Linearize depth

Question

In OpenGL you can linearize a depth value like so:

float linearize_depth(float d,float zNear,float zFar)
{
    float z_n = 2.0 * d - 1.0;
    return 2.0 * zNear * zFar / (zFar + zNear - z_n * (zFar - zNear));
}

(Source: https://stackoverflow.com/a/6657284/10011415)

However, Vulkan handles depth values somewhat differently (https://matthewwellings.com/blog/the-new-vulkan-coordinate-system/). I don't quite understand the math behind it, what changes would I have to make to the function to linearize a depth value with Vulkan?

Answer 1

The important difference between OpenGL and Vulkan here is that the normalized device coordinates (NDC) have a different range for z (the depth). In OpenGL it's -1 to 1 and in Vulkan it's 0 to 1.

However, in OpenGL when the depth is stored into a depth texture and you read from it, the value is further normalized to 0 to 1. This seems to be the case in your example, since the first line of your function maps it back to -1 to 1.

In Vulkan, your depth is always between 0 and 1, so the above function works in Vulkan as well. You can simplify it a bit though:

float linearize_depth(float d,float zNear,float zFar)
{
    return zNear * zFar / (zFar + d * (zNear - zFar));
}