How does latitude and longitude translate into PTZ coordinates for the camera?

You can use the pyproj library to convert the latitude and longitude coordinates to camera PTZ coordinates as follows:

1. install the pyproj library, which can be installed using the pip command: pip install pyproj.
2. uses the pyproj.transform() function to convert the latitude and longitude coordinates to camera PTZ coordinates, where the first parameter is the input latitude and longitude coordinates and the second parameter is the output camera PTZ coordinates.
3. uses pyproj.transform() function to send the output camera PTZ coordinates to the camera to realize the camera positioning and tracking function.

The following answer is based on ChatGPT and GISer Liu:
Here is Python code that converts latitude and longitude into camera PTZ coordinates and tracks it. These include comments, which can be run and implemented directly.

import cv2
import math

# 摄像头参数
height = 2.5  # 安装高度（米）
angle = math.pi / 4  # 安装角度（弧度）
zoom = 1  # 焦距

# 目标坐标（模拟数据）
longitude = 116.404556  # 经度
latitude = 39.915599  # 纬度
altitude = 0  # 海拔高度（米）

# 将经纬度转换为ENU坐标系下的点
def geo_to_enu(longitude, latitude, altitude):
    # 地球半径
    earth_radius = 6378137.0
    # WGS84椭球参数
    e = 0.081819190842622
    a = 6378137.0
    # 弧度制的经纬度和高度
    rad_lat = latitude * math.pi / 180.0
    rad_lon = longitude * math.pi / 180.0
    N = earth_radius / math.sqrt(1 - e ** 2 * math.sin(rad_lat) ** 2)
    x = (N + altitude) * math.cos(rad_lat) * math.cos(rad_lon)
    y = (N + altitude) * math.cos(rad_lat) * math.sin(rad_lon)
    z = (N * (1 - e ** 2) + altitude) * math.sin(rad_lat)
    return x, y, z

# 将ENU坐标系下的点转换为PTZ坐标
def enu_to_ptz(x, y, z, height, angle, zoom):
    # 摄像头水平距离
    d = math.sqrt(x ** 2 + y ** 2)
    # 偏航角
    pan = math.atan2(y, x)
    # 俯仰角
    tilt = math.atan2(z, d - height) - angle
    # 距离
    dist = math.sqrt(d ** 2 + (z - height) ** 2)
    # 缩放比例
    scale = zoom / dist
    # 返回PTZ坐标
    return pan, tilt, scale

# 创建摄像头
camera = cv2.VideoCapture(0)

# 循环处理每一帧图像
while True:
    # 读取一帧图像
    ret, frame = camera.read()
    if not ret:
        break

    # 将图像大小缩小一半，加快处理速度
    frame = cv2.resize(frame, (0, 0), fx=0.5, fy=0.5)

    # 将经纬度转换为ENU坐标系下的点
    x, y, z = geo_to_enu(longitude, latitude, altitude)

    # 将ENU坐标系下的点转换为PTZ坐标
    pan, tilt, scale = enu_to_ptz(x, y, z, height, angle, zoom)

    # 控制云台转动
    # 通过串口或网络将PTZ坐标发送给云台控制器，控制云台的转动

To realize the positioning and tracking of the camera head according to latitude and longitude, the longitude and latitude need to be converted to the PTZ coordinates of the camera. This transformation involves several parameters and formulas, which need to be calculated according to the model and brand of camera. Here are some common conversion methods and formulas.

Cartesian coordinate system conversion
converts latitude and longitude to cartesian coordinates, and then convert the cartesian coordinates to PTZ coordinates. This transformation takes into account factors such as the ellipsoid shape and height of the Earth and can be calculated using open source libraries such as Proj4 or GeoTools.

Calculate the camera's distance and azimuth from the target in terms of latitude, longitude and altitude
In this method, first calculate the camera's distance and azimuth from the target in terms of latitude, longitude and altitude, then calculate the PTZ coordinates in terms of distance and azimuth. This calculation needs to consider the installation height of the camera, field Angle and other factors, which can be calculated using the following formula:

// 计算两点间距离
distance = 6371004 * arccos(cos(rad(90-lat1)) * cos(rad(90-lat2)) + sin(rad(90-lat1)) * sin(rad(90-lat2)) * cos(rad(lng1-lng2)));

// 计算两点间方位角
azimuth = rad2deg(atan2(sin(rad(lng2-lng1)) * cos(rad(lat2)), cos(rad(lat1)) * sin(rad(lat2)) - sin(rad(lat1)) * cos(rad(lat2)) * cos(rad(lng2-lng1))));

// 根据距离和方位角计算 PTZ 坐标
x = distance * sin(rad(azimuth));
y = distance * cos(rad(azimuth));
z = height;

where, lat1 and lng1 represent the latitude and longitude of the camera; lat2 and lng2 represent the latitude and longitude of the target; height represents the mounting height of the camera; distance represents the distance between the camera and the target; azimuth represents the azimuth of the camera and the target; x, y and z respectively represent x, y and z coordinate values in PTZ coordinates.

Calculate the camera's elevation and horizontal Angle from latitude and longitude
In this method, first calculate the camera's elevation and horizontal Angle from latitude and longitude, then calculate the PTZ coordinates from elevation and horizontal Angle. This calculation needs to consider the camera's field of view Angle, horizontal rotation Angle, elevation rotation Angle and other factors, which can be calculated using the following formula:

// 计算相机与目标间的距离
distance = 6371004 * arccos(cos(rad(90-lat1)) * cos(rad

To convert the latitude and longitude to the PTZ coordinates of the camera, you need to consider the following:

Camera mounting height and Angle
Location and altitude of the object on Earth
Earth geometry
You can use the geopy and geographiclib libraries in Python to calculate latitude and longitude and distance, as well as spherical trigonometry formulas to calculate PTZ coordinates.

Here is an example code that takes the latitude, longitude, and altitude of the camera and the target as input, and calculates the pitch Angle, horizontal rotation Angle, and focal length:

from geographiclib.geodesic import Geodesic
from geopy.distance import geodesic
from math import atan2, degrees, radians

# 摄像头的经纬度和高度
camera_lat = 39.9042
camera_lon = 116.4074
camera_alt = 50

# 目标的经纬度和高度
target_lat = 30.5928
target_lon = 114.3055
target_alt = 0

# 计算距离和方位角
geod = Geodesic.WGS84.Inverse(camera_lat, camera_lon, target_lat, target_lon)
azimuth1, azimuth2, distance = geod['azi1'], geod['azi2'], geod['s12'] 

# 计算垂直和水平角度
elevation_angle = degrees(atan2(target_alt - camera_alt, distance))
horizontal_angle = degrees(radians(azimuth1))

# 计算焦距
focal_length = distance

# 输出结果
print("俯仰角：{} 度".format(elevation_angle))
print("水平转动角度：{} 度".format(horizontal_angle))
print("焦距：{} 米".format(focal_length))

Note that this code only considers spherical geometry and does not consider the ellipsoid shape and non-spherical factors of the Earth. In addition, it is also necessary to consider how to map the PTZ coordinates to the control interface of the camera to achieve the function of tracking the target.

def longlat_to_PTZ(longitude, latitude):
    x = longitude * 2 * 603.67 / 360
    y = latitude * 2 * 603.67 / 360
    PTZ = (x,y)
    return PTZ

Here is the Python code to convert the latitude and longitude to the PTZ coordinates of the camera:

import math

def convert_to_ptz(lat, lon, lat0, lon0, zoom):
    # 计算方位角
    azimuth = math.atan2(math.cos(lat) * math.sin(lon - lon0), 
                         math.cos(lat0) * math.sin(lat) - math.sin(lat0) * math.cos(lat) * math.cos(lon - lon0))
    azimuth = math.degrees(azimuth)
    if azimuth < 0:
        azimuth += 360
    
    # 计算俯仰角
    pitch = math.atan2(math.cos(lat0) * math.cos(lat) * math.cos(lon - lon0) + math.sin(lat0) * math.sin(lat), 
                       math.sqrt(1 - (math.cos(lat0) * math.cos(lat) * math.cos(lon - lon0) + math.sin(lat0) * math.sin(lat))**2))
    pitch = math.degrees(pitch)
    
    # 将方位角和俯仰角转换为PTZ坐标
    p = azimuth / 360.0
    t = (90 - pitch) / 180.0
    z = zoom
    
    # 调整PTZ坐标系的坐标范围
    p = max(0, min(1, p))
    t = max(0, min(1, t))
    z = max(0, z)
    
    return p, t, z

Where, lat and lon are the latitude and longitude of the target point, lat0 and lon0 are the latitude and longitude of the camera, and zoom is the focal length.

can call this function to realize the camera head positioning and tracking according to latitude and longitude. The specific operation process is as follows:

Obtain the latitude and longitude coordinates of the target point.
calls the convert_to_ptz function to convert the latitude and longitude into PTZ coordinates for the camera.
Send the PTZ coordinates to the camera to control the movement of the camera's cradle head.

The generated PTZ value does not match, I think we should add altitude

For reference only:

The PTZ coordinates of the camera are generally represented by three parameters, namely, the horizontal rotation Angle of the head(P), the pitch Angle(T) and the focal length scaling ratio(Z).

To convert latitude and longitude to PTZ coordinates, you need to do the following:

1. Obtain the Earth radius r. The WGS84 ellipsoid parameter can be used, i.e. r=6378137 m.
2. Convert latitude and longitude into x, y, and z coordinates in Cartesian coordinate system.
3. Calculate the coordinates of the camera in the Cartesian coordinate system, which is generally set as the height of the earth surface, and can also be adjusted according to the actual situation.
4. Calculate the vector of the camera pointing at the target point, i.e., the target point minus the camera coordinates. 5. Project the vector onto the xoz plane and calculate the horizontal rotation Angle P, that is, P=arctan2(x,z).
6. Calculate the vector length as focal length scaling Z.
7. Project the vector onto the xz plane and calculate the pitch Angle T, i.e. T=arctan2(y, sqrt(x^2 + z^2)).
Here is an example of the code implemented in Python:

import math

# 地球半径
R = 6378137

# 相机位置坐标
camera_x = 0
camera_y = 0
camera_z = R

# 目标点经纬度
target_latitude = 31.23
target_longitude = 121.47

# 经纬度转换为笛卡尔坐标系的x、y、z坐标
lat_rad = math.radians(target_latitude)
lon_rad = math.radians(target_longitude)
x = R * math.cos(lat_rad) * math.cos(lon_rad)
y = R * math.cos(lat_rad) * math.sin(lon_rad)
z = R * math.sin(lat_rad)

# 计算相机指向目标点的向量
dx = x - camera_x
dy = y - camera_y
dz = z - camera_z

# 计算水平方向旋转角度P
P = math.atan2(dx, dz)

# 计算焦距缩放比例Z
Z = math.sqrt(dx * dx + dy * dy + dz * dz)

# 计算俯仰角度T
T = math.atan2(dy, math.sqrt(dx * dx + dz * dz))

# 输出PTZ坐标
print("P=%.2f, T=%.2f, Z=%.2f" % (math.degrees(P), math.degrees(T), Z))

Note that this calculation method only applies to points near the Earth's surface, if the target point is too far away from the Earth's surface, or at a location beyond the Earth's surface, a more complex calculation method will need to be used. At the same time, there may be some errors in the calculation results, which should be adjusted according to the actual situation.

The following is a simple example for reference only, using the Geopy and OpenCV libraries.