# What's the math behind moving from a starting point in the direction of another one?

I am working with decimal-degree coordinates for a software and lack geographic background.

I want to convert the coordinates to a grid to calculate distances and then move around using standard geometry.

The coordinate format is the same used in Google Maps urls (decimal WGS 84) which is not a Cartesian plane.

I am trying to figure out how to calculate the coordinates of intermediate steps when traveling from a point to another with known a speed and start/finish points.

How do I translate a coordinate, given a bearing (in the form of a destination point) by some amount of meters?

Is there an angular equivalent of the line from two points function that I can use to get all the intermediate points?

Update: I am working with city-level distances (~10km max) in Italy. I tried to use Cartesian operations on the WGS 84 coordinates directly: the result in this case is good enough. I lose some millimeters on movements but it does not really matter for my implementation, since in the end the position will be exactly the one I want.

Still, I asked this question in order to comprehend the necessary math operations to translate coordinates either directly or by converting to a 2D plane, doing operations and converting back (without loss of data, possibly).

• Welcome to GIS SE. As a new user, please take the Tour, which details how our "Focused question / Best answer" model operates. You have a number of topics here, without much indication of initial research. While there is a WGS 1984 geographic coordinate system, there doesn't appear to be a WGS98 (nor WSG 98). All geographic coordinate systems are angular not Cartesian, and inappropriate for plane geometry equations. Unfortunately, you've encountered the Second Geodetic Problem; I'd recommend using a software library. Commented May 28, 2018 at 18:02
• Well, for a small area a linear approximation may be good enough. Commented May 28, 2018 at 18:04
• Thanks Vince. I followed lynxlynxlynx suggestion and found it to work for city-level navigation (thanks to you too). I edited the question to be more clear, tough. Commented May 30, 2018 at 13:52