why doesn't convert_ndc have "2"?

[ronly2460]

While this issue #66 mentioned that BARF struggles to reconstruct in NDC, I could not train even NeRF using NDC.

This is the function to convert rays to ndc rays in camera.py

def convert_NDC(opt,center,ray,intr,near=1):
    # shift camera center (ray origins) to near plane (z=1)
    # (unlike conventional NDC, we assume the cameras are facing towards the +z direction)
    center = center+(near-center[...,2:])/ray[...,2:]*ray
    # projection
    cx,cy,cz = center.unbind(dim=-1) # [B,HW]
    rx,ry,rz = ray.unbind(dim=-1) # [B,HW]
    scale_x = intr[:,0,0]/intr[:,0,2] # [B]
    scale_y = intr[:,1,1]/intr[:,1,2] # [B]
    cnx = scale_x[:,None]*(cx/cz)
    cny = scale_y[:,None]*(cy/cz)
    cnz = 1-2*near/cz
    rnx = scale_x[:,None]*(rx/rz-cx/cz)
    rny = scale_y[:,None]*(ry/rz-cy/cz)
    rnz = 2*near/cz
    center_ndc = torch.stack([cnx,cny,cnz],dim=-1) # [B,HW,3]
    ray_ndc = torch.stack([rnx,rny,rnz],dim=-1) # [B,HW,3]
    return center_ndc,ray_ndc

Additionally, the function below is generating ndc rays in vanilla-nerf.

def ndc_rays(H, W, focal, near, rays_o, rays_d):
    # Shift ray origins to near plane
    t = -(near + rays_o[...,2]) / rays_d[...,2]
    rays_o = rays_o + t[...,None] * rays_d
    
    # Projection
    o0 = -1./(W/(2.*focal)) * rays_o[...,0] / rays_o[...,2]
    o1 = -1./(H/(2.*focal)) * rays_o[...,1] / rays_o[...,2]
    o2 = 1. + 2. * near / rays_o[...,2]

    d0 = -1./(W/(2.*focal)) * (rays_d[...,0]/rays_d[...,2] - rays_o[...,0]/rays_o[...,2])
    d1 = -1./(H/(2.*focal)) * (rays_d[...,1]/rays_d[...,2] - rays_o[...,1]/rays_o[...,2])
    d2 = -2. * near / rays_o[...,2]
    
    rays_o = torch.stack([o0,o1,o2], -1)
    rays_d = torch.stack([d0,d1,d2], -1)
    
    return rays_o, rays_d

When I compare two methods, 2 is not multiplied in scale_x and scale_y.

Could you tell me the reason?