I am working with a vector in three-dimensional space.
Is there a method to determine the angle of rotation from the origin to this vector on each axis?
For example, if the vector is located at x=6, y=-10, z=20,
what angle does the vector make with respect to the origin (x=0, y=0, z=0) on the x, y, and z axes?
I have been trying to solve this in Three.js for a while now. Any assistance would be greatly appreciated.
One way to determine the angle between two vectors is by using this formula: v1•v2 = |v1||v2| cos(angle). To calculate the angle, you can use the acos function on the dot product of the two vectors.
In ThreeJS, the dot product can be calculated as follows: dotproductV1V2 = V1.dot(V2)
You can then apply acos to the result in order to determine the angle: Math.acos(dotproductV1V2)
Edit :
Here's an example that illustrates how to find the angle for each component of a vector:
var V1x = new THREE.Vector3(1, 0, 0)
var V1y = new THREE.Vector3(0, 1, 0)
var V1z = new THREE.Vector3(0, 0, 1)
var V2 = new THREE.Vector3(6, -10, 20)
var V2xz = new THREE.Vector3(V2.x, 0, V2.z)
var V2xy = new THREE.Vector3(V2.x, V2.y, 0)
//angle in radian between origin X axis and X axis of V2
var angle_V1V2x = Math.acos(V1x.dot(V2xz.normalize()))
//angle in radian between origin Y axis and Y axis of V2
var angle_V1V2y = Math.acos(V1y.dot(V2xy.normalize()))
//angle in radian between origin Z axis and Z axis of V2
var angle_V1V2z = Math.acos(V1z.dot(V2xz.normalize()))
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