import java.awt.*;

public class BezierCurve {

	final double EPSILON = 0.025;	

	final private int X = 0;
	final private int Y = 1;

	final private int A = 0;
	final private int B = 1;
	final private int C = 2;
	final private int D = 3;

	int[][] p = new int[4][2];	// POINTS
	int[][] c = new int[4][2];	// POLYNOMIAL COEFFICIENTS 

	private int[][] bezierMatrix = 	{
						{-1,  3, -3,  1},
						{ 3, -6,  3,  0},
						{-3,  3,  0,  0},
						{ 1,  0,  0,  0}
					};

	public BezierCurve () {
		
	}

	// set the 4 points of the bezier curve
	public void setPoints(int p0x, int p0y, int p1x, int p1y, int p2x, int p2y, int p3x, int p3y) {
		p[0][X] = p0x;
		p[0][Y] = p0y;

		p[1][X] = p1x;
		p[1][Y] = p1y;

		p[2][X] = p2x;
		p[2][Y] = p2y;

		p[3][X] = p3x;
		p[3][Y] = p3y;

		setCoefficients();
	}

	// draws the coordinates of a point next to that point
	public void writeCoordinates(Graphics g) {
		g.setColor(Color.ORANGE);
		for (int i = 0; i < 4; i++) {
			g.drawString("(" + p[i][X] + ", " + p[i][Y] + ")", p[i][X] + 8, p[i][Y]);
		}
	}

	// draw lines connecting the 4 points
	public void drawGuidelines(Graphics g) {
		g.setColor(Color.GREEN);
	
		g.drawLine(p[0][X], p[0][Y], p[1][X], p[1][Y]);
		g.drawLine(p[1][X], p[1][Y], p[2][X], p[2][Y]);
		g.drawLine(p[2][X], p[2][Y], p[3][X], p[3][Y]);
	}

	// draw the bezier curve
	public void drawCurve(Graphics g) {
		g.setColor(Color.BLACK);
		for (double t = 0 ; t <= 1 ; t += EPSILON) {
			g.drawLine((int)X(t), (int)Y(t), (int)X(t+EPSILON), (int)Y(t+EPSILON));
		}
	}

	// draw a circle around the 4 points defining the curve
	public void drawPoints(Graphics g) {
		for (int i = 0; i < 4; i++) {
			if (i == 0 || i == 3) {
				g.setColor(Color.BLUE);
				g.fillOval(p[i][X] - 5, p[i][Y] - 5, 10, 10);
			}
			else {
				g.setColor(Color.RED);
				g.drawOval(p[i][X] - 5, p[i][Y] - 5, 10, 10);
			}
		}
	}

	// set coordinate of point n to (x, y)
	public void setPoint(int n, int x, int y) {
		p[n][X] = x;
		p[n][Y] = y;
		setCoefficients();
	}

	// get (x, y) coordinates of point n
	public int[] getPoint(int n) {
		int[] coordinates = {p[n][X], p[n][Y]};

		return coordinates;
	}

	// calculate x(t) = Ax*t^3 + Bx*t^2 + Cx*t + Dx
	public double X(double t) {
		return t * ( t * ( t * c[A][X] + c[B][X]) + c[C][X]) + c[D][X];
	}

	// calculate y(t) = Ay*t^3 + By*t^2 + Cy*t + Dy
	public double Y(double t) {
		return t * ( t * ( t * c[A][Y] + c[B][Y]) + c[C][Y]) + c[D][Y];
	}

	// calculate the coefficients
	// multiply the Bezier matrix by the matrix defined by the x values of 4 points
	// multiply the Bezier matrix by the matrix defined by the y values of 4 points
	public void setCoefficients() {
		c[A][X] = 	bezierMatrix[0][0] * p[0][X]
				 + bezierMatrix[0][1] * p[1][X]
				 + bezierMatrix[0][2] * p[2][X]
				 + bezierMatrix[0][3] * p[3][X];

		c[B][X] = 	bezierMatrix[1][0] * p[0][X]
				 + bezierMatrix[1][1] * p[1][X]
				 + bezierMatrix[1][2] * p[2][X]
				 + bezierMatrix[1][3] * p[3][X];

		c[C][X] = 	bezierMatrix[2][0] * p[0][X]
				 + bezierMatrix[2][1] * p[1][X]
				 + bezierMatrix[2][2] * p[2][X]
				 + bezierMatrix[2][3] * p[3][X];

		c[D][X] = 	bezierMatrix[3][0] * p[0][X]
				 + bezierMatrix[3][1] * p[1][X]
				 + bezierMatrix[3][2] * p[2][X]
				 + bezierMatrix[3][3] * p[3][X];
				
		c[A][Y] = 	bezierMatrix[0][0] * p[0][Y]
				 + bezierMatrix[0][1] * p[1][Y]
				 + bezierMatrix[0][2] * p[2][Y]
				 + bezierMatrix[0][3] * p[3][Y];

		c[B][Y] = 	bezierMatrix[1][0] * p[0][Y]
				 + bezierMatrix[1][1] * p[1][Y]
				 + bezierMatrix[1][2] * p[2][Y]
				 + bezierMatrix[1][3] * p[3][Y];

		c[C][Y] = 	bezierMatrix[2][0] * p[0][Y]
				 + bezierMatrix[2][1] * p[1][Y]
				 + bezierMatrix[2][2] * p[2][Y]
				 + bezierMatrix[2][3] * p[3][Y];

		c[D][Y] = 	bezierMatrix[3][0] * p[0][Y]
				 + bezierMatrix[3][1] * p[1][Y]
				 + bezierMatrix[3][2] * p[2][Y]
				 + bezierMatrix[3][3] * p[3][Y];
	}

}