#ifndef UNITY_COMMON_LIGHTING_INCLUDED #define UNITY_COMMON_LIGHTING_INCLUDED #if SHADER_API_MOBILE || SHADER_API_GLES3 || SHADER_API_SWITCH || defined(UNITY_UNIFIED_SHADER_PRECISION_MODEL) #pragma warning (disable : 3205) // conversion of larger type to smaller #endif // Ligthing convention // Light direction is oriented backward (-Z). i.e in shader code, light direction is -lightData.forward //----------------------------------------------------------------------------- // Helper functions //----------------------------------------------------------------------------- // Performs the mapping of the vector 'v' centered within the axis-aligned cube // of dimensions [-1, 1]^3 to a vector centered within the unit sphere. // The function expects 'v' to be within the cube (possibly unexpected results otherwise). // Ref: http://mathproofs.blogspot.com/2005/07/mapping-cube-to-sphere.html real3 MapCubeToSphere(real3 v) { real3 v2 = v * v; real2 vr3 = v2.xy * rcp(3.0); return v * sqrt((real3)1.0 - 0.5 * v2.yzx - 0.5 * v2.zxy + vr3.yxx * v2.zzy); } // Computes the squared magnitude of the vector computed by MapCubeToSphere(). real ComputeCubeToSphereMapSqMagnitude(real3 v) { real3 v2 = v * v; // Note: dot(v, v) is often computed before this function is called, // so the compiler should optimize and use the precomputed result here. return dot(v, v) - v2.x * v2.y - v2.y * v2.z - v2.z * v2.x + v2.x * v2.y * v2.z; } // texelArea = 4.0 / (resolution * resolution). // Ref: http://bpeers.com/blog/?itemid=1017 // This version is less accurate, but much faster than this one: // http://www.rorydriscoll.com/2012/01/15/cubemap-texel-solid-angle/ real ComputeCubemapTexelSolidAngle(real3 L, real texelArea) { // Stretch 'L' by (1/d) so that it points at a side of a [-1, 1]^2 cube. real d = Max3(abs(L.x), abs(L.y), abs(L.z)); // Since 'L' is a unit vector, we can directly compute its // new (inverse) length without dividing 'L' by 'd' first. real invDist = d; // dw = dA * cosTheta / (dist * dist), cosTheta = 1.0 / dist, // where 'dA' is the area of the cube map texel. return texelArea * invDist * invDist * invDist; } // Only makes sense for Monte-Carlo integration. // Normalize by dividing by the total weight (or the number of samples) in the end. // Integrate[6*(u^2+v^2+1)^(-3/2), {u,-1,1},{v,-1,1}] = 4 * Pi // Ref: "Stupid Spherical Harmonics Tricks", p. 9. real ComputeCubemapTexelSolidAngle(real2 uv) { real u = uv.x, v = uv.y; return pow(1 + u * u + v * v, -1.5); } real ConvertEvToLuminance(real ev) { return exp2(ev - 3.0); } real ConvertLuminanceToEv(real luminance) { real k = 12.5f; return log2((luminance * 100.0) / k); } //----------------------------------------------------------------------------- // Attenuation functions //----------------------------------------------------------------------------- // Ref: Moving Frostbite to PBR. // Non physically based hack to limit light influence to attenuationRadius. // Square the result to smoothen the function. real DistanceWindowing(real distSquare, real rangeAttenuationScale, real rangeAttenuationBias) { // If (range attenuation is enabled) // rangeAttenuationScale = 1 / r^2 // rangeAttenuationBias = 1 // Else // rangeAttenuationScale = 2^12 / r^2 // rangeAttenuationBias = 2^24 return saturate(rangeAttenuationBias - Sq(distSquare * rangeAttenuationScale)); } real SmoothDistanceWindowing(real distSquare, real rangeAttenuationScale, real rangeAttenuationBias) { real factor = DistanceWindowing(distSquare, rangeAttenuationScale, rangeAttenuationBias); return Sq(factor); } #define PUNCTUAL_LIGHT_THRESHOLD 0.01 // 1cm (in Unity 1 is 1m) // Return physically based quadratic attenuation + influence limit to reach 0 at attenuationRadius real SmoothWindowedDistanceAttenuation(real distSquare, real distRcp, real rangeAttenuationScale, real rangeAttenuationBias) { real attenuation = min(distRcp, 1.0 / PUNCTUAL_LIGHT_THRESHOLD); attenuation *= DistanceWindowing(distSquare, rangeAttenuationScale, rangeAttenuationBias); // Effectively results in (distRcp)^2 * SmoothDistanceWindowing(...). return Sq(attenuation); } // Square the result to smoothen the function. real AngleAttenuation(real cosFwd, real lightAngleScale, real lightAngleOffset) { return saturate(cosFwd * lightAngleScale + lightAngleOffset); } real SmoothAngleAttenuation(real cosFwd, real lightAngleScale, real lightAngleOffset) { real attenuation = AngleAttenuation(cosFwd, lightAngleScale, lightAngleOffset); return Sq(attenuation); } // Combines SmoothWindowedDistanceAttenuation() and SmoothAngleAttenuation() in an efficient manner. // distances = {d, d^2, 1/d, d_proj}, where d_proj = dot(lightToSample, lightData.forward). real PunctualLightAttenuation(real4 distances, real rangeAttenuationScale, real rangeAttenuationBias, real lightAngleScale, real lightAngleOffset) { real distSq = distances.y; real distRcp = distances.z; real distProj = distances.w; real cosFwd = distProj * distRcp; real attenuation = min(distRcp, 1.0 / PUNCTUAL_LIGHT_THRESHOLD); attenuation *= DistanceWindowing(distSq, rangeAttenuationScale, rangeAttenuationBias); attenuation *= AngleAttenuation(cosFwd, lightAngleScale, lightAngleOffset); // Effectively results in SmoothWindowedDistanceAttenuation(...) * SmoothAngleAttenuation(...). return Sq(attenuation); } // A hack to smoothly limit the influence of the light to the interior of a capsule. // A capsule is formed by sweeping a ball along a line segment. // This function behaves like SmoothWindowedDistanceAttenuation() for a short line segment. // Convention: the surface point is located at the origin of the coordinate system. real CapsuleWindowing(real3 center, real3 xAxis, real halfLength, real rangeAttenuationScale, real rangeAttenuationBias) { // Conceptually, the idea is very simple: after taking the symmetry // of the capsule into account, it is clear that the problem can be // reduced to finding the closest sphere inside the capsule. // We begin our search at the center of the capsule, and then translate // this point along the line of symmetry until we either // a) find the closest point on the line, or b) hit an endpoint of the line segment. // The problem is simplified by working in the coordinate system of the capsule. real x = dot(center, xAxis); // -x, strictly speaking real dx = max(0, abs(x) - halfLength); real r2 = dot(center, center); // r^2 real z2 = max(0, r2 - x * x); // z^2 real d2 = z2 + dx * dx; // Squared distance to the center of the closest sphere return SmoothDistanceWindowing(d2, rangeAttenuationScale, rangeAttenuationBias); } // A hack to smoothly limit the influence of the light to the interior of a pillow. // A "pillow" (for the lack of a better name) is formed by sweeping a ball across a rectangle. // This function behaves like CapsuleAttenuation() for a narrow rectangle. // This function behaves like SmoothWindowedDistanceAttenuation() for a small rectangle. // Convention: the surface point is located at the origin of the coordinate system. real PillowWindowing(real3 center, real3 xAxis, real3 yAxis, real halfLength, real halfHeight, real rangeAttenuationScale, real rangeAttenuationBias) { // Conceptually, the idea is very simple: after taking the symmetry // of the pillow into account, it is clear that the problem can be // reduced to finding the closest sphere inside the pillow. // We begin our search at the center of the pillow, and then translate // this point along and across the plane of symmetry until we either // a) find the closest point on the plane, or b) hit an edge of the rectangle. // The problem is simplified by working in the coordinate system of the pillow. real x = dot(center, xAxis); // -x, strictly speaking real dx = max(0, abs(x) - halfLength); real y = dot(center, yAxis); // -y, strictly speaking real dy = max(0, abs(y) - halfHeight); real r2 = dot(center, center); // r^2 real z2 = max(0, r2 - x * x - y * y); // z^2 real d2 = z2 + dx * dx + dy * dy; // Squared distance to the center of the closest sphere return SmoothDistanceWindowing(d2, rangeAttenuationScale, rangeAttenuationBias); } // Applies SmoothDistanceWindowing() after transforming the attenuation ellipsoid into a sphere. // If r = rsqrt(invSqRadius), then the ellipsoid is defined s.t. r1 = r / invAspectRatio, r2 = r3 = r. // The transformation is performed along the major axis of the ellipsoid (corresponding to 'r1'). // Both the ellipsoid (e.i. 'axis') and 'unL' should be in the same coordinate system. // 'unL' should be computed from the center of the ellipsoid. real EllipsoidalDistanceAttenuation(real3 unL, real3 axis, real invAspectRatio, real rangeAttenuationScale, real rangeAttenuationBias) { // Project the unnormalized light vector onto the axis. real projL = dot(unL, axis); // Transform the light vector so that we can work with // with the ellipsoid as if it was a sphere with the radius of light's range. real diff = projL - projL * invAspectRatio; unL -= diff * axis; real sqDist = dot(unL, unL); return SmoothDistanceWindowing(sqDist, rangeAttenuationScale, rangeAttenuationBias); } // Applies SmoothDistanceWindowing() using the axis-aligned ellipsoid of the given dimensions. // Both the ellipsoid and 'unL' should be in the same coordinate system. // 'unL' should be computed from the center of the ellipsoid. real EllipsoidalDistanceAttenuation(real3 unL, real3 invHalfDim, real rangeAttenuationScale, real rangeAttenuationBias) { // Transform the light vector so that we can work with // with the ellipsoid as if it was a unit sphere. unL *= invHalfDim; real sqDist = dot(unL, unL); return SmoothDistanceWindowing(sqDist, rangeAttenuationScale, rangeAttenuationBias); } // Applies SmoothDistanceWindowing() after mapping the axis-aligned box to a sphere. // If the diagonal of the box is 'd', invHalfDim = rcp(0.5 * d). // Both the box and 'unL' should be in the same coordinate system. // 'unL' should be computed from the center of the box. real BoxDistanceAttenuation(real3 unL, real3 invHalfDim, real rangeAttenuationScale, real rangeAttenuationBias) { real attenuation = 0.0; // Transform the light vector so that we can work with // with the box as if it was a [-1, 1]^2 cube. unL *= invHalfDim; // Our algorithm expects the input vector to be within the cube. if (!(Max3(abs(unL.x), abs(unL.y), abs(unL.z)) > 1.0)) { real sqDist = ComputeCubeToSphereMapSqMagnitude(unL); attenuation = SmoothDistanceWindowing(sqDist, rangeAttenuationScale, rangeAttenuationBias); } return attenuation; } //----------------------------------------------------------------------------- // IES Helper //----------------------------------------------------------------------------- real2 GetIESTextureCoordinate(real3x3 lightToWord, real3 L) { // IES need to be sample in light space real3 dir = mul(lightToWord, -L); // Using matrix on left side do a transpose // convert to spherical coordinate real2 sphericalCoord; // .x is theta, .y is phi // Texture is encoded with cos(phi), scale from -1..1 to 0..1 sphericalCoord.y = (dir.z * 0.5) + 0.5; real theta = atan2(dir.y, dir.x); sphericalCoord.x = theta * INV_TWO_PI; return sphericalCoord; } //----------------------------------------------------------------------------- // Lighting functions //----------------------------------------------------------------------------- // Ref: Horizon Occlusion for Normal Mapped Reflections: http://marmosetco.tumblr.com/post/81245981087 real GetHorizonOcclusion(real3 V, real3 normalWS, real3 vertexNormal, real horizonFade) { real3 R = reflect(-V, normalWS); real specularOcclusion = saturate(1.0 + horizonFade * dot(R, vertexNormal)); // smooth it return specularOcclusion * specularOcclusion; } // Ref: Moving Frostbite to PBR - Gotanda siggraph 2011 // Return specular occlusion based on ambient occlusion (usually get from SSAO) and view/roughness info real GetSpecularOcclusionFromAmbientOcclusion(real NdotV, real ambientOcclusion, real roughness) { return saturate(PositivePow(NdotV + ambientOcclusion, exp2(-16.0 * roughness - 1.0)) - 1.0 + ambientOcclusion); } // ref: Practical Realtime Strategies for Accurate Indirect Occlusion // Update ambient occlusion to colored ambient occlusion based on statitics of how light is bouncing in an object and with the albedo of the object real3 GTAOMultiBounce(real visibility, real3 albedo) { real3 a = 2.0404 * albedo - 0.3324; real3 b = -4.7951 * albedo + 0.6417; real3 c = 2.7552 * albedo + 0.6903; real x = visibility; return max(x, ((x * a + b) * x + c) * x); } // Based on Oat and Sander's 2007 technique // Area/solidAngle of intersection of two cone real SphericalCapIntersectionSolidArea(real cosC1, real cosC2, real cosB) { real r1 = FastACos(cosC1); real r2 = FastACos(cosC2); real rd = FastACos(cosB); real area = 0.0; if (rd <= max(r1, r2) - min(r1, r2)) { // One cap is completely inside the other area = TWO_PI - TWO_PI * max(cosC1, cosC2); } else if (rd >= r1 + r2) { // No intersection exists area = 0.0; } else { real diff = abs(r1 - r2); real den = r1 + r2 - diff; real x = 1.0 - saturate((rd - diff) / max(den, 0.0001)); area = smoothstep(0.0, 1.0, x); area *= TWO_PI - TWO_PI * max(cosC1, cosC2); } return area; } // ref: Practical Realtime Strategies for Accurate Indirect Occlusion // http://blog.selfshadow.com/publications/s2016-shading-course/#course_content // Original Cone-Cone method with cosine weighted assumption (p129 s2016_pbs_activision_occlusion) real GetSpecularOcclusionFromBentAO_ConeCone(real3 V, real3 bentNormalWS, real3 normalWS, real ambientOcclusion, real roughness) { // Retrieve cone angle // Ambient occlusion is cosine weighted, thus use following equation. See slide 129 real cosAv = sqrt(1.0 - ambientOcclusion); roughness = max(roughness, 0.01); // Clamp to 0.01 to avoid edge cases real cosAs = exp2((-log(10.0) / log(2.0)) * Sq(roughness)); real cosB = dot(bentNormalWS, reflect(-V, normalWS)); return SphericalCapIntersectionSolidArea(cosAv, cosAs, cosB) / (TWO_PI * (1.0 - cosAs)); } real GetSpecularOcclusionFromBentAO(real3 V, real3 bentNormalWS, real3 normalWS, real ambientOcclusion, real roughness) { // Pseudo code: //SphericalGaussian NDF = WarpedGGXDistribution(normalWS, roughness, V); //SphericalGaussian Visibility = VisibilityConeSG(bentNormalWS, ambientOcclusion); //SphericalGaussian UpperHemisphere = UpperHemisphereSG(normalWS); //return saturate( InnerProduct(NDF, Visibility) / InnerProduct(NDF, UpperHemisphere) ); // 1. Approximate visibility cone with a spherical gaussian of amplitude A=1 // For a cone angle X, we can determine sharpness so that all point inside the cone have a value > Y // sharpness = (log(Y) - log(A)) / (cos(X) - 1) // For AO cone, cos(X) = sqrt(1 - ambientOcclusion) // -> for Y = 0.1, sharpness = -1.0 / (sqrt(1-ao) - 1) float vs = -1.0f / min(sqrt(1.0f - ambientOcclusion) - 1.0f, -0.001f); // 2. Approximate upper hemisphere with sharpness = 0.8 and amplitude = 1 float us = 0.8f; // 3. Compute warped SG Axis of GGX distribution // Ref: All-Frequency Rendering of Dynamic, Spatially-Varying Reflectance // https://www.microsoft.com/en-us/research/wp-content/uploads/2009/12/sg.pdf float NoV = dot(V, normalWS); float3 NDFAxis = (2 * NoV * normalWS - V) * (0.5f / max(roughness * roughness * NoV, 0.001f)); float umLength1 = length(NDFAxis + vs * bentNormalWS); float umLength2 = length(NDFAxis + us * normalWS); float d1 = 1 - exp(-2 * umLength1); float d2 = 1 - exp(-2 * umLength2); float expFactor1 = exp(umLength1 - umLength2 + us - vs); return saturate(expFactor1 * (d1 * umLength2) / (d2 * umLength1)); } // Ref: Steve McAuley - Energy-Conserving Wrapped Diffuse real ComputeWrappedDiffuseLighting(real NdotL, real w) { return saturate((NdotL + w) / ((1.0 + w) * (1.0 + w))); } // Ref: Stephen McAuley - Advances in Rendering: Graphics Research and Video Game Production real3 ComputeWrappedNormal(real3 N, real3 L, real w) { real NdotL = dot(N, L); real wrappedNdotL = saturate((NdotL + w) / (1 + w)); real sinPhi = lerp(w, 0.f, wrappedNdotL); real cosPhi = sqrt(1.0f - sinPhi * sinPhi); return normalize(cosPhi * N + sinPhi * cross(cross(N, L), N)); } // Jimenez variant for eye real ComputeWrappedPowerDiffuseLighting(real NdotL, real w, real p) { return pow(saturate((NdotL + w) / (1.0 + w)), p) * (p + 1) / (w * 2.0 + 2.0); } // Ref: The Technical Art of Uncharted 4 - Brinck and Maximov 2016 real ComputeMicroShadowing(real AO, real NdotL, real opacity) { real aperture = 2.0 * AO * AO; real microshadow = saturate(NdotL + aperture - 1.0); return lerp(1.0, microshadow, opacity); } real3 ComputeShadowColor(real shadow, real3 shadowTint, real penumbraFlag) { // The origin expression is // lerp(real3(1.0, 1.0, 1.0) - ((1.0 - shadow) * (real3(1.0, 1.0, 1.0) - shadowTint)) // , shadow * lerp(shadowTint, lerp(shadowTint, real3(1.0, 1.0, 1.0), shadow), shadow) // , penumbraFlag); // it has been simplified to this real3 invTint = real3(1.0, 1.0, 1.0) - shadowTint; real shadow3 = shadow * shadow * shadow; return lerp(real3(1.0, 1.0, 1.0) - ((1.0 - shadow) * invTint) , shadow3 * invTint + shadow * shadowTint, penumbraFlag); } // This is the same method as the one above. Simply the shadow is a real3 to support colored shadows. real3 ComputeShadowColor(real3 shadow, real3 shadowTint, real penumbraFlag) { // The origin expression is // lerp(real3(1.0, 1.0, 1.0) - ((1.0 - shadow) * (real3(1.0, 1.0, 1.0) - shadowTint)) // , shadow * lerp(shadowTint, lerp(shadowTint, real3(1.0, 1.0, 1.0), shadow), shadow) // , penumbraFlag); // it has been simplified to this real3 invTint = real3(1.0, 1.0, 1.0) - shadowTint; real3 shadow3 = shadow * shadow * shadow; return lerp(real3(1.0, 1.0, 1.0) - ((1.0 - shadow) * invTint) , shadow3 * invTint + shadow * shadowTint, penumbraFlag); } //----------------------------------------------------------------------------- // Helper functions //--------------------------------------------------------------------------- -- // Ref: "Crafting a Next-Gen Material Pipeline for The Order: 1886". real ClampNdotV(real NdotV) { return max(NdotV, 0.0001); // Approximately 0.0057 degree bias } // Helper function to return a set of common angle used when evaluating BSDF // NdotL and NdotV are unclamped void GetBSDFAngle(real3 V, real3 L, real NdotL, real NdotV, out real LdotV, out real NdotH, out real LdotH, out real invLenLV) { // Optimized math. Ref: PBR Diffuse Lighting for GGX + Smith Microsurfaces (slide 114), assuming |L|=1 and |V|=1 LdotV = dot(L, V); invLenLV = rsqrt(max(2.0 * LdotV + 2.0, FLT_EPS)); // invLenLV = rcp(length(L + V)), clamp to avoid rsqrt(0) = inf, inf * 0 = NaN NdotH = saturate((NdotL + NdotV) * invLenLV); LdotH = saturate(invLenLV * LdotV + invLenLV); } // Inputs: normalized normal and view vectors. // Outputs: front-facing normal, and the new non-negative value of the cosine of the view angle. // Important: call Orthonormalize() on the tangent and recompute the bitangent afterwards. real3 GetViewReflectedNormal(real3 N, real3 V, out real NdotV) { // Fragments of front-facing geometry can have back-facing normals due to interpolation, // normal mapping and decals. This can cause visible artifacts from both direct (negative or // extremely high values) and indirect (incorrect lookup direction) lighting. // There are several ways to avoid this problem. To list a few: // // 1. Setting { NdotV = max(, SMALL_VALUE) }. This effectively removes normal mapping // from the affected fragments, making the surface appear flat. // // 2. Setting { NdotV = abs() }. This effectively reverses the convexity of the surface. // It also reduces light leaking from non-shadow-casting lights. Note that 'NdotV' can still // be 0 in this case. // // It's important to understand that simply changing the value of the cosine is insufficient. // For one, it does not solve the incorrect lookup direction problem, since the normal itself // is not modified. There is a more insidious issue, however. 'NdotV' is a constituent element // of the mathematical system describing the relationships between different vectors - and // not just normal and view vectors, but also light vectors, half vectors, tangent vectors, etc. // Changing only one angle (or its cosine) leaves the system in an inconsistent state, where // certain relationships can take on different values depending on whether 'NdotV' is used // in the calculation or not. Therefore, it is important to change the normal (or another // vector) in order to leave the system in a consistent state. // // We choose to follow the conceptual approach (2) by reflecting the normal around the // ( = 0) boundary if necessary, as it allows us to preserve some normal mapping details. NdotV = dot(N, V); // N = (NdotV >= 0.0) ? N : (N - 2.0 * NdotV * V); N += (2.0 * saturate(-NdotV)) * V; NdotV = abs(NdotV); return N; } // Generates an orthonormal (row-major) basis from a unit vector. TODO: make it column-major. // The resulting rotation matrix has the determinant of +1. // Ref: 'ortho_basis_pixar_r2' from http://marc-b-reynolds.github.io/quaternions/2016/07/06/Orthonormal.html real3x3 GetLocalFrame(real3 localZ) { real x = localZ.x; real y = localZ.y; real z = localZ.z; real sz = FastSign(z); real a = 1 / (sz + z); real ya = y * a; real b = x * ya; real c = x * sz; real3 localX = real3(c * x * a - 1, sz * b, c); real3 localY = real3(b, y * ya - sz, y); // Note: due to the quaternion formulation, the generated frame is rotated by 180 degrees, // s.t. if localZ = {0, 0, 1}, then localX = {-1, 0, 0} and localY = {0, -1, 0}. return real3x3(localX, localY, localZ); } // Generates an orthonormal (row-major) basis from a unit vector. TODO: make it column-major. // The resulting rotation matrix has the determinant of +1. real3x3 GetLocalFrame(real3 localZ, real3 localX) { real3 localY = cross(localZ, localX); return real3x3(localX, localY, localZ); } // Construct a right-handed view-dependent orthogonal basis around the normal: // b0-b2 is the view-normal aka reflection plane. real3x3 GetOrthoBasisViewNormal(real3 V, real3 N, real unclampedNdotV, bool testSingularity = true) { real3x3 orthoBasisViewNormal; if (testSingularity && (abs(1.0 - unclampedNdotV) <= FLT_EPS)) { // In this case N == V, and azimuth orientation around N shouldn't matter for the caller, // we can use any quaternion-based method, like Frisvad or Reynold's (Pixar): orthoBasisViewNormal = GetLocalFrame(N); } else { orthoBasisViewNormal[0] = normalize(V - N * unclampedNdotV); orthoBasisViewNormal[2] = N; orthoBasisViewNormal[1] = cross(orthoBasisViewNormal[2], orthoBasisViewNormal[0]); } return orthoBasisViewNormal; } // Move this here since it's used by both LightLoop.hlsl and RaytracingLightLoop.hlsl bool IsMatchingLightLayer(uint lightLayers, uint renderingLayers) { return (lightLayers & renderingLayers) != 0; } #if SHADER_API_MOBILE || SHADER_API_GLES3 || SHADER_API_SWITCH #pragma warning (enable : 3205) // conversion of larger type to smaller #endif #endif // UNITY_COMMON_LIGHTING_INCLUDED