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Apple Metal iOS why does GLKMatrix4MakeLookAt rock back and forth

I am developing a 3D scene on iOS 16.1 with Xcode 14.3. I have a rectangular plane orbiting the origin at an incline and I want to use GLKMatrix4MakeLookAt to cause the plane to always face the origin.

I am using the code below. The plane does 'face' the origin when it rotates, however I am also seeing this undesired 'rocking' ( yaw ) back and forth. Please see the attached video to understand how it looks.

Why does it do this rocking? How can I get rid of the rocking but still have the plane orbit the origin and always face it? Thank you.

enter image description here

Code:

// Get the lookat scene origin matrix for the rectangle
var lookAtSceneOriginGLKMatrix = GLKMatrix4Identity
var lookAtSceneOriginInverse = GLKMatrix4Identity
var rectangleModelMatrix = float4x4()
var lookAtSceneOriginMat = float4x4()

lookAtSceneOriginGLKMatrix = GLKMatrix4Multiply(lookAtSceneOriginGLKMatrix, GLKMatrix4MakeLookAt(self.currentSatX * self.appDelegate.getCurrentRectangle().getRenderHeight(), self.currentSatY * self.appDelegate.getCurrentRectangle().getRenderHeight(), self.currentSatZ * self.appDelegate.getCurrentRectangle().getRenderHeight(), 0, 0, 0, 0, 1, 0))
var isInvertible = true
lookAtSceneOriginInverse = GLKMatrix4Invert(lookAtSceneOriginGLKMatrix, &isInvertible)
lookAtSceneOriginMat = float4x4(convertToFloat4x4FromGLKMatrix: lookAtSceneOriginInverse)
rectangleModelMatrix = accumulatedRotationMatrix * lookAtSceneOriginMat * float4x4(scaleBy: 0.35)

// Draw the rectangular plane
scene.rectanglePlane?.draw(
    encoder: commandEncoder, modelMatrix: rectangleModelMatrix,
    projectionMatrix: projectionMatrix * viewMatrix
)
Solution

  • As mentioned in a Comment your up vector always pointing to the direction of y axis. It should be perpendicular to the direction vector.

    let x = self.currentSatX * self.appDelegate.getCurrentRectangle().getRenderHeight()
let y = self.currentSaty * self.appDelegate.getCurrentRectangle().getRenderHeight()
let z = self.currentSatZ * self.appDelegate.getCurrentRectangle().getRenderHeight()

let direction = GLKVector3Make(x, y, z) //vector from planes postion to origin

let yAx = GLKVector3Make(0, 1, 0) // y axis

let side = GLKVector3CrossProduct(direction, yAx) //perpendicular vector to direction

let up = GLKVector3CrossProduct(side, direction) //perpendicular vector to side
let normalizedUp = GLKVector3Normalize(up)

lookAtSceneOriginGLKMatrix = GLKMatrix4Multiply(lookAtSceneOriginGLKMatrix, GLKMatrix4MakeLookAt(x, y, z, 0, 0, 0, normalizedUp.x, normalizedUp.y, normalizedUp.z))