The magic of skybox reflections

Skyboxes and environment maps are for sure one of the more powerful tools for physically based rendering to give a scene a touch of realism. A skybox is essentially a cube map rendered onto a cube which we position in the background of our scene.

A cube map is a map of 6 textures, one for each internal side of a cube. A normal 2D texture is sampled using uv-coordinates, representing the "x" and "y" axes of the image. That is, each vertex is assigned a uv coordinate, from which a point on the texture is sampled in the fragment shader.

For cube maps, as they represent the inside of a cube, for convenience, there is no reason to apply uv-coordinates to sample the texture. Instead, one selects a point using a 3D vector, pointing from the center inside of the cube into any of the textured cube faces. This makes cube maps very handy for light calculations in 3D. Reflections are then mathematically very simple to create using a cube map, as we just have to calculate the reflection vector at each surface point, and then sample the cube map using this vector.



Calculating the intensity from the sky using cube map reflection in glsl fragment shader.


Left: Specular reflections in calm water. Middle: Cube map sampled reflections in calm water. Right: Cube map rendered onto sky box in background, reflections sampled from sky box in calm water.

As can be seen, adding skybox reflections creates a feeling that the water actually is water, even though we are simply just simulating its surface. However, one characteristic of water which is missing, causing the water not to look completely realistic, is refraction.

Refraction is the property causing light to scatter when travelling through mediums of different indices of refractions. So, in fact, when looking at water, we expect some of the light to come from reflections from the environment above water, however we also expect some of the light to come from the environment below the surface, which we can see is not true for any of the images above.

The amount of light coming from below and above the surface is calculated using the fresnel equations.

Fresnel equations for refractive indices. R_s and R_p represent the reflectance for s and p-polarized light. R_eff is their average used as effective reflectivity of the material. n1 and n2 are the refractive indices of the materials and theta i and t are the incident and refracted (transmitted) angles.


In the shader, I thus sample the cube map both in the refracted and reflected vector directions. The colors sampled are then interpolated using the effective reflective index.


The result looks more natural and gives a feeling that there is something below the surface of the water too. 



Left: Reflection and Refraction on water surface. Right: Reflection and no refraction on water surface. 


The texture used is not too realistic however, as we would probably not see the bottom of the ocean when that far away into the sea, as it would be too deep. Using a different texture can show the property of refraction in a more realistic setting.



Left: Reflection and refraction making the pebbles on the bottom of the water visible. Right: Perfect reflection making only the environment above sea level visible. 






Thanks to www.humus.name for providing free to use high resolution 3D cube maps.
https://www.humus.name/index.php?page=Textures

1. Scratch a pixel, Reflection, Refraction (Transmission) and Fresnel, URL: https://www.scratchapixel.com/lessons/3d-basic-rendering/introduction-to-shading/reflection-refraction-fresnel
 





Kommentarer

Skicka en kommentar

Populära inlägg i den här bloggen

Dear ImGui - Interactive settings for ocean water

Bild
The last crucial piece of the project implementation relates to GUI. It is tedious having to restart the application for testing different settings, and I wanted to be able to change the settings of the ocean in real time. Using a GUI I wanted the following settings to be modifiable in real time. For ocean: Wave length Amplitude Wind speed Wind direction Normal displacement amount  Vertex count Tile count For application: Camera movement speed Camera rotation speed Enable/disable wireframe mode Enable/disable skybox Enable/disable skybox lighting Selecting skybox cubemap A very convenient and handy tool for debugging graphics applications is Dear ImGui , or simply ImGui. Integrating ImGui is simple and it has an implementation agnostic interface for whichever window environment and graphics library you are using. When the ImGui library is linked properly to the application, dialogs and GUI utils are easily drawn to the screen by initializing an ImGui context. When a context is runn...
Läs mer

CUDA cuFFT vs FFTW

Bild
My initial thoughts were that I was going to perform FFT on the GPU as it intuitively sounds fast to use the multi-core system that the GPU provides. However, depending on the size of the FFT, GPU based algorithms may actually be outperformed by running FFT on the CPU. Transferring memory-buffers to the GPU is a slow operation, and the overhead of transferring data to the GPU does affect the overall performance of running FFT particularly. When using CUDA cuFFT compared to serial FFTW, it has been shown that for small N, approximately N <= 4096, the gain from running cuFFT is lost due to slow memory transfer rates. From lecture: "Fast Fourier Transforms (FFTs) and Graphical Processing Units (GPUs)" - Kate Despain, University of Maryland Institute for Advanced Computer Studies. Originally from University of Waterloo (2007). Comparing FFT and cuFFT including and excluding memory transfer rates. Y axis labeling flops, X axis labeling size of FFT work set.  In my project, ...
Läs mer

Gradients and Choppy waves.

Bild
As mentioned in the last post, the focus of the last days was to fix proper normal calculations using the gradient of the height-field. Gradient, together with creating a displacement in x and z-direction, only required setting up a four more cuda-buffers and performing an inverse FFT-pass on each of them. Calculating the gradient and the x-z displacement is easy, and comes from equation 20 and 29 in Tessendorf's paper, which you should be familiar with now. The input for calculating the x-gradient and z-gradient simply meant multiplying the input for the displacement map with the imaginary number ik, for each k where k is the propagation direction of the wave at each point. Formula for gradient calculation for realistic surface normals (Tessendorf 2001) Left: z-gradient normalized to range 0-1. Right:  z-gradient normalized to range 0-1 One problem that occurred when calculating the surface normals using the gradient values was that the result of the FFT is naturally rather small....
Läs mer