Moving around the surface of an Earth shaped spheroid in Unity

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I'm trying to make a Unity game that allows the user to explore the surface of an Earth shaped spheroid, based on WGS84.

The project so far is on Github, and there's a YouTube video of this behaviour.

A shape the size of Earth is way too big for Unity, so I just spawn tiles near the user, offset so that the first tile is at Unity's origin point. This bit works.

The issue is moving around. I've been using an approach where I get the user's position in ECEF coordinates, then normalise that to provide the global orientation for the player, then I translate the player forward based on that and their rotation.

The issue with this is that normalising the ECEF coordinate means that the player is moving in a spherical shape, but the WGS84 spheroid is not perfectly spherical. So the player sinks into the floor, or flies up if you got south or north, respectively.

My question is, how can I allow the user to move around the surface of the spheroid by way of translation? I feel like there might be some way of taking the major/minor axis of the spheroid into account as the player moves, but I'm not sure how to do that.

unity3d geo math
1 Answers

I have no experience with Unity or computer graphics, I'm approaching it purely from the navigation point of view.

Let's look at the real world. We want to travel either by walking/driving on the surface or flying at some altitude. When we do it, we move in the local coordinate system (North-South, East-West, Up-Down), we can't see any curvature. We assume the Earth is flat.

The problem arises when we try to do it on a computer, which is ruthlessly precise and knows the shape of the Earth. We can't assume the Earth is flat, we can't assume the Earth is a sphere. The Earth is a geoid. Fortunately for some purposes we can simplify things and assume the Earth is an ellipsoid. You chose WGS84. Good!

So how to move around an ellipsoid? Solving the problem analitically is a nightmare. We have to cheat ;) We should assume te Earth is flat for a moment, make a move in a chosen direction in the local coordinate system, write down the altitude of the new position, calculate the global geodetic coordinates (Lat, Long, Alt) of that new point and then replace the altitude with the one obtained while using the local coordinate system. In other words: each time we move forward along a perfectly straight line and diverge from the ellipsoid (just a tiny bit), we force the altitude not to change in relation to the ellipsoid.

Implementation. You need to be able to freely translate coordinates between geodetic (Lat, Long, Alt) and ECEF. Going from geodetic to ECEF is easy. Finding geodetic coordinates for a given ECEF position is much more complex, there are many different algorithms, I'm sure you should be able to find a ready to use implementation somewhere. What you also need is Local Tangent Plane, and to be precise, you are going to use NED. Let's assume your object is initially at some geodetic position. You write down the altitude (relative to the ellipsoid). Then you create a local NED coordinate system with its origin at that point. Then you move the object in that local coordinate system. You write down how much the altitude (or rather the Down coordinate) changed. Then you must calculate the ECEF coordinates of that new position and transform it to geodetic (Lat, Long, Alt). You have the old altitude, you have the altitude change in the NED coordinates, which means you know the new altitude. You then apply that altitude to your new geodetic coordinates (brutally replace the Alt in Lat/Long/Alt with a new value). Then you make another move in the NED coordinates defined for that new position. And so on...

I'm not sure if it is clear, the process is quite complicated. If you can't understand - shout :)

user_7808150
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