render_utils/lib/utils/graphics_utils.py

#
# Copyright (C) 2023, Inria
# GRAPHDECO research group, https://team.inria.fr/graphdeco
# All rights reserved.
#
# This software is free for non-commercial, research and evaluation use 
# under the terms of the LICENSE.md file.
#
# For inquiries contact  george.drettakis@inria.fr
#

import torch
import math
import numpy as np
from typing import NamedTuple

class BasicPointCloud(NamedTuple):
    points : np.array
    colors : np.array
    normals : np.array

def geom_transform_points(points, transf_matrix):
    P, _ = points.shape
    ones = torch.ones(P, 1, dtype=points.dtype, device=points.device)
    points_hom = torch.cat([points, ones], dim=1)
    points_out = torch.matmul(points_hom, transf_matrix.unsqueeze(0))

    denom = points_out[..., 3:] + 0.0000001
    return (points_out[..., :3] / denom).squeeze(dim=0)

def getWorld2View(R, t):
    Rt = np.zeros((4, 4))
    Rt[:3, :3] = R.transpose()
    Rt[:3, 3] = t
    Rt[3, 3] = 1.0
    return np.float32(Rt)

def getWorld2View2(R, t, translate=np.array([.0, .0, .0]), scale=1.0):
    Rt = np.zeros((4, 4))
    Rt[:3, :3] = R.transpose()
    Rt[:3, 3] = t
    Rt[3, 3] = 1.0

    C2W = np.linalg.inv(Rt)
    cam_center = C2W[:3, 3]
    cam_center = (cam_center + translate) * scale
    C2W[:3, 3] = cam_center
    Rt = np.linalg.inv(C2W)
    return np.float32(Rt)

def getProjectionMatrix(znear, zfar, fovX, fovY, K = None, img_h = None, img_w = None):
    if K is None:
        tanHalfFovY = math.tan((fovY / 2))
        tanHalfFovX = math.tan((fovX / 2))
        top = tanHalfFovY * znear
        bottom = -top
        right = tanHalfFovX * znear
        left = -right
    else:
        near_fx = znear / K[0, 0]
        near_fy = znear / K[1, 1]

        left = - (img_w - K[0, 2]) * near_fx
        right = K[0, 2] * near_fx
        bottom = (K[1, 2] - img_h) * near_fy
        top = K[1, 2] * near_fy

    P = torch.zeros(4, 4)

    z_sign = 1.0

    P[0, 0] = 2.0 * znear / (right - left)
    P[1, 1] = 2.0 * znear / (top - bottom)
    P[0, 2] = (right + left) / (right - left)
    P[1, 2] = (top + bottom) / (top - bottom)
    P[3, 2] = z_sign
    P[2, 2] = z_sign * zfar / (zfar - znear)
    P[2, 3] = -(zfar * znear) / (zfar - znear)
    return P

def fov2focal(fov, pixels):
    return pixels / (2 * math.tan(fov / 2))

def focal2fov(focal, pixels):
    return 2*math.atan(pixels/(2*focal))


def _so3_exp_map(
    log_rot: torch.Tensor, eps: float = 0.0001
):
    """
    A helper function that computes the so3 exponential map and,
    apart from the rotation matrix, also returns intermediate variables
    that can be re-used in other functions.
    """

    def hat(v: torch.Tensor) -> torch.Tensor:
        """
        Compute the Hat operator [1] of a batch of 3D vectors.

        Args:
            v: Batch of vectors of shape `(minibatch , 3)`.

        Returns:
            Batch of skew-symmetric matrices of shape
            `(minibatch, 3 , 3)` where each matrix is of the form:
                `[    0  -v_z   v_y ]
                 [  v_z     0  -v_x ]
                 [ -v_y   v_x     0 ]`

        Raises:
            ValueError if `v` is of incorrect shape.

        [1] https://en.wikipedia.org/wiki/Hat_operator
        """

        N, dim = v.shape
        if dim != 3:
            raise ValueError("Input vectors have to be 3-dimensional.")

        h = torch.zeros((N, 3, 3), dtype=v.dtype, device=v.device)

        x, y, z = v.unbind(1)

        h[:, 0, 1] = -z
        h[:, 0, 2] = y
        h[:, 1, 0] = z
        h[:, 1, 2] = -x
        h[:, 2, 0] = -y
        h[:, 2, 1] = x

        return h

    _, dim = log_rot.shape
    if dim != 3:
        raise ValueError("Input tensor shape has to be Nx3.")

    nrms = (log_rot * log_rot).sum(1)
    # phis ... rotation angles
    rot_angles = torch.clamp(nrms, eps).sqrt()
    rot_angles_inv = 1.0 / rot_angles
    fac1 = rot_angles_inv * rot_angles.sin()
    fac2 = rot_angles_inv * rot_angles_inv * (1.0 - rot_angles.cos())
    skews = hat(log_rot)
    skews_square = torch.bmm(skews, skews)

    R = (
        # pyre-fixme[16]: `float` has no attribute `__getitem__`.
        fac1[:, None, None] * skews
        + fac2[:, None, None] * skews_square
        + torch.eye(3, dtype=log_rot.dtype, device=log_rot.device)[None]
    )

    return R, rot_angles, skews, skews_square


def so3_exp_map(log_rot: torch.Tensor, eps: float = 0.0001) -> torch.Tensor:
    """
    Convert a batch of logarithmic representations of rotation matrices `log_rot`
    to a batch of 3x3 rotation matrices using Rodrigues formula [1].

    In the logarithmic representation, each rotation matrix is represented as
    a 3-dimensional vector (`log_rot`) who's l2-norm and direction correspond
    to the magnitude of the rotation angle and the axis of rotation respectively.

    The conversion has a singularity around `log(R) = 0`
    which is handled by clamping controlled with the `eps` argument.

    Args:
        log_rot: Batch of vectors of shape `(minibatch, 3)`.
        eps: A float constant handling the conversion singularity.

    Returns:
        Batch of rotation matrices of shape `(minibatch, 3, 3)`.

    Raises:
        ValueError if `log_rot` is of incorrect shape.

    [1] https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
    """
    return _so3_exp_map(log_rot, eps=eps)[0]