Continuous Laplacian

def sample_pts(x, delta): 
""" Given points X sample points that are shifted by delta in axis aligned directions """
  points = torch.stack(
      [
          x + torch.as_tensor([delta, 0.0, 0.0]).to(x),
          x + torch.as_tensor([-delta, 0.0, 0.0]).to(x),
          x + torch.as_tensor([0.0, delta, 0.0]).to(x),
          x + torch.as_tensor([0.0, -delta, 0.0]).to(x),
          x + torch.as_tensor([0.0, 0.0, delta]).to(x),
          x + torch.as_tensor([0.0, 0.0, -delta]).to(x),
          x
      ],
      dim=0,
  )
  return points
  
  def get_grad_and_lapl(sampled_points_sdf, delta):
   """ Given SDF values for points sampled by sample_pts(...) function compute Laplacian """
   
    gradients = torch.stack(
        [
            0.5 * (points_sdf[0] - points_sdf[1]) / delta,
            0.5 * (points_sdf[2] - points_sdf[3]) / delta,
            0.5 * (points_sdf[4] - points_sdf[5]) / delta,
        ],
        dim=-1,
    )

      hessian = torch.stack(
          [
              (points_sdf[0] + points_sdf[1] - 2 * points_sdf[-1]) / delta**2,
              (points_sdf[2] + points_sdf[3] - 2 * points_sdf[-1]) / delta**2,
              (points_sdf[4] + points_sdf[5] - 2 * points_sdf[-1]) / delta**2,
          ],
          dim=-1,
      )
      lapl = hessian.sum(dim=-1)**2

    return gradients, lapl