swift - Draw SceneKit object between two points

Question

Having made some progress in the geometry side of things I'm moving on to putting together an entire scene. That scene has a couple dozen objects, each defined by a bounding cube whose corners are specified by two SCNVector3s (originally two sets of x,y,z).

Here's an example of what I have so far - it's an 11-element log-periodic antenna, like the old school TV antennas from the 70s. Each of the grey lines is an "element", typically made of aluminum rod. I used SCNCylinders from +ve to -ve Y and the entire thing is less than 100 lines (SK is pretty amazing).

The problem is what happens if the elements are not symmetrical across X and thus the SCNCylinder has to be rotated. I found this example, but I can't understand the specifics... it appears to take advantage of the fact that a sphere is symmetric so angles kind of "go away".

Does anyone have a general function that will take two 3D points and return the SCNVector3 suitable for setting the node's eulerAngle, or a similar solution?

Answer 1

Both solutions mentioned above work very well and I can contribute third solution to this question.

//extension code starts

func normalizeVector(_ iv: SCNVector3) -> SCNVector3 {
    let length = sqrt(iv.x * iv.x + iv.y * iv.y + iv.z * iv.z)
    if length == 0 {
        return SCNVector3(0.0, 0.0, 0.0)
    }

    return SCNVector3( iv.x / length, iv.y / length, iv.z / length)

}

extension SCNNode {

    func buildLineInTwoPointsWithRotation(from startPoint: SCNVector3,
                              to endPoint: SCNVector3,
                              radius: CGFloat,
                              color: UIColor) -> SCNNode {
        let w = SCNVector3(x: endPoint.x-startPoint.x,
                           y: endPoint.y-startPoint.y,
                           z: endPoint.z-startPoint.z)
        let l = CGFloat(sqrt(w.x * w.x + w.y * w.y + w.z * w.z))

        if l == 0.0 {
            // two points together.
            let sphere = SCNSphere(radius: radius)
            sphere.firstMaterial?.diffuse.contents = color
            self.geometry = sphere
            self.position = startPoint
            return self

        }

        let cyl = SCNCylinder(radius: radius, height: l)
        cyl.firstMaterial?.diffuse.contents = color

        self.geometry = cyl

        //original vector of cylinder above 0,0,0
        let ov = SCNVector3(0, l/2.0,0)
        //target vector, in new coordination
        let nv = SCNVector3((endPoint.x - startPoint.x)/2.0, (endPoint.y - startPoint.y)/2.0,
                            (endPoint.z-startPoint.z)/2.0)

        // axis between two vector
        let av = SCNVector3( (ov.x + nv.x)/2.0, (ov.y+nv.y)/2.0, (ov.z+nv.z)/2.0)

        //normalized axis vector
        let av_normalized = normalizeVector(av)
        let q0 = Float(0.0) //cos(angel/2), angle is always 180 or M_PI
        let q1 = Float(av_normalized.x) // x' * sin(angle/2)
        let q2 = Float(av_normalized.y) // y' * sin(angle/2)
        let q3 = Float(av_normalized.z) // z' * sin(angle/2)

        let r_m11 = q0 * q0 + q1 * q1 - q2 * q2 - q3 * q3
        let r_m12 = 2 * q1 * q2 + 2 * q0 * q3
        let r_m13 = 2 * q1 * q3 - 2 * q0 * q2
        let r_m21 = 2 * q1 * q2 - 2 * q0 * q3
        let r_m22 = q0 * q0 - q1 * q1 + q2 * q2 - q3 * q3
        let r_m23 = 2 * q2 * q3 + 2 * q0 * q1
        let r_m31 = 2 * q1 * q3 + 2 * q0 * q2
        let r_m32 = 2 * q2 * q3 - 2 * q0 * q1
        let r_m33 = q0 * q0 - q1 * q1 - q2 * q2 + q3 * q3

        self.transform.m11 = r_m11
        self.transform.m12 = r_m12
        self.transform.m13 = r_m13
        self.transform.m14 = 0.0

        self.transform.m21 = r_m21
        self.transform.m22 = r_m22
        self.transform.m23 = r_m23
        self.transform.m24 = 0.0

        self.transform.m31 = r_m31
        self.transform.m32 = r_m32
        self.transform.m33 = r_m33
        self.transform.m34 = 0.0

        self.transform.m41 = (startPoint.x + endPoint.x) / 2.0
        self.transform.m42 = (startPoint.y + endPoint.y) / 2.0
        self.transform.m43 = (startPoint.z + endPoint.z) / 2.0
        self.transform.m44 = 1.0
        return self
    }
}

//extension ended.

//in your code, you can like this.
let twoPointsNode1 = SCNNode()
        scene.rootNode.addChildNode(twoPointsNode1.buildLineInTwoPointsWithRotation(
            from: SCNVector3(1,-1,3), to: SCNVector3( 7,11,7), radius: 0.2, color: .cyan))
//end

you can reference http://danceswithcode.net/engineeringnotes/quaternions/quaternions.html

BTW, you will get same result when you use a cylinder to make a line between two points from above 3 methods. But indeed, they will have different normal lines. In another words, if you use box between two points, sides of box, except top and bottom, will face different direction from above 3 methods.

let me know pls if you need further explanation.