View Frustum Culling Quad - webgl

Question

I'am trying to apply view frustum culling to my scene.
I basically have this setup:
Rendering one quad displayed as Quadtree
For example if depth is 1 then the quad gets split into 4 smaller quads
Each quad has a texture
I have a first person camera, which means I can only look around but not move (the orogin of my camera is always at (0,0,0))
The Quad at depth 1 looks like this:
1---2
3---4
Where quad 1 represents the nw quadrant of the quadtree, quad 2 the ne quadrant of the quadtree and so on.
My goal is (for example depth 1) that whenever I move my camera and for example quad 1 and 3 are not visible anymore, they should not be rendered anymore.
However my current implementation is not correct. I'am extracting the frustumplanes like this and I think this the error.
createFrustumPlanes(vp) {
let leftPlane = vec4.fromValues(vp[0] + vp[3], vp[4] + vp[7], vp[8] + vp[11], vp[12] + vp[15]);
vec4.normalize(leftPlane, leftPlane);
let rightPlane = vec4.fromValues(-vp[0] + vp[3], -vp[4] + vp[7], -vp[8] + vp[11], -vp[12] + vp[15]);
vec4.normalize(rightPlane, rightPlane);
let bottomPlane = vec4.fromValues(vp[1] + vp[3], vp[5] + vp[7], vp[9] + vp[11], vp[13] + vp[15]);
vec4.normalize(bottomPlane, bottomPlane);
let topPlane = vec4.fromValues(-vp[1] + vp[3], -vp[5] + vp[7], -vp[9] + vp[11], -vp[13] + vp[15]);
vec4.normalize(topPlane, topPlane);
let nearPlane = vec4.fromValues(vp[2] + vp[3], vp[6] + vp[7], vp[10] + vp[11], vp[14] + vp[15]);
vec4.normalize(nearPlane, nearPlane);
let farPlane = vec4.fromValues(-vp[2] + vp[3], -vp[6] + vp[7], -vp[10] + vp[11], -vp[14] + vp[15]);
vec4.normalize(farPlane, farPlane);
return [
leftPlane,
rightPlane,
bottomPlane,
topPlane,
nearPlane,
farPlane
];
}
Where vp is the following this._vpMatrix:
this._lookAtMatrix = mat4.create();
mat4.lookAt(this._lookAtMatrix, vec3.fromValues(0, 0, 0), this._lookAtVector, vec3.fromValues(0, 1, 0));
this._projectionMatrix = mat4.create();
mat4.perspective(this._projectionMatrix, this._FOV * Math.PI / 180.0, this._width / this._height, 0.001, 50);
this._vpMatrix = mat4.create();
mat4.multiply(this._vpMatrix, this._projectionMatrix, this._lookAtMatrix);
How are you extracting frustum planes and from which matrix are the planes created?