To convert latitude and longitude coordinates from Google Maps (which are in a geographic coordinate system) to Cartesian coordinates, you generally follow these steps:

1. Understand the Coordinates: Latitude and longitude are angular measurements, where latitude measures north-south position and longitude measures east-west position on the Earth's surface.

2. Select a Cartesian Coordinate System: There are multiple ways to define a Cartesian coordinate system, but commonly used systems include:

   • ECEF (Earth-Centered, Earth-Fixed): A global 3D coordinate system centered at the Earth’s center.
   • Local Tangent Plane (LTP) or ENU (East-North-Up): This is a local Cartesian system where a specific point on Earth (e.g., a location of interest) acts as the origin.

3. Convert Latitude and Longitude to Cartesian Coordinates in the ECEF System: For the Earth-Centered, Earth-Fixed system, you can use the following formulas: $X = (N + h) \cdot \cos(\text{lat}) \cdot \cos(\text{lon})$ $Y = (N + h) \cdot \cos(\text{lat}) \cdot \sin(\text{lon})$ $Z = \left( \frac{b^2}{a^2} \cdot N + h \right) \cdot \sin(\text{lat})$ Where:

   • $\text{lat}$ and $\text{lon}$ are the latitude and longitude in radians,
   • $h$ is the elevation above the Earth's surface,
   • $a$ is the Earth's equatorial radius (6,378,137 meters),
   • $b$ is the polar radius (6,356,752 meters),
   • $N = \frac{a^2}{\sqrt{a^2 \cdot \cos^2(\text{lat}) + b^2 \cdot \sin^2(\text{lat})}}$.

4. Convert to Local Tangent Plane (if Needed): If you need a local Cartesian system, you can convert the ECEF coordinates to the Local Tangent Plane or ENU system.

Would you like more details on the ECEF system or Local Tangent Plane transformations?

Related Questions

1. How do you convert ECEF coordinates to ENU coordinates?
2. How do latitude and longitude vary with the Earth’s shape?
3. What other projections are available for mapping Earth coordinates?
4. How does elevation affect Cartesian coordinates?
5. What are common uses of Cartesian vs. geographic coordinates?

Tip: The ECEF system is often used in GPS and satellite systems for accurate location tracking on a global scale.