How can I calculate an average terrain slope based on four points?

Question

I'm programming a simple physics system for vehicles in Unity and I'm trying to figure out how to calculate the average slope based on four points in order to apply the gravitational acceleration. I can get the terrain height at the vehicle wheels positions like this:

Terrain.activeTerrain.SampleHeight(wheel.position);

How can I calculate the average terrain slope based on those four points? I thought about calculating direction vectors between different points, but I'm not sure how to combine them into a single slope vector.

Answer 1

(Assuming that all 4 wheels are always coplanar) I think you could take any 3 wheels, take the height sample

var wheels = new Vector3[3]{ wheel1.transform.position, wheel2.transform.position, wheel3.transform.position };
for(var i = 0; i < wheels.Length; i++)
{
    var w = wheels[i];
    w.y = Terrain.activeTerrain.SampleHeight(w)
    wheels[i]= w;
}

and from that resulting 3 points generate a plane

var plane = new Plane(wheels[0], wheels[1], wheels[2]);

Now you can take any of these points and take a vector in straight up direction.

var upPoint = wheels[0] + Vector3.up;

Then you can map that vector onto the plane using closest point on plane.

var planePoint = plane.ClosestPointOnPlane(upPoint);

As a last step normalize the vector between that mapped point and your start wheel point and you should have the direction of the slope + the Y component tells you how steep it is

var planeVector = wheels[0] - planePoint;
var direction = planeVector.normalized;

Debug.Log($"Slope direction is {direction} with a steepness factor of {direction.y} or also {-planeVector.magnitude}");

where both planeVector.magnitude and direction.y should be moving between 0 (completely horizontal surface) and -1 (completely vertical surface)

Something like that I guess ^^

Answer 2

Wouldn't that be the average slope between the middle point of the back wheels and the middle point of the front wheels? You get the tangent of the angle by dividing the difference between those heights and their distance (as projected). Guess that's too simple? Assuming 4 points (x1,y1), (x2,y2), (x3,y3) and (x4,y4). The middlepoints would be xB = (x1+x2)/2, yB=(y1+y2)/2 and xF=(x3+x4)/2 and yF=(y3+y4)/2. Then Tan A = (yF-yB)/(xF-xB)