def intersect_sphere(ray_o, ray_d): ''' ray_o, ray_d: [..., 3] compute the depth of the intersection point between this ray and unit sphere '''

note: d1 becomes negative if this mid point is behind camera

d1 = -torch.sum(ray_d * ray_o, dim=-1) / torch.sum(ray_d * ray_d, dim=-1)
p = ray_o + d1.unsqueeze(-1) * ray_d
# consider the case where the ray does not intersect the sphere
ray_d_cos = 1. / torch.norm(ray_d, dim=-1)
p_norm_sq = torch.sum(p * p, dim=-1)
if (p_norm_sq >= 1.).any():
    raise Exception('Not all your cameras are bounded by the unit sphere; please make sure the cameras are normalized properly!')
d2 = torch.sqrt(1. - p_norm_sq) * ray_d_cos

return d1 + d2

Kai-46 / nerfplusplus

How to understand the intersect_sphere in your code? #18

note: d1 becomes negative if this mid point is behind camera