I think CubicCurves in JavaFX don't quite work as you think they might. A JavaFX CubicCurve is a Bezier curve which is quite different from the cubic polynomials such y=x^3 you normally encounter in high school mathematics. Everything you never wanted to know about Bezier curves is here.
Bezier curves are often used for generating smooth curves in computer graphics. They are defined by start and end points and a set of control points for manipulating the curve. You can best see how it works by playing with an interactive example where you drag around the start, end and control points to form different curves.
How can one draw for example: y=x^3 ?
While it may be possible to solve the Bezier equations to reduce to a polynomial such as y=x^3, you might want to ask that question on math.stackexchange.com where the caliber of mathematicians is going to be much higher than, for instance, me.
Another way to accomplish this is to run a loop, calculating the y value for small increments of x value by applying the function to the x value, then add a LineTo for each of the calculated points in a Path. The following question and answer demonstrates this approach:
is it possible to connect one of the endpoints of the curve to another Node, so when the location of that Node changes the curve adapts to it?
Yes, try the sample application below where the curve end and control points are bound to draggable nodes. The curve adapts to the changes in the location of the anchor nodes as they are dragged around.
import javafx.application.Application;
import javafx.beans.property.DoubleProperty;
import javafx.event.EventHandler;
import javafx.scene.*;
import javafx.scene.input.MouseEvent;
import javafx.scene.paint.Color;
import javafx.scene.shape.*;
import javafx.stage.Stage;
/** Example of how a cubic curve works, drag the anchors around to change the curve. */
public class CubicCurveManipulator extends Application {
public static void main(String[] args) throws Exception { launch(args); }
@Override public void start(final Stage stage) throws Exception {
CubicCurve curve = createStartingCurve();
Line controlLine1 = new BoundLine(curve.controlX1Property(), curve.controlY1Property(), curve.startXProperty(), curve.startYProperty());
Line controlLine2 = new BoundLine(curve.controlX2Property(), curve.controlY2Property(), curve.endXProperty(), curve.endYProperty());
Anchor start = new Anchor(Color.PALEGREEN, curve.startXProperty(), curve.startYProperty());
Anchor control1 = new Anchor(Color.GOLD, curve.controlX1Property(), curve.controlY1Property());
Anchor control2 = new Anchor(Color.GOLDENROD, curve.controlX2Property(), curve.controlY2Property());
Anchor end = new Anchor(Color.TOMATO, curve.endXProperty(), curve.endYProperty());
stage.setTitle("Cubic Curve Manipulation Sample");
stage.setScene(new Scene(new Group(controlLine1, controlLine2, curve, start, control1, control2, end), 400, 400, Color.ALICEBLUE));
stage.show();
}
private CubicCurve createStartingCurve() {
CubicCurve curve = new CubicCurve();
curve.setStartX(100);
curve.setStartY(100);
curve.setControlX1(150);
curve.setControlY1(50);
curve.setControlX2(250);
curve.setControlY2(150);
curve.setEndX(300);
curve.setEndY(100);
curve.setStroke(Color.FORESTGREEN);
curve.setStrokeWidth(4);
curve.setStrokeLineCap(StrokeLineCap.ROUND);
curve.setFill(Color.CORNSILK.deriveColor(0, 1.2, 1, 0.6));
return curve;
}
class BoundLine extends Line {
BoundLine(DoubleProperty startX, DoubleProperty startY, DoubleProperty endX, DoubleProperty endY) {
startXProperty().bind(startX);
startYProperty().bind(startY);
endXProperty().bind(endX);
endYProperty().bind(endY);
setStrokeWidth(2);
setStroke(Color.GRAY.deriveColor(0, 1, 1, 0.5));
setStrokeLineCap(StrokeLineCap.BUTT);
getStrokeDashArray().setAll(10.0, 5.0);
}
}
// a draggable anchor displayed around a point.
class Anchor extends Circle {
Anchor(Color color, DoubleProperty x, DoubleProperty y) {
super(x.get(), y.get(), 10);
setFill(color.deriveColor(1, 1, 1, 0.5));
setStroke(color);
setStrokeWidth(2);
setStrokeType(StrokeType.OUTSIDE);
x.bind(centerXProperty());
y.bind(centerYProperty());
enableDrag();
}
// make a node movable by dragging it around with the mouse.
private void enableDrag() {
final Delta dragDelta = new Delta();
setOnMousePressed(new EventHandler<MouseEvent>() {
@Override public void handle(MouseEvent mouseEvent) {
// record a delta distance for the drag and drop operation.
dragDelta.x = getCenterX() - mouseEvent.getX();
dragDelta.y = getCenterY() - mouseEvent.getY();
getScene().setCursor(Cursor.MOVE);
}
});
setOnMouseReleased(new EventHandler<MouseEvent>() {
@Override public void handle(MouseEvent mouseEvent) {
getScene().setCursor(Cursor.HAND);
}
});
setOnMouseDragged(new EventHandler<MouseEvent>() {
@Override public void handle(MouseEvent mouseEvent) {
double newX = mouseEvent.getX() + dragDelta.x;
if (newX > 0 && newX < getScene().getWidth()) {
setCenterX(newX);
}
double newY = mouseEvent.getY() + dragDelta.y;
if (newY > 0 && newY < getScene().getHeight()) {
setCenterY(newY);
}
}
});
setOnMouseEntered(new EventHandler<MouseEvent>() {
@Override public void handle(MouseEvent mouseEvent) {
if (!mouseEvent.isPrimaryButtonDown()) {
getScene().setCursor(Cursor.HAND);
}
}
});
setOnMouseExited(new EventHandler<MouseEvent>() {
@Override public void handle(MouseEvent mouseEvent) {
if (!mouseEvent.isPrimaryButtonDown()) {
getScene().setCursor(Cursor.DEFAULT);
}
}
});
}
// records relative x and y co-ordinates.
private class Delta { double x, y; }
}
}
Sample Program output:
