Rotating a Vector2 around a point

Question

I'm trying to understand what happens when we rotate a Vector around an arbitrary point. If p.x was 0 then the angle would be 90 and I understand that, but I can't visualize why it is 45 when I use p.x = 50.

var v = new THREE.Vector2(100,0);
var p = new THREE.Vector2(50,0);

v.rotateAround(p, 90 * Math.PI/180);
console.log('Angle: ', v.angle() * 180/Math.PI);

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Answer 1

You are rotating the point v around the point p. This is done by rotating the vector v-p around the origin and adding the resulting vector (read point translation) back to p.

As v-p=(50,0) the 90° rotation gives (0,50) and adding back pgives the point (50,50) which is at angle 45° relative to the origin, but still straight up from p.

  |           v after rotation
  |         o
  |         .
  |         .
  |         .
  |         .
--o---------+---------o-----
origin      p         v at start