How to calculate rotation in 2D in Javascript

Question

I am not so familiar trigonometry, but I have only two points to rotate in 2D:

                    *nx, ny
               .     -
          .           -
     .  angle          -
*cx,cy.................*x,y

cx, cy = rotation center
x,y = current x,y
nx, ny = new coordinates

How to calculate new points in a certain angle?

Answer 1

function rotate(cx, cy, x, y, angle) {
    var radians = (Math.PI / 180) * angle,
        cos = Math.cos(radians),
        sin = Math.sin(radians),
        nx = (cos * (x - cx)) + (sin * (y - cy)) + cx,
        ny = (cos * (y - cy)) - (sin * (x - cx)) + cy;
    return [nx, ny];
}

The first two parameters are the X and Y coordinates of the central point (the origin around which the second point will be rotated). The next two parameters are the coordinates of the point that we'll be rotating. The last parameter is the angle, in degrees.

As an example, we'll take the point (2, 1) and rotate it around the point (1, 1) by 90 degrees clockwise.

rotate(1, 1, 2, 1, 90);
// > [1, 0]

Three notes about this function:

1. For clockwise rotation, the last parameter angle should be positive. For counterclockwise rotation (like in the diagram you provided), it should be negative.

2. Note that even if you provide arguments that should yield a point whose coordinates are whole numbers -- i.e. rotating the point (5, 0) by 90 degrees about the origin (0, 0), which should yield (0, -5) -- JavaScript's rounding behavior means that either coordinate could still be a value that's frustratingly close to the expected whole number, but is still a float. For example:

   rotate(0, 0, 5, 0, 90);
   // > [3.061616997868383e-16, -5]
   

   For this reason, both elements of the resulting array should be expected as a float. You can convert them to integers using Math.round(), Math.ceil(), or Math.floor() as needed.

3. Finally, note that this function assumes a Cartesian coordinate system, meaning that values on the Y axis become higher as you go "up" in the coordinate plane. In HTML / CSS, the Y axis is inverted -- values on the Y axis become higher as you move down the page.

Answer 2

1. First, translate the rotation center to the origin
2. Calculate the new coordinates (nx, ny)
3. Translate back to the original rotation center

Step 1

Your new points are

1. center: (0,0)
2. point: (x-cx, y-cy)

Step 2

1. nx = (x-cx)*cos(theta) - (y-cy)*sin(theta)
2. ny = (y-cy)*cos(theta) + (x-cx)*sin(theta)

Step 3

Translate back to original rotation center:

1. nx = (x-cx)*cos(theta) - (y-cy)*sin(theta) + cx
2. ny = (y-cy)*cos(theta) + (x-cx)*sin(theta) + cy

For deeper explanation, with some fancy diagrams, I recommend looking at this.

Answer 3

above accepted answer not work for me correctly, rotation are reversed , here is working function

/*
 CX @ Origin X  
 CY @ Origin Y
 X  @ Point X to be rotated
 Y  @ Point Y to be rotated  
 anticlock_wise @ to rotate point in clockwise direction or anticlockwise , default clockwise 
 return @ {x,y}  
*/
function rotate(cx, cy, x, y, angle,anticlock_wise = false) {
    if(angle == 0){
        return {x:parseFloat(x), y:parseFloat(y)};
    }if(anticlock_wise){
        var radians = (Math.PI / 180) * angle;
    }else{
        var radians = (Math.PI / -180) * angle;
    }
    var cos = Math.cos(radians);
    var sin = Math.sin(radians);
    var nx = (cos * (x - cx)) + (sin * (y - cy)) + cx;
    var ny = (cos * (y - cy)) - (sin * (x - cx)) + cy;
    return {x:nx, y:ny};
 }

Answer 4

According to Polar coordinate system artycle on Wikipedia:

x = r * cos(deg)
y = r * sin(deg)

• r (radius) is equal to distance between Rotation Centre and Rotated Point
• deg (degrees) is angle measured in degrees

Answer 5

I think it is better to use matrices for such operations.

Here is the example with gl-matrix (but you can use something like THREEJS as well).

import * as glm from 'gl-matrix';
const rotateVector = (() => {
  
  const q = glm.quat.create();  
  // const m = glm.mat4.create(); // 2nd way

  return (v: glm.vec3, point: glm.vec3, axis: glm.vec3, angle: number) => {

      glm.quat.setAxisAngle(q, axis, angle);
      // glm.mat4.fromRotation(m, angle, axis); // 2nd way
      glm.vec3.sub(v, v, point);
      glm.vec3.transformQuat(v, v, q);
      // glm.vec3.transformMat4(v, v, m); // 2nd way
      glm.vec3.add(v, v, point);
      return v;
  }
})();

In 2D case you need to rotate around z-axis:

rotateVector([x, y, 0], [cX, cY, 0], [0, 0, 1], angleInRadians);