content: # modified from https://github.com/Profactor/continuous-remeshing
  import torch
  import numpy as np
  import trimesh
  from typing import Tuple
  
  def to_numpy(*args):
      def convert(a):
          if isinstance(a,torch.Tensor):
              return a.detach().cpu().numpy()
          assert a is None or isinstance(a,np.ndarray)
          return a
      
      return convert(args[0]) if len(args)==1 else tuple(convert(a) for a in args)
  
  def laplacian(
          num_verts:int,
          edges: torch.Tensor #E,2
          ) -> torch.Tensor: #sparse V,V
      """create sparse Laplacian matrix"""
      V = num_verts
      E = edges.shape[0]
  
      #adjacency matrix,
      idx = torch.cat([edges, edges.fliplr()], dim=0).type(torch.long).T  # (2, 2*E)
      ones = torch.ones(2*E, dtype=torch.float32, device=edges.device)
      A = torch.sparse.FloatTensor(idx, ones, (V, V))
  
      #degree matrix
      deg = torch.sparse.sum(A, dim=1).to_dense()
      idx = torch.arange(V, device=edges.device)
      idx = torch.stack([idx, idx], dim=0)
      D = torch.sparse.FloatTensor(idx, deg, (V, V))
  
      return D - A
  
  def _translation(x, y, z, device):
      return torch.tensor([[1., 0, 0, x],
                      [0, 1, 0, y],
                      [0, 0, 1, z],
                      [0, 0, 0, 1]],device=device) #4,4
  
  def _projection(r, device, l=None, t=None, b=None, n=1.0, f=50.0, flip_y=True):
      """
          see https://blog.csdn.net/wodownload2/article/details/85069240/
      """
      if l is None:
          l = -r
      if t is None:
          t = r
      if b is None:
          b = -t
      p = torch.zeros([4,4],device=device)
      p[0,0] = 2*n/(r-l)
      p[0,2] = (r+l)/(r-l)
      p[1,1] = 2*n/(t-b) * (-1 if flip_y else 1)
      p[1,2] = (t+b)/(t-b)
      p[2,2] = -(f+n)/(f-n)
      p[2,3] = -(2*f*n)/(f-n)
      p[3,2] = -1
      return p #4,4
  
  def _orthographic(r, device, l=None, t=None, b=None, n=1.0, f=50.0, flip_y=True):
      if l is None:
          l = -r
      if t is None:
          t = r
      if b is None:
          b = -t
      o = torch.zeros([4,4],device=device)
      o[0,0] = 2/(r-l)
      o[0,3] = -(r+l)/(r-l)
      o[1,1] = 2/(t-b) * (-1 if flip_y else 1)
      o[1,3] = -(t+b)/(t-b)
      o[2,2] = -2/(f-n)
      o[2,3] = -(f+n)/(f-n)
      o[3,3] = 1
      return o #4,4
  
  def make_star_cameras(az_count,pol_count,distance:float=10.,r=None,image_size=[512,512],device='cuda'):
      if r is None:
          r = 1/distance
      A = az_count
      P = pol_count
      C = A * P
  
      phi = torch.arange(0,A) * (2*torch.pi/A)
      phi_rot = torch.eye(3,device=device)[None,None].expand(A,1,3,3).clone()
      phi_rot[:,0,2,2] = phi.cos()
      phi_rot[:,0,2,0] = -phi.sin()
      phi_rot[:,0,0,2] = phi.sin()
      phi_rot[:,0,0,0] = phi.cos()
      
      theta = torch.arange(1,P+1) * (torch.pi/(P+1)) - torch.pi/2
      theta_rot = torch.eye(3,device=device)[None,None].expand(1,P,3,3).clone()
      theta_rot[0,:,1,1] = theta.cos()
      theta_rot[0,:,1,2] = -theta.sin()
      theta_rot[0,:,2,1] = theta.sin()
      theta_rot[0,:,2,2] = theta.cos()
  
      mv = torch.empty((C,4,4), device=device)
      mv[:] = torch.eye(4, device=device)
      mv[:,:3,:3] = (theta_rot @ phi_rot).reshape(C,3,3)
      mv = _translation(0, 0, -distance, device) @ mv
  
      return mv, _projection(r,device)
  
  def make_star_cameras_orthographic(az_count,pol_count,distance:float=10.,r=None,image_size=[512,512],device='cuda'):
      mv, _ = make_star_cameras(az_count,pol_count,distance,r,image_size,device)
      if r is None:
          r = 1
      return mv, _orthographic(r,device)
  
  def make_sphere(level:int=2,radius=1.,device='cuda') -> Tuple[torch.Tensor,torch.Tensor]:
      sphere = trimesh.creation.icosphere(subdivisions=level, radius=1.0, color=None)
      vertices = torch.tensor(sphere.vertices, device=device, dtype=torch.float32) * radius
      faces = torch.tensor(sphere.faces, device=device, dtype=torch.long)
      return vertices,faces
  
  from pytorch3d.renderer import (
      FoVOrthographicCameras,
      look_at_view_transform,
  )
  
  def get_camera(R, T, focal_length=1 / (2**0.5)):
      focal_length = 1 / focal_length
      camera = FoVOrthographicCameras(device=R.device, R=R, T=T, min_x=-focal_length, max_x=focal_length, min_y=-focal_length, max_y=focal_length)
      return camera
  
  def make_star_cameras_orthographic_py3d(azim_list, device, focal=2/1.35, dist=1.1):
      R, T = look_at_view_transform(dist, 0, azim_list)
      focal_length = 1 / focal
      return FoVOrthographicCameras(device=R.device, R=R, T=T, min_x=-focal_length, max_x=focal_length, min_y=-focal_length, max_y=focal_length).to(device)
  