cam_utils.py

import numpy as np
from scipy.spatial.transform import Rotation as R

import torch

def dot(x, y):
    if isinstance(x, np.ndarray):
        return np.sum(x * y, -1, keepdims=True)
    else:
        return torch.sum(x * y, -1, keepdim=True)


def length(x, eps=1e-20):
    if isinstance(x, np.ndarray):
        return np.sqrt(np.maximum(np.sum(x * x, axis=-1, keepdims=True), eps))
    else:
        return torch.sqrt(torch.clamp(dot(x, x), min=eps))


def safe_normalize(x, eps=1e-20):
    return x / length(x, eps)


def look_at(campos, target, opengl=True):
    # campos: [N, 3], camera/eye position
    # target: [N, 3], object to look at
    # return: [N, 3, 3], rotation matrix
    if not opengl:
        # camera forward aligns with -z
        forward_vector = safe_normalize(target - campos)
        up_vector = np.array([0, 1, 0], dtype=np.float32)
        right_vector = safe_normalize(np.cross(forward_vector, up_vector))
        up_vector = safe_normalize(np.cross(right_vector, forward_vector))
    else:
        # camera forward aligns with +z
        forward_vector = safe_normalize(campos - target)
        up_vector = np.array([0, 1, 0], dtype=np.float32)
        right_vector = safe_normalize(np.cross(up_vector, forward_vector))
        up_vector = safe_normalize(np.cross(forward_vector, right_vector))
    R = np.stack([right_vector, up_vector, forward_vector], axis=1)
    return R


# elevation & azimuth to pose (cam2world) matrix
def orbit_camera(elevation, azimuth, radius=1, is_degree=True, target=None, opengl=True):
    # radius: scalar
    # elevation: scalar, in (-90, 90), from +y to -y is (-90, 90)
    # azimuth: scalar, in (-180, 180), from +z to +x is (0, 90)
    # return: [4, 4], camera pose matrix
    if is_degree:
        elevation = np.deg2rad(elevation)
        azimuth = np.deg2rad(azimuth)
    x = radius * np.cos(elevation) * np.sin(azimuth)
    y = - radius * np.sin(elevation)
    z = radius * np.cos(elevation) * np.cos(azimuth)
    if target is None:
        target = np.zeros([3], dtype=np.float32)
    campos = np.array([x, y, z]) + target  # [3]
    T = np.eye(4, dtype=np.float32)
    T[:3, :3] = look_at(campos, target, opengl)
    T[:3, 3] = campos
    return T


class OrbitCamera:
    def __init__(self, W, H, r=2, fovy=60, near=0.01, far=100):
        self.W = W
        self.H = H
        self.radius = r  # camera distance from center
        self.fovy = np.deg2rad(fovy)  # deg 2 rad
        self.near = near
        self.far = far
        self.center = np.array([0, 0, 0], dtype=np.float32)  # look at this point
        # self.rot = R.from_matrix(np.eye(3))
        self.rot = R.from_matrix(np.array([[1., 0., 0.,],
                                           [0., 0., -1.],
                                           [0., 1., 0.]]))
        self.up = np.array([0, 1, 0], dtype=np.float32)  # need to be normalized!
        self.side = np.array([1, 0, 0], dtype=np.float32)

    @property
    def fovx(self):
        return 2 * np.arctan(np.tan(self.fovy / 2) * self.W / self.H)

    @property
    def campos(self):
        return self.pose[:3, 3]

    # pose (c2w)
    @property
    def pose(self):
        # first move camera to radius
        res = np.eye(4, dtype=np.float32)
        res[2, 3] = self.radius  # opengl convention...
        # rotate
        rot = np.eye(4, dtype=np.float32)
        rot[:3, :3] = self.rot.as_matrix()
        res = rot @ res
        # translate
        res[:3, 3] -= self.center
        return res

    # view (w2c)
    @property
    def view(self):
        return np.linalg.inv(self.pose)

    # projection (perspective)
    @property
    def perspective(self):
        y = np.tan(self.fovy / 2)
        aspect = self.W / self.H
        return np.array(
            [
                [1 / (y * aspect), 0, 0, 0],
                [0, -1 / y, 0, 0],
                [
                    0,
                    0,
                    -(self.far + self.near) / (self.far - self.near),
                    -(2 * self.far * self.near) / (self.far - self.near),
                ],
                [0, 0, -1, 0],
            ],
            dtype=np.float32,
        )

    # intrinsics
    @property
    def intrinsics(self):
        focal = self.H / (2 * np.tan(self.fovy / 2))
        return np.array([focal, focal, self.W // 2, self.H // 2], dtype=np.float32)

    @property
    def mvp(self):
        return self.perspective @ np.linalg.inv(self.pose)  # [4, 4]

    def orbit(self, dx, dy):
        # rotate along camera up/side axis!
        side = self.rot.as_matrix()[:3, 0]
        up = self.rot.as_matrix()[:3, 1]
        rotvec_x = up * np.radians(-0.05 * dx)
        rotvec_y = side * np.radians(-0.05 * dy)
        self.rot = R.from_rotvec(rotvec_x) * R.from_rotvec(rotvec_y) * self.rot

    def scale(self, delta):
        self.radius *= 1.1 ** (-delta)

    def pan(self, dx, dy, dz=0):
        # pan in camera coordinate system (careful on the sensitivity!)
        self.center += 0.0001 * self.rot.as_matrix()[:3, :3] @ np.array([-dx, -dy, dz])