How to rotate object depending on center cell

Question

I have a grid at which I place an object I want to rotate right around a fixed cell (cell3). The object contains coordinates, like:

activeObject = {
    coords: {
        cell1: {
             x: 0,
             y: 0
        },
        cell2: {
             x: 1,
             y: 1
        },
        cell3: {
             x: 2,
             y: 2
        },
        cell4: {
             x: 2,
             y: 3
        },
        cell5: {
             x: 3,
             y: 3
        },
    }
}

Output:

I want to rotate this object around cell3 e.g. using x: 2, y: 2 without hard coding each cell position using some kind of (basic) trigonometry. I realize that I have to check how far is each cell from cell3, and the orientation. But I don't know how to do the calculation as I am not so good with trigonometry. The new active object would be:

activeObject = {
    coords: {
        cell1: {
             x: 4,
             y: 0
        },
        cell2: {
             x: 4,
             y: 1
        },
        cell3: {
             x: 2,
             y: 2
        },
        cell4: {
             x: 1,
             y: 2
        },
        cell5: {
             x: 1,
             y: 3
        },
    }
}

Output:

Answer 1

Some basic thoughts

• if the pivot is not the origin, then some correction must apply to the transformation.
• if a point is at (1, 2), then rotated around the origin
  • 90° CW: became (2, -1)
  • 90° CCW: became (-2, 1)
• the conclusion of the point (x, y)
  • 90° CW: became (y, -x)
  • 90° CCW: became (-y, x)
• at least apply the correction for the pivot

Some Math is found here.

function Point(x, y) {
    this.x = x;
    this.y = y;
}

Point.prototype.rotateCW = function (c) {
    // x' =  x cos phi + y sin phi \ formula with pivot at (0, 0)
    // y' = -x sin phi + y cos phi /
    // phi = 90°                   insert phi
    // cos 90° = 0   sin 90° = 1   calculate cos and sin 
    // x' =  y                     \ formula with pivot at (0, 0)
    // y' = -x                     /
    // x' =  (cy - y) + cx         \ formula with different pivot needs correction 
    // y' = -(cx - x) + cy         /
    // y' = -cx + x + cy          /
    return new Point(
        c.x + c.y - this.y,
        c.y - c.x + this.x
    );
}

Point.prototype.rotateCCW = function (c) {
    // source: https://en.wikipedia.org/wiki/Rotation_(mathematics)#Two_dimensions
    // x' =  x cos phi + y sin phi  \ formula with pivot at (0, 0)
    // y' = -x sin phi + y cos phi  /
    // phi = -90°
    // cos -90° = 0   sin -90° = -1
    // x' = -y                      \ formula with pivot at (0, 0)
    // y' =  x                      /
    // x' = -(cy - y) + cx          \ formula with different pivot needs correction 
    // x' = -cy + y + cx            /
    // y' =  (cx - x) + cy         /
    return new Point(
        c.x - c.y + this.y,
        c.y + c.x - this.x
    );
}

var activeObject = {
        coords: {
            cell1: new Point(0, 0),
            cell2: new Point(1, 1),
            cell3: new Point(2, 2),
            cell4: new Point(2, 3),
            cell5: new Point(3, 3),
        }
    },
    pivot = new Point(2, 2),
    rotated = { coords: {} };

Object.keys(activeObject.coords).forEach(function (k) {
    rotated.coords[k] = activeObject.coords[k].rotateCW(pivot);
});

document.write('<pre>' + JSON.stringify(rotated, 0, 4) + '</pre>');