Angle between 3 points in 3d space

Question

I have 3 points containing X, Y, Z coordinates:

var A = {x: 100, y: 100, z: 80},
    B = {x: 100, y: 175, z: 80},
    C = {x: 100, y: 100, z: 120};
         


        

Answer 1

@Roger algorithm in swift

func SCNVector3Angle(start: SCNVector3, mid: SCNVector3, end: SCNVector3) -> Double {
    let v1 = (start - mid)
    let v2 = (end - mid)
    let v1norm = v1.normalized()
    let v2norm = v2.normalized()

    let res = v1norm.x * v2norm.x + v1norm.y * v2norm.y + v1norm.z * v2norm.z
    let angle: Double = Double(GLKMathRadiansToDegrees(acos(res)))
    return angle
}

/**
* Subtracts two SCNVector3 vectors and returns the result as a new SCNVector3.
*/
func - (left: SCNVector3, right: SCNVector3) -> SCNVector3 {
    return SCNVector3Make(left.x - right.x, left.y - right.y, left.z - right.z)
}

extension SCNVector3
{
    /**
    * Returns the length (magnitude) of the vector described by the SCNVector3
    */
    func length() -> Float {
        return sqrtf(x*x + y*y + z*z)
    }

    /**
    * Normalizes the vector described by the SCNVector3 to length 1.0 and returns
    * the result as a new SCNVector3.
    */
    func normalized() -> SCNVector3 {
        return self / length()
    }
}