Develop Reference

on Javafx, Is there any way to draw a regular polygon without knowing the coordinates of all points(but merely knowing the number of sides?)

So for example, to draw a regular dodecagon on Javafx, you have to know all the coordinates of 12 points. But I was wondering if there's any way to draw it without knowing the coordinates of the points(but merely knowing that there are 12 sides for that polygon) so that if the user types '6', then it draws a regular hexagon and if the user types '12', it draws a regular dodecagon.

No, it's impossible to draw a polygon without knowing the the coordinates of the corners. How would such a object be rendered without the rendering engine knowing the coordinates of the vertices it needs to render?
You can of course calculate the coordinates of the points of a regular polygon given a center point, the distance of the corners from the center and the angle of one of the corners from the center point by convertion polar coordinates to cartesian coordinates:
private static void setPolygonSides(Polygon polygon, double centerX, double centerY, double radius, int sides) {
polygon.getPoints().clear();
final double angleStep = Math.PI * 2 / sides;
double angle = 0; // assumes one point is located directly beneat the center point
for (int i = 0; i < sides; i++, angle += angleStep) {
polygon.getPoints().addAll(
Math.sin(angle) * radius + centerX, // x coordinate of the corner
Math.cos(angle) * radius + centerY // y coordinate of the corner
);
}
}
#Override
public void start(Stage primaryStage) {
Spinner<Integer> spinner = new Spinner(3, Integer.MAX_VALUE, 3);
Polygon polygon = new Polygon();
setPolygonSides(polygon, 200, 200, 150, spinner.getValue());
spinner.valueProperty().addListener((observable, oldValue, newValue) -> {
setPolygonSides(polygon, 200, 200, 150, spinner.getValue());
});
StackPane stackPane = new StackPane(polygon);
stackPane.setPrefSize(400, 400);
HBox root = new HBox(spinner, stackPane);
Scene scene = new Scene(root);
primaryStage.setScene(scene);
primaryStage.show();
}

How to use AffineTransform with very little coordinates?

I have a set of two dimensions points. Their X and Y are greater than -2 and lesser than 2. Such point could be : (-0.00012 ; 1.2334 ).
I would want to display these points on a graph, using rectangles (a rectangle illustrates a point, and has its coordinates set to its point's ones - moreover, it has a size of 10*10).
Rectangles like (... ; Y) should be displayed above any rectangles like (... ; Y-1) (positive Y direction is up). Thus, I must set the graph's origin not at the top-left hand-corner, but somewhere else.
I'm trying to use Graphics2D's AffineTransform to do that.
I get the minimal value for all the X coordinates
I get the minimal value for all the Y coordinates
I get the maximal value for all the X coordinates
I get the maximal value for all the Y coordinates
I get the distance xmax-xmin and ymax-ymin
Then, I wrote the code I give you below.
Screenshots
Some days ago, using my own method to scale, I had this graph:
(so as I explained, Y are inverted and that's not a good thing)
For the moment, i.e., with the code I give you below, I have only one point that takes all the graph's place! Not good at all.
I would want to have:
(without lines, and without graph's axis. The important here is that points are correctly displayed, according to their coordinates).
Code
To get min and max coordinates value:
x_min = Double.parseDouble((String) list_all_points.get(0).get(0));
x_max = Double.parseDouble((String) list_all_points.get(0).get(0));
y_min = Double.parseDouble((String) list_all_points.get(0).get(1));
y_max = Double.parseDouble((String) list_all_points.get(0).get(1));
for(StorableData s : list_all_points) {
if(Double.parseDouble((String) s.get(0)) < x_min) {
x_min = Double.parseDouble((String) s.get(0));
}
if(Double.parseDouble((String) s.get(0)) > x_max) {
x_max = Double.parseDouble((String) s.get(0));
}
if(Double.parseDouble((String) s.get(1)) < y_min) {
y_min = Double.parseDouble((String) s.get(1));
}
if(Double.parseDouble((String) s.get(1)) > y_max) {
y_max = Double.parseDouble((String) s.get(1));
}
}
To draw a point:
int x, y;
private void drawPoint(Cupple storable_data) {
//x = (int) (storable_data.getNumber(0) * scaling_coef + move_x);
//y = (int) (storable_data.getNumber(1) * scaling_coef + move_y);
x = storable_data.getNumber(0).intValue();
y = storable_data.getNumber(1).intValue();
graphics.fillRect(x, y, 10, 10);
graphics.drawString(storable_data.toString(), x - 5, y - 5);
}
To paint the graph:
#Override
public void paint(Graphics graphics) {
this.graphics = graphics;
Graphics2D graphics_2d = ((Graphics2D) this.graphics);
AffineTransform affine_transform = graphics_2d.getTransform();
affine_transform.scale(getWidth()/(x_max - x_min), getHeight()/(y_max - y_min));
affine_transform.translate(x_min, y_min);
graphics_2d.transform(affine_transform);
for(StorableData storable_data : list_all_points) {
graphics_2d.setColor(Color.WHITE);
this.drawPoint((Cupple) storable_data);
}

I suggest you map each data point to a point on the screen, thus avoiding the following coordinate system pitfalls. Take your list of points and create from them a list of points to draw. Take into account that:
The drawing is pixel-based, so you will want to scale your points (or you would have rectangles 1 to 4 pixels wide...).
You will need to translate all your points because negative values will be outside the boundaries of the component on which you draw.
The direction of the y axis is reversed in the drawing coordinates.
Once that is done, use the new list of points for the drawing and the initial one for calculations. Here is an example:
public class Graph extends JPanel {
private static int gridSize = 6;
private static int scale = 100;
private static int size = gridSize * scale;
private static int translate = size / 2;
private static int pointSize = 10;
List<Point> dataPoints, scaledPoints;
Graph() {
setBackground(Color.WHITE);
// points taken from your example
Point p1 = new Point(-1, -2);
Point p2 = new Point(-1, 0);
Point p3 = new Point(1, 0);
Point p4 = new Point(1, -2);
dataPoints = Arrays.asList(p1, p2, p3, p4);
scaledPoints = dataPoints.stream()
.map(p -> new Point(p.x * scale + translate, -p.y * scale + translate))
.collect(Collectors.toList());
}
#Override
public Dimension getPreferredSize() {
return new Dimension(size, size);
}
#Override
protected void paintComponent(Graphics g) {
super.paintComponent(g);
Graphics2D g2d = (Graphics2D) g;
// draw a grid
for (int i = 0; i < gridSize; i++) {
g2d.drawLine(i * scale, 0, i * scale, size);
g2d.drawLine(0, i * scale, size, i * scale);
}
// draw the rectangle
g2d.setPaint(Color.RED);
g2d.drawPolygon(scaledPoints.stream().mapToInt(p -> p.x).toArray(),
scaledPoints.stream().mapToInt(p -> p.y).toArray(),
scaledPoints.size());
// draw the points
g2d.setPaint(Color.BLUE);
// origin
g2d.fillRect(translate, translate, pointSize, pointSize);
g2d.drawString("(0, 0)", translate, translate);
// data
for (int i = 0; i < dataPoints.size(); i++) {
Point sp = scaledPoints.get(i);
Point dp = dataPoints.get(i);
g2d.fillRect(sp.x, sp.y, pointSize, pointSize);
g2d.drawString("(" + dp.x + ", " + dp.y + ")", sp.x, sp.y);
}
}
public static void main(String[] args) {
JFrame frame = new JFrame();
frame.setContentPane(new Graph());
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
frame.pack();
frame.setLocationRelativeTo(null);
frame.setVisible(true);
}
}
And another:
You might want to have the points aligned on the grid intersections and not below and to the right of them. I trust you will figure this one out.
Also, I ordered the points so that drawPolygon will paint the lines in the correct order. If your points are arbitrarily arranged, look for ways to find the outline. If you want lines between all points like in your example, iterate over all combinations of them with drawLine.

3D Scatter Chart JavaFX: How to show legend and measures near axis

Looking this post, I've tried to implement in javaFX, with many difficulties, a Scatter Chart 3D where the grid is my x,y and z axis and the spheres are my points.
How Can I put a legend, axis labels and the range numbers along the axis? I can use only javaFX without external library.
I'm desperate.. I'm trying for days..without results
Please:help me
Thanks.
Code
import java.util.ArrayList;
import java.util.List;
import java.util.Random;
import javafx.application.Application;
import javafx.event.EventHandler;
import javafx.scene.Group;
import javafx.scene.PerspectiveCamera;
import javafx.scene.Scene;
import javafx.scene.SceneAntialiasing;
import javafx.scene.input.ScrollEvent;
import javafx.scene.layout.Pane;
import javafx.scene.layout.StackPane;
import javafx.scene.paint.Color;
import javafx.scene.paint.Paint;
import javafx.scene.paint.PhongMaterial;
import javafx.scene.shape.Line;
import javafx.scene.shape.Rectangle;
import javafx.scene.shape.Sphere;
import javafx.scene.transform.Rotate;
import javafx.stage.Stage;
public class GraphingData extends Application {
private static Random rnd = new Random();
// size of graph
int graphSize = 400;
// variables for mouse interaction
private double mousePosX, mousePosY;
private double mouseOldX, mouseOldY;
private final Rotate rotateX = new Rotate(150, Rotate.X_AXIS);
private final Rotate rotateY = new Rotate(120, Rotate.Y_AXIS);
#Override
public void start(Stage primaryStage) {
// create axis walls
Group grid = createGrid(graphSize);
// initial cube rotation
grid.getTransforms().addAll(rotateX, rotateY);
// add objects to scene
StackPane root = new StackPane();
root.getChildren().add(grid);
root.setStyle( "-fx-border-color: red;");
// create bars
double gridSizeHalf = graphSize / 2;
double size = 30;
//Drawing a Sphere
Sphere sphere = new Sphere();
//Setting the properties of the Sphere
sphere.setRadius(10.0);
sphere.setTranslateX(-50);
sphere.setTranslateY(-50);
//Preparing the phong material of type specular color
PhongMaterial material6 = new PhongMaterial();
//setting the specular color map to the material
material6.setDiffuseColor(Color.GREEN);
sphere.setMaterial(material6);
grid.getChildren().addAll(sphere);
// scene
Scene scene = new Scene(root, 1600, 900, true, SceneAntialiasing.BALANCED);
scene.setCamera(new PerspectiveCamera());
scene.setOnMousePressed(me -> {
mouseOldX = me.getSceneX();
mouseOldY = me.getSceneY();
});
scene.setOnMouseDragged(me -> {
mousePosX = me.getSceneX();
mousePosY = me.getSceneY();
rotateX.setAngle(rotateX.getAngle() - (mousePosY - mouseOldY));
rotateY.setAngle(rotateY.getAngle() + (mousePosX - mouseOldX));
mouseOldX = mousePosX;
mouseOldY = mousePosY;
});
makeZoomable(root);
primaryStage.setResizable(false);
primaryStage.setScene(scene);
primaryStage.show();
}
/**
* Axis wall
*/
public static class Axis extends Pane {
Rectangle wall;
public Axis(double size) {
// wall
// first the wall, then the lines => overlapping of lines over walls
// works
wall = new Rectangle(size, size);
getChildren().add(wall);
// grid
double zTranslate = 0;
double lineWidth = 1.0;
Color gridColor = Color.RED;
for (int y = 0; y <= size; y += size / 10) {
Line line = new Line(0, 0, size, 0);
line.setStroke(gridColor);
line.setFill(gridColor);
line.setTranslateY(y);
line.setTranslateZ(zTranslate);
line.setStrokeWidth(lineWidth);
getChildren().addAll(line);
}
for (int x = 0; x <= size; x += size / 10) {
Line line = new Line(0, 0, 0, size);
line.setStroke(gridColor);
line.setFill(gridColor);
line.setTranslateX(x);
line.setTranslateZ(zTranslate);
line.setStrokeWidth(lineWidth);
getChildren().addAll(line);
}
}
public void setFill(Paint paint) {
wall.setFill(paint);
}
}
public void makeZoomable(StackPane control) {
final double MAX_SCALE = 20.0;
final double MIN_SCALE = 0.1;
control.addEventFilter(ScrollEvent.ANY, new EventHandler<ScrollEvent>() {
#Override
public void handle(ScrollEvent event) {
double delta = 1.2;
double scale = control.getScaleX();
if (event.getDeltaY() < 0) {
scale /= delta;
} else {
scale *= delta;
}
scale = clamp(scale, MIN_SCALE, MAX_SCALE);
control.setScaleX(scale);
control.setScaleY(scale);
event.consume();
}
});
}
/**
* Create axis walls
*
* #param size
* #return
*/
private Group createGrid(int size) {
Group cube = new Group();
// size of the cube
Color color = Color.LIGHTGRAY;
List<Axis> cubeFaces = new ArrayList<>();
Axis r;
// back face
r = new Axis(size);
r.setFill(color.deriveColor(0.0, 1.0, (1 - 0.5 * 1), 1.0));
r.setTranslateX(-0.5 * size);
r.setTranslateY(-0.5 * size);
r.setTranslateZ(0.5 * size);
cubeFaces.add(r);
// bottom face
r = new Axis(size);
r.setFill(color.deriveColor(0.0, 1.0, (1 - 0.4 * 1), 1.0));
r.setTranslateX(-0.5 * size);
r.setTranslateY(0);
r.setRotationAxis(Rotate.X_AXIS);
r.setRotate(90);
cubeFaces.add(r);
// right face
r = new Axis(size);
r.setFill(color.deriveColor(0.0, 1.0, (1 - 0.3 * 1), 1.0));
r.setTranslateX(-1 * size);
r.setTranslateY(-0.5 * size);
r.setRotationAxis(Rotate.Y_AXIS);
r.setRotate(90);
// cubeFaces.add( r);
// left face
r = new Axis(size);
r.setFill(color.deriveColor(0.0, 1.0, (1 - 0.2 * 1), 1.0));
r.setTranslateX(0);
r.setTranslateY(-0.5 * size);
r.setRotationAxis(Rotate.Y_AXIS);
r.setRotate(90);
cubeFaces.add(r);
// top face
r = new Axis(size);
r.setFill(color.deriveColor(0.0, 1.0, (1 - 0.1 * 1), 1.0));
r.setTranslateX(-0.5 * size);
r.setTranslateY(-1 * size);
r.setRotationAxis(Rotate.X_AXIS);
r.setRotate(90);
// cubeFaces.add( r);
// front face
r = new Axis(size);
r.setFill(color.deriveColor(0.0, 1.0, (1 - 0.1 * 1), 1.0));
r.setTranslateX(-0.5 * size);
r.setTranslateY(-0.5 * size);
r.setTranslateZ(-0.5 * size);
// cubeFaces.add( r);
cube.getChildren().addAll(cubeFaces);
return cube;
}
public static double normalizeValue(double value, double min, double max, double newMin, double newMax) {
return (value - min) * (newMax - newMin) / (max - min) + newMin;
}
public static double clamp(double value, double min, double max) {
if (Double.compare(value, min) < 0)
return min;
if (Double.compare(value, max) > 0)
return max;
return value;
}
public static Color randomColor() {
return Color.rgb(rnd.nextInt(255), rnd.nextInt(255), rnd.nextInt(255));
}
public static void main(String[] args) {
launch(args);
}
}

Here's a basic idea to create some measures on the axes. It is not production-ready but should give you enough to start with.
private Group createGrid(int size) {
// existing code omitted...
cube.getChildren().addAll(cubeFaces);
double gridSizeHalf = size / 2;
double labelOffset = 30 ;
double labelPos = gridSizeHalf - labelOffset ;
for (double coord = -gridSizeHalf ; coord < gridSizeHalf ; coord+=50) {
Text xLabel = new Text(coord, labelPos, String.format("%.0f", coord));
xLabel.setTranslateZ(labelPos);
xLabel.setScaleX(-1);
Text yLabel = new Text(labelPos, coord, String.format("%.0f", coord));
yLabel.setTranslateZ(labelPos);
yLabel.setScaleX(-1);
Text zLabel = new Text(labelPos, labelPos, String.format("%.0f", coord));
zLabel.setTranslateZ(coord);
cube.getChildren().addAll(xLabel, yLabel, zLabel);
zLabel.setScaleX(-1);
}
return cube;
}
I would just place a legend outside the graph, which would just be a 2D grid pane not rotating...

I know this question is getting old but 2D labels in a JavaFX 3D scene is a topic that comes up a lot and I never see it answered "the right way".
Translating the labels like in James_D's answer will translate into 3D space a 2D label which will look correct until you move the camera. Assuming you want a scatter chart that doesn't move or rotate then this will be fine. Other wise you will need to automatically transform the 2D labels whenever you move your camera. (ie... the mouse handler). You could remove your scatter chart and readd the whole thing to the scene each time but that will be murder on your heap memory and won't be feasible for data sets of any real useful size.
The right way to do it is to use OpenGL or DirectDraw text renders which redraw the labels on each render loop pass but JavaFX 3D doesn't give you access (currently). So the "right way in JavaFX" is to float 2D labels on top of a 3D subscene and then translate them whenever the camera moves. This requires that you transform the 3D coordinate projection of the 3D location you want the label to a 2D screen projection.
To generically manage 2D labels connected to a Point3D in JavaFX 3D you need to do a transform along the following:
Point3D coordinates = node.localToScene(javafx.geometry.Point3D.ZERO);
SubScene oldSubScene = NodeHelper.getSubScene(node);
coordinates = SceneUtils.subSceneToScene(oldSubScene, coordinates);
double x = coordinates.getX();
double y = coordinates.getY();
label.getTransforms().setAll(new Translate(x, y));
Where the node is some actual 3D object already in the 3D subscene. For my applications I simply use a Sphere of an extremely small size it cannot be seen. If you were to follow James_D's example, you could translate the sphere(s) to the same locations that you translated the original axis labels.
The label is a standard JavaFX 2D label that you add to your scene... typically through a StackPane such that the labels are floating on top of the 3D subscene.
Now whenever the camera moves/rotates, this causes this transform to be called which slides the label on the 2D layer. Without direct access to the underlying GL or DD calls this is pretty much the only way to do something like this in JavaFX 3D but it works pretty well.
Here is a video example of it working.
Here is an open source example of implementing a simple version of floating 2D labels. (Warning, I'm the contributing author for the sample, not trying to promote the library.)

Java: Drawing "Random" Stars

I'm trying to take this code I finally got working for drawing one star and am confused on how to get it working for drawing 25 different stars (such as different sides and spikinness but I am unsure how to go about it exactly. I assume I would make a new random variable int randomStars = (int)(Math.random()*25+1); // Variable for 25 Random Stars to randomly generate the stars but I'm kind of confused where to take it from there.
I'd appreciate the help.
My Code (Using DrawingPanel.java):
import java.awt.*;
public class StarSampler {
public static void main(String[] args)
{
DrawingPanel panel = new DrawingPanel(500, 500);
Graphics2D g = panel.getGraphics();
g.setColor(Color.BLUE);
panel.setBackground(new Color(250, 0, 0));
fillStar(g, 250, 250, 150, 5, .3); // How to rotate it to start at center?
}
public static void fillStar(Graphics2D g, int ctrX, int ctrY, int radius, int nPoints, double spikiness)
{
double xDouble[] = new double[2*nPoints];
double yDouble[] = new double[2*nPoints];
int xPoint[] = new int[2*nPoints];
int yPoint[] = new int[2*nPoints];
nPoints = (int) (nPoints * 2);
int randomStars = (int)(Math.random()*25+1); // Variable for 25 Random Stars
// Would Nestest loop go here? for (randomStars++; randomStars < 25; randomStars++)
for (int i = 0; i < nPoints; i++)
{
double iRadius = (i % 2 == 0) ? radius : (radius * spikiness);
double angle = (270) + (i * 360.0) / (nPoints);
xPoint[i] = (int) (ctrX + iRadius * Math.cos(Math.toRadians(angle)));
yPoint[i] = (int) (ctrY + iRadius * Math.sin(Math.toRadians(angle)));
}
g.fillPolygon(xPoint, yPoint, nPoints); // Creates polygon
}
}
My Output:

Build up slowly. First concentrate on positioning two stars, just two. Pick the coordinates for the centre of the stars and place them. Adjust to get it right (your first attempt will probably have errors). Test, fix, test again, fix again. Repeat.
Then play with the spikiness and other changes so the stars aren't identical. When, and only when, that is tested and working move on to three, four etc. stars. With more stars you will have to be more careful to avoid overlaps.

Algorithm to verify if a shape is inside another - javafx

I have a rectangular and circle. I need to verify whether a rectangle is inside that circle.
I tried to Shape.intersects but intersects is checked the number 1.
Does anyone know this kind of algorithm in javafx?
Just to exemplifly, in the figure only rectangles 1, 2, 3, and 4 are inside the circle.
thanks for your help.

Solution
The basic idea behind this solution is that any polygon is contained within any convex (see comments) shape iff every point within the polygon is within the shape. The intersects() method that you're attempting to use returns true if at least one point of the polygon is within the shape. You've already figured out that it'll work, but it'll also offer false positives for any partially-intersected shapes. To fix it, we define our own intersection test which looks at all points.
This can be generalized to scan any given polygon for "total intersection" with any given shape:
public boolean totalIntersects(Polygon poly, Shape testShape) {
List<Point> points = flatDoublesToPoints(poly.getPoints());
boolean inside = true; // If this is false after testing all points, the poly has at least one point outside of the shape.
for(Point point : points) {
if(!testShape.intersects(point.x, point.y, 1, 1)) { // The 3rd and 4th parameters here are "width" and "height". 1 for a point.
inside = false;
}
}
return inside;
}
where flatDoublesToPoints() and Point are defined as:
private List<Point> flatDoublesToPoints(List<Double> flatDoubles) {
List<Point> points = new ArrayList<>();
for(int i = 0; i < flatDoubles.size(); i += 2) {
points.add(new Point(flatDoubles.get(i), flatDoubles.get(i + 1)));
}
return points;
}
class Point {
public double x, y;
public Point(double x, double y) {
this.x = x;
this.y = y;
}
}
flatDoublesToPoints() is needed to split the "flat" {x1, y1, x2, y2, x3, y3...} polygon lists into a more easy-to-understand data structure. If you're doing tons of comparisons, it may be helpful to skip this step, however, and operate on the "flat list" directly for memory reasons.
Application
The following applies the other methods to a situation extremely similar to yours. (Not exact, because I didn't have your code.)
public class Main extends Application {
public static final int SIZE = 600;
#Override
public void start(Stage primaryStage) throws Exception {
Pane rootPane = new Pane();
List<Rectangle> rects = new ArrayList<>();
for (int j = 0; j < 2; j++) {
for(int i = 0; i < 5; i++) {
Rectangle r = new Rectangle(i * 100, j == 0 ? 0 : 300, 100, 200);
r.setFill(Color.BEIGE);
r.setStroke(Color.BLACK);
rects.add(r);
}
}
rootPane.getChildren().addAll(rects);
Circle circle = new Circle(350, 100, 200);
circle.setStroke(Color.BLACK);
circle.setFill(null);
rootPane.getChildren().add(circle);
List<Polygon> polys = new ArrayList<>();
for(Rectangle rect : rects) {
polys.add(rectangleToPolygon(rect));
}
List<Polygon> intersects = getTotalIntersections(polys, circle);
System.out.println(intersects);
primaryStage.setScene(new Scene(rootPane, SIZE, SIZE));
primaryStage.show();
}
public List<Polygon> getTotalIntersections(List<Polygon> polys, Shape testShape) {
List<Polygon> intersections = new ArrayList<>();
for(Polygon poly : polys) {
if(totalIntersects(poly, testShape)) {
intersections.add(poly);
}
}
return intersections;
}
public static Polygon rectangleToPolygon(Rectangle rect) {
double[] points = {rect.getX(), rect.getY(),
rect.getX() + rect.getWidth(), rect.getY(),
rect.getX() + rect.getWidth(), rect.getY() + rect.getHeight(),
rect.getX(), rect.getY() + rect.getHeight()};
return new Polygon(points);
}
public static void main(String[] args) {
Main.launch(args);
}
}
This code will print the following:
[Polygon[points=[200.0, 0.0, 300.0, 0.0, 300.0, 200.0, 200.0, 200.0], fill=0x000000ff], Polygon[points=[300.0, 0.0, 400.0, 0.0, 400.0, 200.0, 300.0, 200.0], fill=0x000000ff], Polygon[points=[400.0, 0.0, 500.0, 0.0, 500.0, 200.0, 400.0, 200.0], fill=0x000000ff]]
Which is your three polygons labeled 2, 3, and 4.

I don't think that JavaFX will have some special methods for this case.
To draw that circle you need coordinates (X_c, Y_c) of center and radius (R).
To draw rectangles you need to have coordinates ((X_1, Y_1), (X_2, Y_2) etc.) of angle points.
Then all you need is to check if all points of the rectangle is inside of the circle:
(X_1 - X_c)^2 + (Y_1 - Y_c)^2 < R^2
(X_2 - X_c)^2 + (Y_2 - Y_c)^2 < R^2
...

Try this :
import javafx.geometry.Point2D;
import javafx.scene.shape.Circle;
import javafx.scene.shape.Rectangle;
/*
Check if a rectangle is contained with in a circle by checking
all rectangle corners.
For the rectangle to be contained in a circle, all its corners should be
in a distance smaller or equal to the circle's radius, from the circle's center.
Note:
Requires some more testing. I tested only a few test cases.
I am not familiar with javafx. This solution does not take into
calculation rectangle's arc or other attributes I may not be aware of.
*/
public class Test{
//apply
public static void main(String[] args){
Circle circle = new Circle(0 ,0, 100);
Rectangle rec = new Rectangle(0, 0, 50 , 50);
System.out.println("Is rectungle inside the circle ? "
+ isContained(circle,rec));
}
//check if rectangle is contained within a circle
private static boolean isContained(Circle circle,Rectangle rec) {
boolean isInside = true;
//get circle center & radius
Point2D center = new Point2D(circle.getCenterX(), circle.getCenterY());
double radius= circle.getRadius();
Point2D[] corners = getRectangleCorners(rec);
for(Point2D corner : corners) {
//if any corner falls outside the circle
//the rectangle is not contained in the circle
if(distanceBetween2Points(corner, center) > radius) {
return false;
}
}
return isInside;
}
//calculate distance between two points
//(updated a per fabian's suggestion)
private static double distanceBetween2Points
(Point2D corner, Point2D center) {
return corner.distance(center);
}
private static Point2D[] getRectangleCorners(Rectangle rec) {
Point2D[] corners = new Point2D[4];
corners[0] = new Point2D(rec.getX(), rec.getY());
corners[1] = new Point2D(rec.getX()+ rec.getWidth() , rec.getY());
corners[2] = new Point2D(rec.getX()+ rec.getWidth(), rec.getY()+ rec.getHeight());
corners[3] = new Point2D(rec.getX(), rec.getY()+ rec.getHeight());
return corners;
}
}

There is a working simple solution here : https://stackoverflow.com/a/8721483/1529139
Copy-paste here:
class Boundary {
private final Point[] points; // Points making up the boundary
...
/**
* Return true if the given point is contained inside the boundary.
* See: http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html
* #param test The point to check
* #return true if the point is inside the boundary, false otherwise
*
*/
public boolean contains(Point test) {
int i;
int j;
boolean result = false;
for (i = 0, j = points.length - 1; i < points.length; j = i++) {
if ((points[i].y > test.y) != (points[j].y > test.y) &&
(test.x < (points[j].x - points[i].x) * (test.y - points[i].y) / (points[j].y-points[i].y) + points[i].x)) {
result = !result;
}
}
return result;
}
}