Get Fov from ProjectionMatrix?

pcace · October 26, 2023, 1:40pm

Hi there,

i am trying to figure out how i would get the FOV from the projection Matrix from camera. but i cannot really get the right informations.
in the end i need to change the projectionMatrix so that it represents a bigger FOV.

what i have:

const babylonProjectionMatrix = camera.getProjectionMatrix(true).clone();

wich looks like:

{
    "0": -0.8108331561088562,
    "1": -0.42402830719947815,
    "2": -0.4034222960472107,
    "3": 0,
    "4": 0,
    "5": 0.6892840266227722,
    "6": -0.7244912385940552,
    "7": 0,
    "8": 0.5852773189544678,
    "9": -0.5874415636062622,
    "10": -0.5588943362236023,
    "11": 0,
    "12": -2744.837890625,
    "13": -814.970703125,
    "14": -511.23333740234375,
    "15": 1
}

this should represent a camera with a 45° FOV. what do i need to change or calculate so that it represents a for example 50° FOV?

i tried to use this logic here but it seems that the babylon matrix is not like openGL

Bildschirmfoto vom 2023-10-26 15-32-47

Any help would be awesome!

(i want to do this, because i am feeding the matrix into loaders.gl to receive tiling information from the actual camera perspective. but my virtual camera needs a little bigger fov)

pcace · October 26, 2023, 1:48pm

guess in the meantime i do this:

      const loadersCamera = camera.clone("loadersCam")
      loadersCamera.fov = camera.fov + 1

it does exactly what i need… Anyway. If someone could explain what i am doing here with the matrix it still would be very nice!!

Thanks a lot!

Evgeni_Popov · October 27, 2023, 11:11am

The best way is to look at how the matrix is computed:

github.com

BabylonJS/Babylon.js/blob/master/packages/dev/core/src/Maths/math.vector.ts#L7160-L7189


      
          public static PerspectiveFovLHToRef<T extends Matrix>(

              fov: number,

              aspect: number,

              znear: number,

              zfar: number,

              result: T,

              isVerticalFovFixed = true,

              halfZRange?: boolean,

              projectionPlaneTilt: number = 0,

              reverseDepthBufferMode: boolean = false

          ): T {

              const n = znear;

              const f = zfar;

          

              const t = 1.0 / Math.tan(fov * 0.5);

              const a = isVerticalFovFixed ? t / aspect : t;

              const b = isVerticalFovFixed ? t : t * aspect;

              const c = reverseDepthBufferMode && n === 0 ? -1 : f !== 0 ? (f + n) / (f - n) : 1;

              const d = reverseDepthBufferMode && n === 0 ? 2 * f : f !== 0 ? (-2.0 * f * n) / (f - n) : -2 * n;

              const rot = Math.tan(projectionPlaneTilt);

This file has been truncated. show original

The b variable is 1/tan(fov*0.5) (because by default isVerticalFovFixed==true), so by reading the 5th value of the matrix, you could easily deduce the fov value.