Volumetric lighting is typically driven by a single-phase function that determines how much of the total scattered light is scattered toward the camera. The angle between the incoming light direction and the vector from our camera to the world space position of a given fragment is what primarily drives the Mie-scattering phase function.
Implementing a Shadow Mapper for Directional Lighting
The first order of business is to set up shadow mapping in my deferred renderer, which is going to serve two purposes: to render shadows (obviously) and to cull the container of the “volume” that represents the lighting so that we achieve clean casts onto the illuminated parts of surfaces, as seen in the image above. Because the shadow map encodes information that reveals which parts of the scene can be viewed from the light’s perspective, we can use this information to cultivate nice-looking volumetric beams that extend directly from the lit regions.
To facilitate shadow mapping, we’re going to want to render all of the geometries in our scene from the light’s perspective, like so:
void setLightSpaceVP(const phoenix::Shader& shader)
{
shader.use();
glm::vec3 lightViewForward = glm::normalize(directLight._direction);
glm::vec3 lightViewRight = glm::normalize(glm::cross(phoenix::UP, lightViewForward));
glm::vec3 lightViewUp = glm::normalize(glm::cross(lightViewForward, lightViewRight));
glm::mat3 rotation;
rotation[0] = lightViewForward;
rotation[1] = lightViewRight;
rotation[2] = lightViewUp;
std::array<glm::vec3, phoenix::NUM_FRUSTUM_CORNERS> frustumCorners{ {
glm::vec3(-phoenix::FRUSTUM_HALF_WIDTH, -phoenix::FRUSTUM_HALF_WIDTH, phoenix::FRUSTUM_HALF_WIDTH),
glm::vec3(-phoenix::FRUSTUM_HALF_WIDTH, -phoenix::FRUSTUM_HALF_WIDTH, -phoenix::FRUSTUM_HALF_WIDTH),
glm::vec3(-phoenix::FRUSTUM_HALF_WIDTH, phoenix::FRUSTUM_HALF_WIDTH, phoenix::FRUSTUM_HALF_WIDTH),
glm::vec3(-phoenix::FRUSTUM_HALF_WIDTH, phoenix::FRUSTUM_HALF_WIDTH, -phoenix::FRUSTUM_HALF_WIDTH),
glm::vec3(phoenix::FRUSTUM_HALF_WIDTH, -phoenix::FRUSTUM_HALF_WIDTH, phoenix::FRUSTUM_HALF_WIDTH),
glm::vec3(phoenix::FRUSTUM_HALF_WIDTH, -phoenix::FRUSTUM_HALF_WIDTH, -phoenix::FRUSTUM_HALF_WIDTH),
glm::vec3(phoenix::FRUSTUM_HALF_WIDTH, phoenix::FRUSTUM_HALF_WIDTH, phoenix::FRUSTUM_HALF_WIDTH),
glm::vec3(phoenix::FRUSTUM_HALF_WIDTH, phoenix::FRUSTUM_HALF_WIDTH, -phoenix::FRUSTUM_HALF_WIDTH)
} };
for (size_t i = 0; i < phoenix::NUM_FRUSTUM_CORNERS; ++i)
{
frustumCorners[i] = frustumCorners[i] * rotation;
}
float minX = frustumCorners[0].x, minY = frustumCorners[0].y, minZ = frustumCorners[0].z, maxX = frustumCorners[0].x, maxY = frustumCorners[0].y, maxZ = frustumCorners[0].z;
for (size_t i = 0; i < phoenix::NUM_FRUSTUM_CORNERS; ++i)
{
if (frustumCorners[i].x < minX)
{
minX = frustumCorners[i].x;
}
if (frustumCorners[i].x > maxX)
{
maxX = frustumCorners[i].x;
}
if (frustumCorners[i].y < minY)
{
minY = frustumCorners[i].y;
}
if (frustumCorners[i].y > maxY)
{
maxY = frustumCorners[i].y;
}
if (frustumCorners[i].z < minZ)
{
minZ = frustumCorners[i].z;
}
if (frustumCorners[i].z > maxZ)
{
maxZ = frustumCorners[i].z;
}
}
glm::mat4 lightView(rotation);
lightView[3][0] = -(minX + maxX) * 0.5f;
lightView[3][1] = -(minY + maxY) * 0.5f;
lightView[3][2] = -(minZ + maxZ) * 0.5f;
lightView[0][3] = 0.0f;
lightView[1][3] = 0.0f;
lightView[2][3] = 0.0f;
lightView[3][3] = 1.0f;
glm::vec3 frustumExtents(maxX - minX, maxY - minY, maxZ - minZ);
glm::vec3 halfExtents = frustumExtents * 0.5f;
glm::mat4 lightSpaceVP = glm::orthoLH(-halfExtents.x, halfExtents.x, -halfExtents.y, halfExtents.y, -halfExtents.z, halfExtents.z) * lightView;
shader.setMat4(phoenix::G_LIGHT_SPACE_VP, lightSpaceVP);
}
// ...
void execShadowMapPass(const phoenix::Shader& shader, phoenix::Model& object)
{
glViewport(0, 0, phoenix::HIGH_RES_WIDTH, phoenix::HIGH_RES_HEIGHT);
glBindFramebuffer(GL_FRAMEBUFFER, shadowMapRenderTarget->_FBO);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
setLightSpaceVP(shader);
renderObject(shader, object);
glBindFramebuffer(GL_FRAMEBUFFER, 0);
glViewport(0, 0, phoenix::SCREEN_WIDTH, phoenix::SCREEN_HEIGHT);
}
As a bit of a hack, I rotated a frustum with half-widths of size 25 so that it was aligned with the direction of the lighting; that’s enough to cover the entire Sponza scene.
We can use the result from the shadow map in a subsequent pass to assess occlusion information:
Executing the Lighting Pass
As I mentioned before, much of the volumetric light scattering is going to be driven by a single-phase function, which I’ll explain after the jump:
#version 460 core
layout (location = 3) out vec4 FragColor;
const int SCREEN_WIDTH = 2460;
const int SCREEN_HEIGHT = 1440;
const int NUM_STEPS_INT = 15;
const float NUM_STEPS = float(NUM_STEPS_INT);
const float G = 0.7f; // Controls how much light will scatter in the forward direction
const float PI = 3.14159265359f;
const float SPECULAR_FACTOR = 16.0f;
const mat4 DITHER_PATTERN = mat4
(vec4(0.0f, 0.5f, 0.125f, 0.625f),
vec4(0.75f, 0.22f, 0.875f, 0.375f),
vec4(0.1875f, 0.6875f, 0.0625f, 0.5625f),
vec4(0.9375f, 0.4375f, 0.8125f, 0.3125f));
struct Light
{
vec3 _color;
float _intensity;
};
struct DirectLight
{
struct Light _light;
vec3 _direction;
};
in vec2 TexCoords;
uniform sampler2D gPositionMap;
uniform sampler2D gNormalMap;
uniform sampler2D gAlbedoSpecularMap;
uniform sampler2D gShadowMap;
uniform DirectLight gDirectLight;
uniform mat4 gLightSpaceVP;
uniform vec3 gViewPos;
uniform float gAmbientFactor;
const vec3 P = texture(gPositionMap, TexCoords).rgb;
const vec3 N = texture(gNormalMap, TexCoords).rgb;
const vec4 ALBEDO_SPECULAR = texture(gAlbedoSpecularMap, TexCoords);
const vec4 LIGHT_SPACE_POS = gLightSpaceVP * vec4(P, 1.0f);
const vec3 LIGHT_SPACE_POS_POST_W = LIGHT_SPACE_POS.xyz / LIGHT_SPACE_POS.w * 0.5f + 0.5f;
const vec3 L = normalize(-gDirectLight._direction);
const float NoL = dot(N, L);
// Mie-scattering phase function approximated by the Henyey-Greenstein phase function
float calcScattering(float cosTheta)
{
return (1.0f - G * G) / (4.0f * PI * pow(1.0f + G * G - 2.0f * G * cosTheta, 1.5f));
}
float calcShadow()
{
if (LIGHT_SPACE_POS_POST_W.z > 1.0f)
{
return 0.0f;
}
float bias = max(0.05f * (1.0f - NoL), 0.005f);
float depth = texture(gShadowMap, LIGHT_SPACE_POS_POST_W.xy).r;
return LIGHT_SPACE_POS_POST_W.z - bias > depth ? 1.0f : 0.0f;
}
void main()
{
vec3 V = P - gViewPos;
float stepSize = length(V) / NUM_STEPS;
V = normalize(V);
vec3 step = V * stepSize;
vec3 position = gViewPos;
position += step * DITHER_PATTERN[int(TexCoords.x * SCREEN_WIDTH) % 4][int(TexCoords.y * SCREEN_HEIGHT) % 4];
vec3 volumetric = vec3(0.0f);
for (int i = 0; i < NUM_STEPS_INT; ++i)
{
vec4 lightSpacePos = gLightSpaceVP * vec4(position, 1.0f);
vec3 lightSpacePosPostW = lightSpacePos.xyz / lightSpacePos.w * 0.5f + 0.5f;
float depth = texture(gShadowMap, lightSpacePosPostW.xy).r;
if (depth > lightSpacePosPostW.z)
{
volumetric += calcScattering(dot(V, -L)) * gDirectLight._light._color;
}
position += step;
}
volumetric /= NUM_STEPS;
V = normalize(gViewPos - P);
vec3 diffuse = clamp(NoL, 0.0f, 1.0f) * gDirectLight._light._color * ALBEDO_SPECULAR.rgb;
vec3 H = normalize(L + V);
vec3 specular = pow(clamp(dot(N, H), 0.0f, 1.0f), SPECULAR_FACTOR) * gDirectLight._light._color * ALBEDO_SPECULAR.a;
float shadow = calcShadow();
if (shadow < 1.0f)
{
FragColor = vec4((1.0f - shadow) * (diffuse + specular) + volumetric, 1.0f);
}
else
{
FragColor = vec4(gAmbientFactor * ALBEDO_SPECULAR.rgb + volumetric, 1.0f);
}
}
The function is very simple, and what it tells us is that given a point on the raymarch, if it is visible from the light’s perspective, then we need to add a calibrated amount determined by the angle between V and L to the running total that serves as the amount of volumetric lighting on a given fragment. I chose to add a consistent amount for every point on the raymarch that was not in shadow.
What we’re adding for a given point that’s exposed to the light is driven by the Henyey-Greenstein phase function:
I went with a slightly different numerator in my implementation, but it’s worth testing different values of g and simplifying or reintegrating terms into our numerator to see what leads to the desired rendering effect. Such options can be exposed to artists as toggles or calibration bars.
So that was easy, but there are a few things I want to illustrate. Ignoring the dithering offset, which is a common strategy of introducing noise for dealing with anti-aliasing artifacts that result from insufficient sampling, a raymarch consisting of 100 steps is going to result in something that looks like this:
Now, that’s pretty good, but it’s always worth asking ourselves if it’s possible to achieve a similar effect using fewer steps in our raymarching. Let’s try 15:
That’s not quite what we had in mind. What if we were to reincorporate the Bayer matrix (i.e., DITHER_PATTERN) while maintaining the smaller number of raymarching steps:
Adding Filtering
That’s much better. I also ran a subsequent Gaussian blur, where the first pass uses the result from our lighting pass as an input. The second pass—the vertical-filtering pass—then operates using the result from the first blur and renders onto the default framebuffer object:
#version 460 core
out vec4 FragColor;
const float H_BLUR = 3.0f / 2460.0f; // Sample radius in texels
const float V_BLUR = 3.0f / 1440.0f;
in vec2 TexCoords;
uniform sampler2D gPreviousFrameMap;
uniform vec2 gDir;
void main()
{
vec4 sum = vec4(0.0f);
// 9-tap Gaussian filter
sum += texture(gPreviousFrameMap, vec2(TexCoords.x - 4.0f * H_BLUR * gDir.x, TexCoords.y - 4.0f * V_BLUR * gDir.y)) * 0.0162162162f;
sum += texture(gPreviousFrameMap, vec2(TexCoords.x - 3.0f * H_BLUR * gDir.x, TexCoords.y - 3.0f * V_BLUR * gDir.y)) * 0.0540540541f;
sum += texture(gPreviousFrameMap, vec2(TexCoords.x - 2.0f * H_BLUR * gDir.x, TexCoords.y - 2.0f * V_BLUR * gDir.y)) * 0.1216216216f;
sum += texture(gPreviousFrameMap, vec2(TexCoords.x - 1.0f * H_BLUR * gDir.x, TexCoords.y - 1.0f * V_BLUR * gDir.y)) * 0.1945945946f;
sum += texture(gPreviousFrameMap, TexCoords) * 0.2270270270f;
sum += texture(gPreviousFrameMap, vec2(TexCoords.x + 1.0f * H_BLUR * gDir.x, TexCoords.y + 1.0f * V_BLUR * gDir.y)) * 0.1945945946f;
sum += texture(gPreviousFrameMap, vec2(TexCoords.x + 2.0f * H_BLUR * gDir.x, TexCoords.y + 2.0f * V_BLUR * gDir.y)) * 0.1216216216f;
sum += texture(gPreviousFrameMap, vec2(TexCoords.x + 3.0f * H_BLUR * gDir.x, TexCoords.y + 3.0f * V_BLUR * gDir.y)) * 0.0540540541f;
sum += texture(gPreviousFrameMap, vec2(TexCoords.x + 4.0f * H_BLUR * gDir.x, TexCoords.y + 4.0f * V_BLUR * gDir.y)) * 0.0162162162f;
FragColor = vec4(sum.rgb, 1.0f);
}
void execBlurPasses(const phoenix::Shader& blurShader)
{
blurShader.use();
glBindFramebuffer(GL_FRAMEBUFFER, blurRenderTarget->_FBO);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
blurShader.setVec2(phoenix::G_DIR, glm::vec2(1.0f, 0.0f));
utils->renderQuad(blurShader, previousFrameMap);
glBindFramebuffer(GL_FRAMEBUFFER, 0);
blurShader.setVec2(phoenix::G_DIR, glm::vec2(0.0f, 1.0f));
utils->renderQuad(blurShader, blurRenderTarget->_textureID);
}
That’s definitely a nice softening of the dithering artifacts. Here’s another perspective in the case of the 100 samples:
I highly recommend checking out sections 3.5 and onward in GPU Pro 5 for the remainder of Vos’s work, which explains how to control the amount of scattering so that we can yield a dustier and smokier feel to the rather uniform appearance we have thus far.
Resources
GPU Pro 5
Alexandre Pestana’s Post on Volumetric Lights
Andrew Pham 