前言
用到的技术：approximated ACES tone-mapping，PrefilteredDFG_Karis函数，伽马校正
代码详解
#define saturate(x) clamp(x, 0.0, 1.0)
#define PI 3.14159265359
//------------------------------------------------------------------------------
// Distance field functions
//------------------------------------------------------------------------------
float sdPlane(in vec3 p) {
return p.y;
}
float sdSphere(in vec3 p, float s) {
return length(p) - s;
}
float sdTorus(in vec3 p, in vec2 t) {
return length(vec2(length(p.xz) - t.x, p.y)) - t.y;
}
vec2 opUnion(vec2 d1, vec2 d2) {
return d1.x < d2.x ? d1 : d2;
}
vec2 scene(in vec3 position) {
vec2 scene = opUnion(
vec2(sdPlane(position), 1.0),
vec2(sdSphere(position - vec3(0.0, 0.4, 0.0), 0.4), 12.0)
);
return scene;
}
//------------------------------------------------------------------------------
// Ray casting
//------------------------------------------------------------------------------
float shadow(in vec3 origin, in vec3 direction) {
float hit = 1.0;
float t = 0.02;
for (int i = 0; i < 1000; i++) {
float h = scene(origin + direction * t).x;
if (h < 0.001) return 0.0;
t += h;
hit = min(hit, 10.0 * h / t);
if (t >= 2.5) break;
}
return clamp(hit, 0.0, 1.0);
}
vec2 traceRay(in vec3 origin, in vec3 direction) {
float material = -1.0;
float t = 0.02;
for (int i = 0; i < 1000; i++) {
vec2 hit = scene(origin + direction * t);
if (hit.x < 0.002 || t > 20.0) break;
t += hit.x;
material = hit.y;
}
if (t > 20.0) {
material = -1.0;
}
return vec2(t, material);
}
vec3 normal(in vec3 position) {
vec3 epsilon = vec3(0.001, 0.0, 0.0);
vec3 n = vec3(
scene(position + epsilon.xyy).x - scene(position - epsilon.xyy).x,
scene(position + epsilon.yxy).x - scene(position - epsilon.yxy).x,
scene(position + epsilon.yyx).x - scene(position - epsilon.yyx).x);
return normalize(n);
}
//------------------------------------------------------------------------------
// BRDF
//------------------------------------------------------------------------------
float pow5(float x) {
float x2 = x * x;
return x2 * x2 * x;
}
float D_GGX(float linearRoughness, float NoH, const vec3 h) {
// Walter et al. 2007, "Microfacet Models for Refraction through Rough Surfaces"
float oneMinusNoHSquared = 1.0 - NoH * NoH;
float a = NoH * linearRoughness;
float k = linearRoughness / (oneMinusNoHSquared + a * a);
float d = k * k * (1.0 / PI);
return d;
}
float V_SmithGGXCorrelated(float linearRoughness, float NoV, float NoL) {
// Heitz 2014, "Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs"
float a2 = linearRoughness * linearRoughness;
float GGXV = NoL * sqrt((NoV - a2 * NoV) * NoV + a2);
float GGXL = NoV * sqrt((NoL - a2 * NoL) * NoL + a2);
return 0.5 / (GGXV + GGXL);
}
vec3 F_Schlick(const vec3 f0, float VoH) {
// Schlick 1994, "An Inexpensive BRDF Model for Physically-Based Rendering"
return f0 + (vec3(1.0) - f0) * pow5(1.0 - VoH);
}
float F_Schlick(float f0, float f90, float VoH) {
return f0 + (f90 - f0) * pow5(1.0 - VoH);
}
float Fd_Burley(float linearRoughness, float NoV, float NoL, float LoH) {
// Burley 2012, "Physically-Based Shading at Disney"
float f90 = 0.5 + 2.0 * linearRoughness * LoH * LoH;
float lightScatter = F_Schlick(1.0, f90, NoL);
float viewScatter = F_Schlick(1.0, f90, NoV);
return lightScatter * viewScatter * (1.0 / PI);
}
float Fd_Lambert() {
return 1.0 / PI;
}
//------------------------------------------------------------------------------
// Indirect lighting
//------------------------------------------------------------------------------
vec3 Irradiance_SphericalHarmonics(const vec3 n) {
// Irradiance from "Ditch River" IBL (http://www.hdrlabs.com/sibl/archive.html)
return max(
vec3( 0.754554516862612, 0.748542953903366, 0.790921515418539)
+ vec3(-0.083856548007422, 0.092533500963210, 0.322764661032516) * (n.y)
+ vec3( 0.308152705331738, 0.366796330467391, 0.466698181299906) * (n.z)
+ vec3(-0.188884931542396, -0.277402551592231, -0.377844212327557) * (n.x)
, 0.0);
}
// https://www.unrealengine.com/zh-CN/blog/physically-based-shading-on-mobile
vec2 PrefilteredDFG_Karis(float roughness, float NoV) {
// Karis 2014, "Physically Based Material on Mobile"
const vec4 c0 = vec4(-1.0, -0.0275, -0.572, 0.022);
const vec4 c1 = vec4( 1.0, 0.0425, 1.040, -0.040);
vec4 r = roughness * c0 + c1;
float a004 = min(r.x * r.x, exp2(-9.28 * NoV)) * r.x + r.y;
return vec2(-1.04, 1.04) * a004 + r.zw;
}
//------------------------------------------------------------------------------
// Tone mapping and transfer functions
//------------------------------------------------------------------------------
vec3 Tonemap_ACES(const vec3 x) {
// Narkowicz 2015, "ACES Filmic Tone Mapping Curve"
const float a = 2.51;
const float b = 0.03;
const float c = 2.43;
const float d = 0.59;
const float e = 0.14;
return (x * (a * x + b)) / (x * (c * x + d) + e);
}
// gamma矫正
vec3 OECF_sRGBFast(const vec3 linear) {
return pow(linear, vec3(1.0 / 2.2));
}
//------------------------------------------------------------------------------
// Rendering
//------------------------------------------------------------------------------
vec3 render(in vec3 origin, in vec3 direction, out float distance) {
// Sky gradient
vec3 color = vec3(0.65, 0.85, 1.0) + direction.y * 0.72;
// (distance, material)
vec2 hit = traceRay(origin, direction);
distance = hit.x;
float material = hit.y;
// We've hit something in the scene
if (material > 0.0) {
vec3 position = origin + distance * direction;
vec3 v = normalize(-direction);
vec3 n = normal(position);
vec3 l = normalize(vec3(0.6, 0.7, -0.7));
vec3 h = normalize(v + l);
vec3 r = normalize(reflect(direction, n));
float NoV = abs(dot(n, v)) + 1e-5;
float NoL = saturate(dot(n, l));
float NoH = saturate(dot(n, h));
float LoH = saturate(dot(l, h));
vec3 baseColor = vec3(0.0);
float roughness = 0.0;
float metallic = 0.0;
float intensity = 2.0;
float indirectIntensity = 0.64;
if (material < 4.0) {
// Checkerboard floor
float f = mod(floor(6.0 * position.z) + floor(6.0 * position.x), 2.0);
baseColor = 0.4 + f * vec3(0.6);
roughness = 0.1;
} else if (material < 16.0) {
// Metallic objects
baseColor = vec3(0.3, 0.0, 0.0);
roughness = 0.2;
}
float linearRoughness = roughness * roughness;
vec3 diffuseColor = (1.0 - metallic) * baseColor.rgb;
vec3 f0 = 0.04 * (1.0 - metallic) + baseColor.rgb * metallic;
float attenuation = shadow(position, l);
// specular BRDF
float D = D_GGX(linearRoughness, NoH, h);
float V = V_SmithGGXCorrelated(linearRoughness, NoV, NoL);
vec3 F = F_Schlick(f0, LoH);
vec3 Fr = (D * V) * F;
// diffuse BRDF
vec3 Fd = diffuseColor * Fd_Burley(linearRoughness, NoV, NoL, LoH);
color = Fd + Fr;
color *= (intensity * attenuation * NoL) * vec3(0.98, 0.92, 0.89);
// diffuse indirect
vec3 indirectDiffuse = Irradiance_SphericalHarmonics(n) * Fd_Lambert();
vec2 indirectHit = traceRay(position, r);
vec3 indirectSpecular = vec3(0.65, 0.85, 1.0) + r.y * 0.72;
if (indirectHit.y > 0.0) {
if (indirectHit.y < 4.0) {
vec3 indirectPosition = position + indirectHit.x * r;
// Checkerboard floor
float f = mod(floor(6.0 * indirectPosition.z) + floor(6.0 * indirectPosition.x), 2.0);
indirectSpecular = 0.4 + f * vec3(0.6);
} else if (indirectHit.y < 16.0) {
// Metallic objects
indirectSpecular = vec3(0.3, 0.0, 0.0);
}
}
// indirect contribution
vec2 dfg = PrefilteredDFG_Karis(roughness, NoV);
//https://zhuanlan.zhihu.com/p/53086060里面的6.3.1 流派1：2D LUT
vec3 specularColor = f0 * dfg.x + dfg.y;
vec3 ibl = diffuseColor * indirectDiffuse + indirectSpecular * specularColor;
color += ibl * indirectIntensity;
}
return color;
}
//------------------------------------------------------------------------------
// Setup and execution
//------------------------------------------------------------------------------
mat3 setCamera(in vec3 origin, in vec3 target, float rotation) {
vec3 forward = normalize(target - origin);
vec3 orientation = vec3(sin(rotation), cos(rotation), 0.0);
vec3 left = normalize(cross(forward, orientation));
vec3 up = normalize(cross(left, forward));
return mat3(left, up, forward);
}
void mainImage(out vec4 fragColor, in vec2 fragCoord) {
// Normalized coordinates
vec2 p = -1.0 + 2.0 * fragCoord.xy / iResolution.xy;
// Aspect ratio
p.x *= iResolution.x / iResolution.y;
// Camera position and "look at"
vec3 origin = vec3(0.0, 0.8, 0.0);
vec3 target = vec3(0.0);
origin.x += 1.7 * cos(iTime * 0.2);
origin.z += 1.7 * sin(iTime * 0.2);
mat3 toWorld = setCamera(origin, target, 0.0);
vec3 direction = toWorld * normalize(vec3(p.xy, 2.0));
// Render scene
float distance;
vec3 color = render(origin, direction, distance);
// Tone mapping
color = Tonemap_ACES(color);
// Exponential distance fog 指数雾
color = mix(color, 0.8 * vec3(0.7, 0.8, 1.0), 1.0 - exp2(-0.011 * distance * distance));
// Gamma compression伽马校正
color = OECF_sRGBFast(color);
fragColor = vec4(color, 1.0);
}
