Source Code: Download the code
Video: Watch the video
Finally, I would like to present my instant radiosity application for the Cornell Box [10], which is based on the articles [1] and [2]. The environment of the scene consists of a white ceiling, a white floor, a white back wall, a red left wall, a green right wall, two equal sized white boxes and a point light source as a primary light source.
With GeForce GTX 680 graphics card, I manage to have more than 60 fps, where diffuse component of direct and indirect illumination including shadows are recomputed for each primary light source position update.
Computing direct lighting
Initially, geometry world space positions, normals and albedo are rendered into g-buffer, followed by shadow maps generation pass.
Shadows
Cube shadow maps are believed to be the standard solution for constructing shadows from a point light source. Since a cube texture is sampled with a vector, obtaining soft shadows with percentage closer filtering (PCF) is not that straightforward. Instead, I am using virtual shadow depth cube map approach [3]. According to the provided solution, the six faces of the cube map are rendered to six tiles within a single 2D depth texture (unwrapped cube map), which could be sampled with PCF. In my implementation the size of a shadow map is 1024x1024.
To handle filtering on the border of the tile, a small margin should be added to each tile. Moreover, while rendering the shadow map, field of view for the camera is taken more than 90 degrees [8].
On a Direct3D side, the virtual shadow cube map could be rendered in one pass using instancing mechanism in geometry shader and passing the output to the concrete tile identified by SV_ViewportArrayIndex semantic.
Now, we need to have an efficient way to access depth values from the unwrapped cube map for comparison in a shading pass, having a vector from the light center to the pixel on the object under processing. The authors in [3],[8] suggests using an indirection cube map, which is, basically, a cube texture, each face of which contains texture coordinates for redirection into a corresponding tile within the unwrapped cube map, taking into consideration tile borders for PCF.
The indirection cube map could be generated totally on a GPU side with the following steps:
- create a cube texture with format to store texture coordinates (u, v);
- set input layout to null and draw a triangle strip with 4 vertices defining the positions for the vertices of a cube face;
- using SV_VertexId semantic in the vertex shader calculate clip space position of the vertex and pass it to the geometry shader;
- using instancing mechanism in the geometry shader calculate texture coordinates associated with each of the vertex corresponding to the tile texture coordinates in unwrapped cube map;
- pass calculated texture coordinates as an attribute of the vertex to the pixel shader along with SV_RenderTargetArrayIndex semantic to identify a cube face index;
- in the pixel shader write received interpolated texture coordinates to the render target presenting a face of cube map.
Lighting
During a full screen triangle pass, we compute diffuse contribution with shadow intensity from direct lighting from the primary light source based on initially filled g-buffer content.
Direct lighting + direct shadows
Computing indirect lighting
Depositing virtual point lights
After the position of a primary light has been changed or we are doing this for the first time, virtual point lights have to be recalculated. In this implementation 256 vpls are employed per primary light source. To define direction of vpls, uniformly distributed sampling points on a unit sphere are computed. As soon as sampling points have been evaluated on the application side, they are passed to the dedicated compute shader stage where ray tracing with the scene takes place. Each executing thread, presenting a shooting ray, is responsible for finding the nearest object in the scene intersected by the ray. The new vpl is positioned on the point where the ray hits the geometry. Its color and direction are defined by the surface color and surface normal at the hit point. In the end, the obtained data is output to the unordered access view to be later used by indirect lighting and shadows render passes.
Shadows
Next, for each vpl paraboloid shadow map (512x512) is calculated covering a hemisphere [5],[6]. If polygons large with respect to the light source, distortion of edges during paraboloid projection can occur. To address that issue hardware tessellation stage is used. Currently, the scene is tessellated statically with inner and edge tessellation factors equal to 8. More appropriate solution would be to tessellate the geometry adaptively for each vpl, calculating the screen space area of a triangle in the patch constant function and then increasing tessellation factors according to the screen space size.
Instead of evaluating each vpl contribution on the whole g-buffer, the latter is split into 4x4 tiles. The tile presents low resolution version of the entire image. The result is stored in so-called split g-buffer, which contains split version of world space position and normal buffers. Normal buffer storage in the split g-buffer is depicted below.
World space normals
For each tile we assign approximately equal number of vpls and pixel shader pass is launched to compute diffuse intensity and shadow factor contributed by each of the assigned vpls to a given pixel in a tile.
Once the indirect lighting has been computed for each tile, the results are combined (gathered) into a single full-sized buffer.
Direct + indirect lighting
For post processing and shading passes, I am using full screen triangle approach described here [9], initially demonstrated in FXAA demo from NVidia SDK. It utilizes SV_VertexId semantic provided by the input assembler stage to generate clip space position and texture coordinates in vertex shader with binding no explicit vertex buffer with vertices data.
Interaction
Computed indirect lighting for each tile
Combined indirect lighting
After indirect lighting has been gathered a structured noise pattern (4x4) is visible because of different vpls sets for the tiles. To get rid of the artifacts, additional smooth pass is done with a geometry aware filter, taking into account the scene geometry [7]. In particular, the following filter could be used:
\(\Large filter(t)=\frac{\displaystyle\sum_{t_i\in K(t)}\omega(t,t_i)I(t_i)}{\displaystyle\sum_{t_i\in K(t)}\omega(t,t_i) }\),
where \(I(t_i)\) is a pixel value from the input image \(I\) in the rectangular neighborhood \(K(t)\) around a pixel location \(t\) and \(\omega(t,t_i)\) is a weighting function that produces weight for two pixel locations
\(t\) and \(t_i\) so that to avoid blurring across depth discontinuities or across strong normal changes.
Indirect lighting + indirect shadows after applying geometry aware filter
Computed indirect lighting is additively blended over already computed direct lighting.
Full screen triangle
For post processing and shading passes, I am using full screen triangle approach described here [9], initially demonstrated in FXAA demo from NVidia SDK. It utilizes SV_VertexId semantic provided by the input assembler stage to generate clip space position and texture coordinates in vertex shader with binding no explicit vertex buffer with vertices data.
Interaction
- F1 - turn on/off direct light
- F2 - turn on/off shadows from direct light
- F3 - turn on/off indirect light
- F4 - turn on/off shadows from indirect light
Current settings are displayed to the right side of the window title.
- Left/Right arrow - move the light to the left or right side
- Up/Down arrow - move the light forward or backward
- Ctrl + Up/Down arrow - move the light up or down
Added some more screen shots to have better observation of color bleeding
References
1.Hannu Saransaari, Samuli Laine, Janne Kontkanen, Jaakko Lehtinen, Timo Aila, "Incremental Instant Radiosity" in Shader X6: Advanced Rendering Techniques, 2008
2.Samuli Laine, Hannu Saransaari, Janne Kontkanen, Jaakko Lehtinen, Timo Aila, "Incremental Instant Radiosity for Real-Time Indirect Illumination" in Eurographics Symposium on Rendering, 2007
3.Gary King and William Newhall, "Efficient Omnidirectional Shadow Maps" in Wolfgang Engel. ShaderX 3: Advanced Rendering with DirectX and OpenGL, 2005
4.Alexender Keller and Wolfgang Heidrich, "Interleaved Sampling"
5.Stefan Brabec Thomas Annen Hans-Peter Seidel, "Shadow Mapping for Hemispherical and Omnidirectional Light Sources"
6.Jason Zink "Dual Paraboloid Mapping"
7.Elmar Eisemann, Michael Schwarz, Ulf Assarsson, Michael Wimmer. 2012. "Real-Time Shadows" pp. 344-347
8.NVIDIA Presentation "GPU Programming Exposed: The Naked Truth Behind NVIDIA's Demos" pp. 130-141
9.http://www.altdevblogaday.com/2011/08/08/interesting-vertex-shader-trick/
10.http://www.graphics.cornell.edu/online/box/
