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'''
MIT License
Copyright (c) 2019 Shunsuke Saito, Zeng Huang, and Ryota Natsume
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
'''
import cv2
import numpy as np
from .glm import ortho
class Camera:
def __init__(self, width=1600, height=1200):
# Focal Length
# equivalent 50mm
focal = np.sqrt(width * width + height * height)
self.focal_x = focal
self.focal_y = focal
# Principal Point Offset
self.principal_x = width / 2
self.principal_y = height / 2
# Axis Skew
self.skew = 0
# Image Size
self.width = width
self.height = height
self.near = 1
self.far = 10
# Camera Center
self.eye = np.array([0, 0, -3.6])
self.center = np.array([0, 0, 0])
self.direction = np.array([0, 0, -1])
self.right = np.array([1, 0, 0])
self.up = np.array([0, 1, 0])
self.ortho_ratio = None
def sanity_check(self):
self.center = self.center.reshape([-1])
self.direction = self.direction.reshape([-1])
self.right = self.right.reshape([-1])
self.up = self.up.reshape([-1])
assert len(self.center) == 3
assert len(self.direction) == 3
assert len(self.right) == 3
assert len(self.up) == 3
@staticmethod
def normalize_vector(v):
v_norm = np.linalg.norm(v)
return v if v_norm == 0 else v / v_norm
def get_real_z_value(self, z):
z_near = self.near
z_far = self.far
z_n = 2.0 * z - 1.0
z_e = 2.0 * z_near * z_far / (z_far + z_near - z_n * (z_far - z_near))
return z_e
def get_rotation_matrix(self):
rot_mat = np.eye(3)
d = self.eye - self.center
d = -self.normalize_vector(d)
u = self.up
self.right = -np.cross(u, d)
u = np.cross(d, self.right)
rot_mat[0, :] = self.right
rot_mat[1, :] = u
rot_mat[2, :] = d
# s = self.right
# s = self.normalize_vector(s)
# rot_mat[0, :] = s
# u = self.up
# u = self.normalize_vector(u)
# rot_mat[1, :] = -u
# rot_mat[2, :] = self.normalize_vector(self.direction)
return rot_mat
def get_translation_vector(self):
rot_mat = self.get_rotation_matrix()
trans = -np.dot(rot_mat.T, self.eye)
return trans
def get_intrinsic_matrix(self):
int_mat = np.eye(3)
int_mat[0, 0] = self.focal_x
int_mat[1, 1] = self.focal_y
int_mat[0, 1] = self.skew
int_mat[0, 2] = self.principal_x
int_mat[1, 2] = self.principal_y
return int_mat
def get_projection_matrix(self):
ext_mat = self.get_extrinsic_matrix()
int_mat = self.get_intrinsic_matrix()
return np.matmul(int_mat, ext_mat)
def get_extrinsic_matrix(self):
rot_mat = self.get_rotation_matrix()
int_mat = self.get_intrinsic_matrix()
trans = self.get_translation_vector()
extrinsic = np.eye(4)
extrinsic[:3, :3] = rot_mat
extrinsic[:3, 3] = trans
return extrinsic[:3, :]
def set_rotation_matrix(self, rot_mat):
self.direction = rot_mat[2, :]
self.up = -rot_mat[1, :]
self.right = rot_mat[0, :]
def set_intrinsic_matrix(self, int_mat):
self.focal_x = int_mat[0, 0]
self.focal_y = int_mat[1, 1]
self.skew = int_mat[0, 1]
self.principal_x = int_mat[0, 2]
self.principal_y = int_mat[1, 2]
def set_projection_matrix(self, proj_mat):
res = cv2.decomposeProjectionMatrix(proj_mat)
int_mat, rot_mat, camera_center_homo = res[0], res[1], res[2]
camera_center = camera_center_homo[0:3] / camera_center_homo[3]
camera_center = camera_center.reshape(-1)
int_mat = int_mat / int_mat[2][2]
self.set_intrinsic_matrix(int_mat)
self.set_rotation_matrix(rot_mat)
self.center = camera_center
self.sanity_check()
def get_gl_matrix(self):
z_near = self.near
z_far = self.far
rot_mat = self.get_rotation_matrix()
int_mat = self.get_intrinsic_matrix()
trans = self.get_translation_vector()
extrinsic = np.eye(4)
extrinsic[:3, :3] = rot_mat
extrinsic[:3, 3] = trans
axis_adj = np.eye(4)
axis_adj[2, 2] = -1
axis_adj[1, 1] = -1
model_view = np.matmul(axis_adj, extrinsic)
projective = np.zeros([4, 4])
projective[:2, :2] = int_mat[:2, :2]
projective[:2, 2:3] = -int_mat[:2, 2:3]
projective[3, 2] = -1
projective[2, 2] = (z_near + z_far)
projective[2, 3] = (z_near * z_far)
if self.ortho_ratio is None:
ndc = ortho(0, self.width, 0, self.height, z_near, z_far)
perspective = np.matmul(ndc, projective)
else:
perspective = ortho(-self.width * self.ortho_ratio / 2, self.width * self.ortho_ratio / 2,
-self.height * self.ortho_ratio / 2, self.height * self.ortho_ratio / 2,
z_near, z_far)
return perspective, model_view
def KRT_from_P(proj_mat, normalize_K=True):
res = cv2.decomposeProjectionMatrix(proj_mat)
K, Rot, camera_center_homog = res[0], res[1], res[2]
camera_center = camera_center_homog[0:3] / camera_center_homog[3]
trans = -Rot.dot(camera_center)
if normalize_K:
K = K / K[2][2]
return K, Rot, trans
def MVP_from_P(proj_mat, width, height, near=0.1, far=10000):
'''
Convert OpenCV camera calibration matrix to OpenGL projection and model view matrix
:param proj_mat: OpenCV camera projeciton matrix
:param width: Image width
:param height: Image height
:param near: Z near value
:param far: Z far value
:return: OpenGL projection matrix and model view matrix
'''
res = cv2.decomposeProjectionMatrix(proj_mat)
K, Rot, camera_center_homog = res[0], res[1], res[2]
camera_center = camera_center_homog[0:3] / camera_center_homog[3]
trans = -Rot.dot(camera_center)
K = K / K[2][2]
extrinsic = np.eye(4)
extrinsic[:3, :3] = Rot
extrinsic[:3, 3:4] = trans
axis_adj = np.eye(4)
axis_adj[2, 2] = -1
axis_adj[1, 1] = -1
model_view = np.matmul(axis_adj, extrinsic)
zFar = far
zNear = near
projective = np.zeros([4, 4])
projective[:2, :2] = K[:2, :2]
projective[:2, 2:3] = -K[:2, 2:3]
projective[3, 2] = -1
projective[2, 2] = (zNear + zFar)
projective[2, 3] = (zNear * zFar)
ndc = ortho(0, width, 0, height, zNear, zFar)
perspective = np.matmul(ndc, projective)
return perspective, model_view
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