Using Quadratic Eq for a Half Circle

Question

Does any math minded forumer know how to fit a
QuadCurve2D to half a circle?
I made an app to test it out but no matter where i placed the
three points i couldnt get a fit over a circle.
It seems like the sides always "slump" down too much.
The problem im trying to solve is...
I have three points on a half circle in 3D space (so, with x, y, z):
A start point, 90 degs, and 180 degrees.
I need to find a java curve that can connect those three points
in a "circle" type way.
Like i said before, quad never seemed to line up - though i
would have thought that was the way to do this.
And before anyone chimes in with "use arc"... this half circle will
be rotated in every which way in three space so im looking for a
curve that will connect those three points retaining shape.
Im thinking about just making the circle a hexagon and then rotating
the points and connecting the points for a jagged edge -
but id prefer not to do this.
Id appreciate any advice, Thanks!
i found a site with an applet to play with these curves
http://www.doc.ic.ac.uk/~dfg/AndysSplineTutorial/Quadratic.html

Answer 1

apparently this is as close as you will get to matching a bezier
curve to a half circle but its VERY damned close.
play around with the iterations for cool curve effects.
enjoy.
import javax.swing.*;
import javax.swing.event.*;
import java.awt.*;
import java.awt.event.*;
import java.awt.geom.*;
public class BezierTest{
public static void main(String[] args) {
     new BezierTest();
public BezierTest(){
//     fr.addMouseListener(this);
//     fr.addMouseMotionListener(this);
     displayFrame();
public void displayFrame(){
     fr.setContentPane(panel);
     fr.pack();
     fr.setLocationRelativeTo(null);
     fr.show();
public class Panel extends JPanel{
public Panel(){
     this.setPreferredSize(new Dimension(500, 500));
     this.setBackground(Color.white);
public void paintComponent(Graphics gr){
     super.paintComponent(gr);
     Graphics2D g = (Graphics2D)gr;
     // Points
     Point P1 = new Point(50, 300);
     Point P2 = new Point(450, 300);
     Point C1 = new Point(50, 34);
     Point C2 = new Point(450, 34);
     // circle
     g.setPaint(Color.black);
     g.drawOval(50, 100, 400, 400);
     // real curve
     g.setPaint(Color.red);
     cc.setCurve(P1, C1, C2, P2);
     g.draw(cc);
     // iterated curve
     g.setPaint(Color.black);
     double x1 = P1.x;
     double y1 = P1.y;
     double x2;
     double y2;
     double z = .5;
//     for(double z = .1; z <= .5; z = z + .1){
     for(double t = 0; t <= 1; t = t + z){
     x2 =
     (P1.x + t * (-P1.x * 3 + t * (3 * P1.x - P1.x * t))) +
     t * (3 * C1.x + t * (-6 * C1.x + C1.x * 3 * t)) +
     t * t * (C2.x * 3 - C2.x * 3 * t) +
     P2.x * t * t * t;
     y2 =
     (P1.y + t * (-P1.y * 3 + t * (3 * P1.y - P1.y * t))) +
     t * (3 * C1.y + t * (-6 * C1.y + C1.y * 3 * t)) +
     t * t * (C2.y * 3 - C2.y * 3 * t) +
     P2.y * t * t * t;
System.out.println("X: " + x2);
System.out.println("Y: " + y2);
System.out.println("\n");
     g.drawLine((int)x1, (int)y1, (int)x2, (int)y2);
     x1 = x2;
     y1 = y2;
     CubicCurve2D cc = new CubicCurve2D.Double();
     JFrame fr = new JFrame("Bezier Test");
     Panel panel = new Panel();
}