mesh_reconstruction/func.py

# 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