An application which simulates a simple flip of a page in a book. Ported from C# - https://github.com/hetelek/BookFlip

BookFlip.java

import java.awt.Color;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.Point;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;
import javax.swing.JFrame;
import javax.swing.JPanel;

// Ported from C# - https://github.com/hetelek/BookFlip

class MainForm
{
	public static void main(String[] args)
	{
		JFrame frame = new JFrame("BookFlip");
		frame.add(new BookFlip());
		frame.setSize(200, 200);
		frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
		frame.setVisible(true);
	}
}

public class BookFlip extends JPanel
{
	static final boolean POLYGON_MODE = true;
	MouseHandler mouseHandler = new MouseHandler();
	Point creaseOrigin, bottomRight, mousePoint;
	int pageWidth, pageHeight;
	boolean isBendingPaper;
	
	public BookFlip()
	{
		super();
		
		this.addMouseListener(mouseHandler);
		this.addMouseMotionListener(mouseHandler);
	}
	
	private void redrawPanel(Graphics2D g)
	{
		pageWidth = this.getWidth() / 2;
		pageHeight = this.getHeight();
		bottomRight = new Point(this.getWidth(), pageHeight);
		creaseOrigin = new Point(pageWidth, pageHeight);
		
		drawPages(g);
	}
	
	private void drawPages(Graphics2D g)
	{
		g.clearRect(0, 0, this.getWidth(), this.getHeight());
		
		g.setColor(Color.BLUE);
		g.fillRect(0, 0, pageWidth, pageHeight);
		
		g.setColor(Color.RED);
		g.fillRect(pageWidth, 0, pageWidth, pageHeight);
	}
	
	@Override
	public void paintComponent(Graphics g)
	{
		super.paintComponent(g);
		
		Graphics2D g2d = (Graphics2D)g;
		this.redrawPanel(g2d);
		
		if (isBendingPaper)
		{
			double distance = getDistance(mousePoint, creaseOrigin);
			if (distance > pageWidth)
				mousePoint = getClosestPointOnCircle(mousePoint);
			
			if (mousePoint.y >= pageHeight)
				return;
			
			Point midpoint = getMidpoint(mousePoint, bottomRight);
			
			double m = -(double)(mousePoint.x - bottomRight.x) / (mousePoint.y - bottomRight.y);
			double b = -((m * midpoint.x) - midpoint.y);
			double x = (pageHeight - b) / m;
			
			int yForEdgePoint = (int)(m * (pageWidth * 2) + b);
			
			Point bottomPoint = new Point((int)x, pageHeight);
			Point rightEdgePoint = new Point(pageWidth * 2, yForEdgePoint);

			g2d.setColor(Color.GREEN);
			if (POLYGON_MODE)
			{
				int[] xPoints = { rightEdgePoint.x, mousePoint.x, bottomPoint.x };
				int[] yPoints = { rightEdgePoint.y, mousePoint.y, bottomPoint.y };
				
				g2d.fillPolygon(xPoints, yPoints, xPoints.length);
				
				xPoints[1] = bottomRight.x;
				yPoints[1] = bottomRight.y;
				
				g2d.setColor(Color.YELLOW);
				g2d.fillPolygon(xPoints, yPoints, xPoints.length);
			}
			else
			{
				g2d.drawLine(rightEdgePoint.x, rightEdgePoint.y, bottomPoint.x, bottomPoint.y);
				g2d.drawLine(mousePoint.x, mousePoint.y, bottomPoint.x, bottomPoint.y);
				g2d.drawLine(mousePoint.x, mousePoint.y, rightEdgePoint.x, rightEdgePoint.y);
			}
			isBendingPaper = false;
		}
	}
	
	private Point getMidpoint(Point p1, Point p2)
	{
		int x = (p1.x + p2.x) / 2;
		int y = (p1.y + p2.y) / 2;
		return new Point(x, y);
	}
	
	private double getDistance(Point p1, Point p2)
	{
		double x = Math.pow(p2.x - p1.x, 2);
		double y = Math.pow(p2.y - p1.y, 2);
		return Math.sqrt(x + y);
	}
	
	private Point getClosestPointOnCircle(Point p)
	{
		// no idea how this works, source below
		// http://stackoverflow.com/questions/300871/best-way-to-find-a-point-on-a-circle-closest-to-a-given-point
		double vX = p.x - creaseOrigin.x;
		double vY = p.y - creaseOrigin.y;
		double magV = Math.sqrt(vX * vX + vY * vY);
		double aX = creaseOrigin.x + vX / magV * pageWidth;
		double aY = creaseOrigin.y + vY / magV * pageWidth;
		
		return new Point((int)aX, (int)aY);
	}
	
	private class MouseHandler extends MouseAdapter
	{	
		@Override
		public void mouseDragged(MouseEvent e)
		{
			mousePoint = new Point(e.getX(), e.getY());
			isBendingPaper = true;
			repaint();
		}
		
		@Override
		public void mouseReleased(MouseEvent e)
		{
			mousePoint = new Point(e.getX(), e.getY());
			isBendingPaper = false;
			repaint();
		}
	}
}