		return target;
+
+	},
+
+	// get the irradiance (radiance convolved with cosine lobe) in the direction of the normal
+	// target is a Vector3
+	// https://graphics.stanford.edu/papers/envmap/envmap.pdf
+	getIrradianceAt: function ( normal, target ) {
+
+		// normal is assumed to be unit length
+
+		var x = normal.x, y = normal.y, z = normal.z;
+
+		var coeff = this.coefficients;
+
+		// band 0
+		target = coeff[ 0 ] * 0.886227; // π * 0.282095
+
+		// band 1
+		target += coeff[ 1 ] * 2.0 * 0.511664 * y; // ( 2 * π / 3 ) * 0.488603
+		target += coeff[ 2 ] * 2.0 * 0.511664 * z;
+		target += coeff[ 3 ] * 2.0 * 0.511664 * x;
+
+		// band 2
+		target += coeff[ 4 ] * 2.0 * 0.429043 * x * y; // ( π / 4 ) * 1.092548
+		target += coeff[ 5 ] * 2.0 * 0.429043 * y * z;
+		target += coeff[ 6 ] * ( 0.743125 * z * z - 0.247708 ); // ( π / 4 ) * 0.315392 * 3
+		target += coeff[ 7 ] * 2.0 * 0.429043 * x * z;
+		target += coeff[ 8 ] * 0.429043 * ( x * x - y * y ); // ( π / 4 ) * 0.546274
+
+		return target;
+
+	},
+
+	add: function ( sh ) {
+
+		for ( var i = 0; i < 9; i ++ ) {
+
+			this.coefficients[ i ].add( sh.coefficients[ i ] );
+
+		}
+
+		return this;
+
+	},
+
+
+	scale: function ( s ) {
+
+		for ( var i = 0; i < 9; i ++ ) {
+
+			this.coefficients[ i ].multiplyScalar( s );
+
+		}
+
+		return this;
+
+	},
+
+	lerp: function ( sh, alpha ) {
+
+		for ( var i = 0; i < 9; i ++ ) {
+
+			this.coefficients[ i ].lerp( sh.coefficients[ i ], alpha );
+
+		}
+
+		return this;
+
+	},
+
+	equals: function ( sh ) {
+
+		for ( var i = 0; i < 9; i ++ ) {
+
+			if ( ! this.coefficients[ i ].equals( sh.coefficients[ i ] ) ) {
+
+				return false;
+
+			}
+
+		}
+
+		return true;
+
+	},
+
+	copy: function ( sh ) {
+
+		return this.set( sh.coefficients );
+
+	},
+
+	clone: function () {
+
+		return new this.constructor().copy( this );
+
+	}
+
+} );
+
+Object.assign( SphericalHarmonics3, {
+
+	// evaluate the basis functions
+	// shBasis is an Array[ 9 ]
+	getBasisAt: function ( normal, shBasis ) {
+
+		// normal is assumed to be unit length
+
+		var x = normal.x, y = normal.y, z = normal.z;
+
+		// band 0
+		shBasis[ 0 ] = 0.282095;
+
+		// band 1
+		shBasis[ 1 ] = 0.488603 * y;
+		shBasis[ 2 ] = 0.488603 * z;
+		shBasis[ 3 ] = 0.488603 * x;
+
+		// band 2
+		shBasis[ 4 ] = 1.092548 * x * y;
+		shBasis[ 5 ] = 1.092548 * y * z;
+		shBasis[ 6 ] = 0.315392 * ( 3 * z * z - 1 );
+		shBasis[ 7 ] = 1.092548 * x * z;
+		shBasis[ 8 ] = 0.546274 * ( x * x - y * y );
+
+	}
+
+} );
+
+export { SphericalHarmonics3 };