module BABYLON { export class SphericalPolynomial { public x: Vector3 = Vector3.Zero(); public y: Vector3 = Vector3.Zero(); public z: Vector3 = Vector3.Zero(); public xx: Vector3 = Vector3.Zero(); public yy: Vector3 = Vector3.Zero(); public zz: Vector3 = Vector3.Zero(); public xy: Vector3 = Vector3.Zero(); public yz: Vector3 = Vector3.Zero(); public zx: Vector3 = Vector3.Zero(); public addAmbient(color: Color3): void { var colorVector = new Vector3(color.r, color.g, color.b); this.xx = this.xx.add(colorVector); this.yy = this.yy.add(colorVector); this.zz = this.zz.add(colorVector); } public scale(scale: number) { this.x = this.x.scale(scale); this.y = this.y.scale(scale); this.z = this.z.scale(scale); this.xx = this.xx.scale(scale); this.yy = this.yy.scale(scale); this.zz = this.zz.scale(scale); this.yz = this.yz.scale(scale); this.zx = this.zx.scale(scale); this.xy = this.xy.scale(scale); } public static FromHarmonics(harmonics: SphericalHarmonics): SphericalPolynomial { var result = new SphericalPolynomial(); result.x = harmonics.L11.scale(1.02333); result.y = harmonics.L1_1.scale(1.02333); result.z = harmonics.L10.scale(1.02333); result.xx = harmonics.L00.scale(0.886277).subtract(harmonics.L20.scale(0.247708)).add(harmonics.L22.scale(0.429043)); result.yy = harmonics.L00.scale(0.886277).subtract(harmonics.L20.scale(0.247708)).subtract(harmonics.L22.scale(0.429043)); result.zz = harmonics.L00.scale(0.886277).add(harmonics.L20.scale(0.495417)); result.yz = harmonics.L2_1.scale(0.858086); result.zx = harmonics.L21.scale(0.858086); result.xy = harmonics.L2_2.scale(0.858086); result.scale(1.0 / Math.PI); return result; } /** * Constructs a spherical polynomial from an array. * @param data defines the 9x3 coefficients (x, y, z, xx, yy, zz, yz, zx, xy) */ public static FromArray(data: ArrayLike>): SphericalPolynomial { const sp = new SphericalPolynomial(); Vector3.FromArrayToRef(data[0], 0, sp.x); Vector3.FromArrayToRef(data[1], 0, sp.y); Vector3.FromArrayToRef(data[2], 0, sp.z); Vector3.FromArrayToRef(data[3], 0, sp.xx); Vector3.FromArrayToRef(data[4], 0, sp.yy); Vector3.FromArrayToRef(data[5], 0, sp.zz); Vector3.FromArrayToRef(data[6], 0, sp.yz); Vector3.FromArrayToRef(data[7], 0, sp.zx); Vector3.FromArrayToRef(data[8], 0, sp.xy); return sp; } } export class SphericalHarmonics { public L00: Vector3 = Vector3.Zero(); public L1_1: Vector3 = Vector3.Zero(); public L10: Vector3 = Vector3.Zero(); public L11: Vector3 = Vector3.Zero(); public L2_2: Vector3 = Vector3.Zero(); public L2_1: Vector3 = Vector3.Zero(); public L20: Vector3 = Vector3.Zero(); public L21: Vector3 = Vector3.Zero(); public L22: Vector3 = Vector3.Zero(); public addLight(direction: Vector3, color: Color3, deltaSolidAngle: number): void { var colorVector = new Vector3(color.r, color.g, color.b); var c = colorVector.scale(deltaSolidAngle); this.L00 = this.L00.add(c.scale(0.282095)); this.L1_1 = this.L1_1.add(c.scale(0.488603 * direction.y)); this.L10 = this.L10.add(c.scale(0.488603 * direction.z)); this.L11 = this.L11.add(c.scale(0.488603 * direction.x)); this.L2_2 = this.L2_2.add(c.scale(1.092548 * direction.x * direction.y)); this.L2_1 = this.L2_1.add(c.scale(1.092548 * direction.y * direction.z)); this.L21 = this.L21.add(c.scale(1.092548 * direction.x * direction.z)); this.L20 = this.L20.add(c.scale(0.315392 * (3.0 * direction.z * direction.z - 1.0))); this.L22 = this.L22.add(c.scale(0.546274 * (direction.x * direction.x - direction.y * direction.y))); } public scale(scale: number): void { this.L00 = this.L00.scale(scale); this.L1_1 = this.L1_1.scale(scale); this.L10 = this.L10.scale(scale); this.L11 = this.L11.scale(scale); this.L2_2 = this.L2_2.scale(scale); this.L2_1 = this.L2_1.scale(scale); this.L20 = this.L20.scale(scale); this.L21 = this.L21.scale(scale); this.L22 = this.L22.scale(scale); } public convertIncidentRadianceToIrradiance(): void { // Convert from incident radiance (Li) to irradiance (E) by applying convolution with the cosine-weighted hemisphere. // // E_lm = A_l * L_lm // // In spherical harmonics this convolution amounts to scaling factors for each frequency band. // This corresponds to equation 5 in "An Efficient Representation for Irradiance Environment Maps", where // the scaling factors are given in equation 9. // Constant (Band 0) this.L00 = this.L00.scale(3.141593); // Linear (Band 1) this.L1_1 = this.L1_1.scale(2.094395); this.L10 = this.L10.scale(2.094395); this.L11 = this.L11.scale(2.094395); // Quadratic (Band 2) this.L2_2 = this.L2_2.scale(0.785398); this.L2_1 = this.L2_1.scale(0.785398); this.L20 = this.L20.scale(0.785398); this.L21 = this.L21.scale(0.785398); this.L22 = this.L22.scale(0.785398); } public convertIrradianceToLambertianRadiance(): void { // Convert from irradiance to outgoing radiance for Lambertian BDRF, suitable for efficient shader evaluation. // L = (1/pi) * E * rho // // This is done by an additional scale by 1/pi, so is a fairly trivial operation but important conceptually. this.scale(1.0 / Math.PI); // The resultant SH now represents outgoing radiance, so includes the Lambert 1/pi normalisation factor but without albedo (rho) applied // (The pixel shader must apply albedo after texture fetches, etc). } public static FromPolynomial(polynomial: SphericalPolynomial): SphericalHarmonics { var result = new SphericalHarmonics(); result.L00 = polynomial.xx.scale(0.376127).add(polynomial.yy.scale(0.376127)).add(polynomial.zz.scale(0.376126)); result.L1_1 = polynomial.y.scale(0.977204); result.L10 = polynomial.z.scale(0.977204); result.L11 = polynomial.x.scale(0.977204); result.L2_2 = polynomial.xy.scale(1.16538); result.L2_1 = polynomial.yz.scale(1.16538); result.L20 = polynomial.zz.scale(1.34567).subtract(polynomial.xx.scale(0.672834)).subtract(polynomial.yy.scale(0.672834)); result.L21 = polynomial.zx.scale(1.16538); result.L22 = polynomial.xx.scale(1.16538).subtract(polynomial.yy.scale(1.16538)); result.scale(Math.PI); return result; } /** * Constructs a spherical harmonics from an array. * @param data defines the 9x3 coefficients (l00, l1-1, l10, l11, l2-2, l2-1, l20, l21, l22) */ public static FromArray(data: ArrayLike>): SphericalHarmonics { const sh = new SphericalHarmonics(); Vector3.FromArrayToRef(data[0], 0, sh.L00); Vector3.FromArrayToRef(data[1], 0, sh.L1_1); Vector3.FromArrayToRef(data[2], 0, sh.L10); Vector3.FromArrayToRef(data[3], 0, sh.L11); Vector3.FromArrayToRef(data[4], 0, sh.L2_2); Vector3.FromArrayToRef(data[5], 0, sh.L2_1); Vector3.FromArrayToRef(data[6], 0, sh.L20); Vector3.FromArrayToRef(data[7], 0, sh.L21); Vector3.FromArrayToRef(data[8], 0, sh.L22); return sh; } } }