Combine rotation XZ (horizontal) with YZ (vertical). Math formula

Question

I'm trying to make a rotation vertically and horizontally around a point at the same time but I'm not able to combine both.

I have this formula for the horizontal rotation:

camera.position.x = x * Math.cos(inc) + z * Math.sin(inc)
camera.position.z = z * Math.cos(inc) - x * Math.sin(inc)

And this one for the vertical:

camera.position.y = y * Math.cos(inc) + z * Math.sin(inc)
camera.position.z = z * Math.cos(inc) - y * Math.sin(inc)

I guess I need to use a Matrix, but not sure how. Here an example with Three.js: https://codepen.io/josema/pen/xyQoga

Answer 1

As @DMGregory mentioned above what I really needed was a way to translate a polar/spherical coordinates into cartesian coordinates.

In other words, I have two angles and one radius and I need to convert it into a Vector3/XYZ.

Here is the code:

function polarToCartesian( angleV, angleH, radius ) {

  var phi = ( 90 - angleV ) * DEG2RAD
  var theta = ( angleH + 180 ) * DEG2RAD

  return {
    x: -(radius * Math.sin(phi) * Math.sin(theta)),
    y: radius * Math.cos(phi),
    z: radius * Math.sin(phi) * Math.cos(theta),
  }

}

Source: https://gist.github.com/jhermsmeier/72626d5fd79c5875248fd2c1e8162489