Rotating a point around another point Java

Question

Here is a code segment in java intended to rotate the vertices with coordinates A(10,10),B(20,10),C(20,20),D(10,20) of a square by an angle about the center point of the square. The side of the square is 10 points. The angle of rotation is 90 degree. Ideally after rotation A must become B, B must become C, C must become D and D becomes A.

private Point getRotation(Point start, int side, int rotation){

    int x = start.getX();
    int y = start.getY();

    int pivot_x = x + (side/2);
    int pivot_y = y + (side/2);

    float angle = (float)Math.toRadians(rotation);

    int xR = (int)(pivot_x + (x -pivot_x)*Math.cos(angle) - (y - pivot_y)*Math.sin(angle));
    int yR = (int)(pivot_y + (x -pivot_x)*Math.sin(angle) + (y - pivot_y)*Math.cos(angle));

    return new Point(xR,yR);        
}

public static void main(String[] args) {
    Square s = new Square();
    Point rotatedPoint1= s.getRotation(new Point(10,10), 10, 90);
    System.out.println("{"+rotatedPoint1.getX()+","+rotatedPoint1.getY()+"}");

    Point rotatedPoint2= s.getRotation(new Point(20,10), 10, 90);
    System.out.println("{"+rotatedPoint2.getX()+","+rotatedPoint2.getY()+"}");

    Point rotatedPoint3= s.getRotation(new Point(20,20), 10, 90);
    System.out.println("{"+rotatedPoint3.getX()+","+rotatedPoint3.getY()+"}");

    Point rotatedPoint4= s.getRotation(new Point(10,20), 10, 90);
    System.out.println("{"+rotatedPoint4.getX()+","+rotatedPoint4.getY()+"}");
}

The result that is achieved are not correct

• point A(10,10) rotated to (20,10) ---- correct

• point B(20,10) rotated to (30,10) ---- INCORRECT

• point C(20,20) rotated to (30,20) ---- INCORRECT

• point D(10,20) rotated to (20,20) ---- INCORRECT

The formula applied is

if (h,k) are the points about which the point (x,y) needs to be rotated by an angle THETA, then the Coordinates after rotation (xR, yR) are

• xR = h + (x-h)cos(THETA) - (y-k)sin(THETA)
• yR = k + (x-h)sin(THETA) + (y-k)cos(THETA)

Where is the problem?

Answer 1

The problem is your calculation of the square's centroid.

It's supposed to be the same point for all four vertices. However, you calculate as (x+5,y+5) based on each new pair when you call the function. That is:

• Call for (10,10), pivot is (15,15)
• Call for (20,10), pivot is (25,15)
• Call for (20,20), pivot is (25,25)
• Call for (10,20), pivot is (15,25)

And you should have rotated them all around the same pivot (15,15).

So you should calculate the pivot before calling the getRotation() method, and pass the pre-calculated pivot as parameter instead of passing the length of the side.