Find centre point of a rotated BufferedImage

Question

What I'm basically trying to do is rotate a BufferedImage and then draw it based on it's new centre point.

So, originally I would've just done;

graphics.drawImage(image, x - (image.getWidth() / 2), y - (image.getHeight() / 2), this);

However, I'm unsure how to do it when I rotate the image using AffineTransform.

If I remember from basic Maths at school I'll need to use Cos for the X and Sin for the Y, however I've been googling for an algorithm but can't seem to come across anything.

Answer 1

I found out how to get the coordinates of the rotated point. If x1,y1 are the original coordinates and at the AffineTransform then you can get the coordinates of the rotated point in the original coordinate system with

Point2D point1origCoords = at.transform(new Point2D.Double(x1,y1),null);

The coordinates of the point in the new coordinate system after the affine transformation would be the same as the original coordinates. They stay the same because it's the coordinate system that gets transformed instead, so you need to apply the affine transformation to them.

Here is a demo of a rotation about the origin:

And the code used to generate it:

import java.awt.BasicStroke;
import java.awt.Color;
import java.awt.Font;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.geom.AffineTransform;
import java.awt.geom.Ellipse2D;
import java.awt.geom.NoninvertibleTransformException;
import java.awt.geom.Point2D;
import javax.swing.JFrame;
import javax.swing.JPanel;


public class Triangle extends JPanel {

    public void drawTriangle(Graphics2D g, 
            int x1, int y1, int x2, int y2, int x3, int y3, 
            int s, Color c, AffineTransform at) throws NoninvertibleTransformException{ 
        g.setStroke(new BasicStroke(3.0f));
        g.setPaint(c);
        int d = 10;
        g.drawLine(x1*s, y1*s, x2*s, y2*s);
        g.drawLine(x2*s, y2*s, x3*s, y3*s);
        g.drawLine(x3*s, y3*s, x1*s, y1*s);
        Ellipse2D center_of_triangle = new Ellipse2D.Double(.33*(x1+x2+x3)*s, .33*(y1+y2+y3)*s,4,4);
        g.draw(center_of_triangle);

        float dash1[] = {2.0f};
        BasicStroke dashed =
                new BasicStroke(1.0f,
                        BasicStroke.CAP_BUTT,
                        BasicStroke.JOIN_MITER,
                        10.0f, dash1, 0.0f);
        g.setStroke(dashed);

        g.drawLine(0,0,x1*s,y1*s);
        g.drawLine(0,0,x2*s,y2*s);
        g.drawLine(0,0,x3*s,y3*s);

        g.setColor(Color.black);
        Point2D point1origCoords = at.transform(new Point2D.Double(x1,y1),null);  
        Point2D point2origCoords = at.transform(new Point2D.Double(x2,y2),null);
        Point2D point3origCoords = at.transform(new Point2D.Double(x3,y3),null);
        g.drawString("("+String.format("%.2f",point1origCoords.getX())+", "
                +String.format("%.2f",point1origCoords.getY())+")",
                x1*s,y1*s+2*d);
        g.drawString("("+String.format("%.2f",point2origCoords.getX())+", "
                +String.format("%.2f",point2origCoords.getY())+")", x2*s-4*d,y2*s-d);
        g.drawString("("+String.format("%.2f",point3origCoords.getX())+", "
                +String.format("%.2f",point3origCoords.getY())+")", x3*s+d,y3*s);

        // center of the triangle
        Point2D.Double center = new Point2D.Double(.33*(x1+x2+x3), .33*(y1+y2+y3));
        Point2D centerorigCoords = at.transform(center,null);
        g.drawString("("+String.format("%.2f",centerorigCoords.getX())+", "
                +String.format("%.2f",centerorigCoords.getY())+")",
                (int)Math.round(center.x*s),(int)Math.round(center.y*s)-d);

    }

    public void drawGrid(Graphics2D g, int s) {  
        int w = getWidth();
        int h = getHeight();
        float dash1[] = {2.0f};
        BasicStroke dashed =
                new BasicStroke(1.0f,
                        BasicStroke.CAP_BUTT,
                        BasicStroke.JOIN_MITER,
                        10.0f, dash1, 0.0f);
        g.setStroke(dashed);
        g.setColor(Color.gray);

        int j = 0;
        while( j <= h ) {
            g.drawLine(0,h-j,w,h-j);
            j+=s;
        }
        j = 0;
        while( j <= w ) {
            g.drawLine(j,0,j,h);
            j+=s;
        }
    }

    public void paintComponent(Graphics g){
        final int s=20;
        Graphics2D g2 = (Graphics2D) g;
        g2.setColor(Color.black);
        Font big = new Font("Times New Roman", Font.BOLD,20);
        g2.setFont(big); 
        drawGrid(g2,s);  
        AffineTransform at = new AffineTransform();
        // no rotation
        at.rotate(Math.toRadians(0));
        g2.transform(at);
        // rotated triangle
        try {
            drawTriangle(g2,2,26,3,12,8,21,s,Color.blue,at);
        } catch (NoninvertibleTransformException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }
        at.rotate(Math.toRadians(-45));
        g2.transform(at);
        try {
            drawTriangle(g2,2,26,3,12,8,21,s,Color.magenta,at);
        } catch (NoninvertibleTransformException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }
    }

    public static void main(String[] args) {

        JFrame frame = new JFrame("Window"); //frame is the window
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        Triangle panel = new Triangle(); //panel is the graphics area where we can draw

        frame.add(panel); //put the panel inside the window
        frame.setSize(600,600); //set the window size to 600x600 pixels
        frame.setVisible(true); 
    }
}