CODEWITHSUNDEEP
javascriptmath3d
josef.van.niekerk
josef.van.niekerk

Reputation: 12121

Calculate θ and ø angles between origin and x,y,z coordinate

I'm using three.js for a small 3D POC project. The following snippet calculates the new x,y,z position for a 3D object in orbit around the origin (0,0,0):

x = rho * Math.cos(theta) * Math.sin(phi);
y = rho * Math.sin(theta) * Math.sin(phi);
z = rho * Math.cos(phi);

In the above example, theta and phi are known and used to calculate the new x,y,z coordinate for the orbiting 3D subject.

The above works well, but I also want to do the inverse.

How do I go about calculating theta and phi, if I only have an x,y,z point, this all in relation to the origin point (0,0,0)?

Upvotes: 1

Views: 2025

Answers (1)

Paul S.
Paul S.

Reputation: 66364

IIRC

r = Math.sqrt(x*x + y*y + z*z);
θ = Math.acos(z/r);
φ = Math.atan2(y, x);

x = r * Math.sin(θ) * Math.cos(φ);
y = r * Math.sin(θ) * Math.sin(φ);
z = r * Math.cos(θ);

You seem to have your θ and φ swapped the other way around (which is just a notation choice)

Upvotes: 3

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