我正在尝试在给定虚幻引擎4中的3D世界坐标的情况下获取图像平面上的2D坐标。
世界坐标系为 x(从右向左增加(、y(从屏幕外到内增加(、z(从下到上增加(
我想要的图像坐标系是左下角的原点和x(从左到右增加(，y(从下到上增加(
我设置了我的相机内在和外在，如下所示，而相机位于
(-474.9739990234375, -67.140998840332031, 128.10400390625)
它的旋转是
(0, 0.80071002244949341, 99.797645568847656)
与世界坐标的起源有关。
import numpy as np
fov = 69.4
width = 1920.0
height = 1080.0
aspect_ratio = width / height
fx = width / (2 * np.tan(fov * np.pi / 2 / 180))
fy = height / (2 * np.tan(fov / aspect_ratio / 2 / 180 * np.pi))
intrinsic = [[-fx, 0, width / 2], [0, fy, height / 2], [0 , 0, 1]]
pitch = 0.80071002244949341 * np.pi / 180
yaw = 99.797645568847656 * np.pi / 180
roll = 0 * np.pi / 180
ry = [[np.cos(pitch), 0, np.sin(pitch)], [0, 1, 0], [-np.sin(pitch), 0, np.cos(pitch)]]
rx = [[1, 0, 0], [0, np.cos(roll), -np.sin(roll)], [0, np.sin(roll), np.cos(roll)]]
rz = [[np.cos(yaw), -np.sin(yaw), 0], [np.sin(yaw), np.cos(yaw), 0], [0, 0, 1]]
rotation_matrix = np.matmul(np.matmul(rx, ry), rz)
translation_matrix = np.array([[-474.9739990234375, -67.140998840332031, 128.10400390625]])
extrinsic = np.concatenate([rotation_matrix, translation_matrix.T], axis=1)
extrinsic = np.concatenate([extrinsic, np.array([[0, 0, 0, 1]])], axis=0)
extrinsic = np.linalg.inv(extrinsic)
extrinsic = extrinsic[:3]
print(extrinsic)
假设我在场景中有一个对象，该对象也在摄像机视图中。它的坐标是
[-582.88897705078125, 143.63600158691406, 88.338996887207031]
使用下面的代码，我应该得到图像平面上 3D 点的投影。
world_coordinate = np.array([[-582.88897705078125, 143.63600158691406, 88.338996887207031, 1]])
camera_coordinate = np.dot(extrinsic, world_coordinate.T)
print(camera_coordinate)
camera_coordinate[0] *= 1
tmp = camera_coordinate[1].copy()
camera_coordinate[1] = camera_coordinate[2]
camera_coordinate[2] = tmp
print(camera_coordinate)
image_coordinate = np.dot(intrinsic, camera_coordinate)
image_coordinate /= image_coordinate[2]
print(image_coordinate)
但我得到了
[[-3.52097326e+03]
[-3.59180874e+02]
[ 1.00000000e+00]]
它不在于图像平面上。我该如何解决这个问题？
事实证明这是一个
错误。实际世界坐标系为x(从屏幕外到内增加(，y(从左到右增加(，z(从下到上增加(。
只需将项目将 yz 平面映射到图像空间，然后就完成了。