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I am coding a method that calculates the intersection of a line and a circle as a first step to write some kind of ray casting demo. In case an intersection is calculated it gets the shortest distance to the two points of intersection that will be the collision point, then it repeats the process where the new line originates from the collision point.
I was motivated by this video of a laser hitting different circles.
The method receives the angle of the line, the point where it originates, the size of the window, the radius of the circles, the array of centers of the circles and the GraphicsContext object from JavaFX.
The method has a couple of booleans to determine whether a collision has been made or not, and an ArrayList to store the collisions that will be later drawn on a JavaFX Canvas.
Inside a while loop the equation of the line is defined with the form y = m*x + b. Then checks which of the circles has a distance between the circle center and the line smaller than the radius of the line, this is calculated with the method explained here: math.stackexchange.com.
In case the distance to the center is smaller than the radius a collision occurs against that circle. As far as I know to find the intersection between a line and a circle you need to solve the equation system: y = m*x + b, (x-x1)^2 + (y-y1)^2 = r^2, that I solved via substitution. This results in a second degree polinomial equation that has a real solution if: p1*p1 >= 4*p0*p2.
The solution with the shortest distance to the origin point is the one that the line hits first and is the solution to our problem. A new angle is calculated with the center of the circle, the collision point and the origin point. With this a new line is defined and the loop repeats until no collision against the circles is calculated, situation where the collision against the borders of the window is calculated.
At the end a for loop draws all of the lines defined as couples of points inside collisionList.
This is the code, I've tried to comment it as best as I could:
private void extendPoint(double angle, Point origin, double x, double y, double radius, ArrayList<Point> pointList) {
double newAngle = angle; //Angle that defines the direction of the line
//This is used if the line does not hit a circle
double angle11 = Math.atan2(origin.getY(), origin.getX());
double angle_11 = Math.atan2(origin.getY(), -origin.getX());
double angle_1_1 = angle11 + Math.PI;
double angle1_1 = angle_11 + Math.PI;
boolean noCollision = true; //Will be true if the line does not hit a circle
boolean repeat = true; //If no collision has been made the while loop stops with this
Point currentPoint = Point.copy(origin); // (x0, y0)
Point collision = new Point(-1,-1); //Stores the collision point
Point newDirection = new Point(-1,-1); //Stores the new direction after a collision, returns(magnitud, angle) of a vector
ArrayList <Point> collisionList = new ArrayList<>(); //ArrayList of collision points that will be drawn later
collisionList.add(origin); //The origin point is added as a collision for representation purposes
while(repeat == true) {
//Line equation that passes through a point with an angle
//y = a*x - a*x0 + y0; -> y = m*x + b;
double m = Math.tan(-newAngle);
double a = m;
double b = -m*currentPoint.getX() + (currentPoint.getY());
for(int i = 0; i < pointList.size(); i++) {
Point gridPoint = pointList.get(i); //(x1, y1)
//From: https://math.stackexchange.com/questions/2552687/distance-between-line-and-point
//Given a line defined as A*x + B*y + C = 0
//x*(y1-y0)+y*(x1-x0)+(-y0*(x1-x0)-x0*(y1-y0)
double A = gridPoint.getY()-currentPoint.getY();
double B = gridPoint.getX()-currentPoint.getX();
double C = -currentPoint.getY()*B + currentPoint.getX()*A;
// double d_cp_gp = Math.abs(m*gridPoint.getX()-b*(gridPoint.getY()))/(Math.sqrt(m*m + 1));
double d_cp_gp = Math.abs(A + B + C)/Math.sqrt(A*A + B*B);
if(d_cp_gp < radius) {
System.out.println("radio " + d_cp_gp);
//The intersection between a line and a circunference:
//Circunference: (x-x1)^2 + (y-y1)^2 = r^2
//Line: y = tan(alpha)*(x-x0)+y0 -> y = a*x + b; a = tan(alfa), b = -tan(alfa)*x0 + y0
//Substituting the line equation in the circunference equation:
//x^2*(1+a^2) + x*(-2x1 + 2*a*b) + 2*a*b + x1^2+b^2-r^2 = 0
double p2 = 1 + a*a;
double p1 = -2*gridPoint.getX() + 2*a*b;
double p0 = gridPoint.getX()*gridPoint.getX() + b*b - radius*radius;
double p0_ = 4*p0*p2;
System.out.println(p1*p1 + " " + p0_);
//Check if the second order equation has solutions
if(p1*p1 >= p0_) {
System.out.println("IT HAS SOLUTION");
//Solution
double root = Math.sqrt(p1*p1 - p0_);
double sol1x = (-p1 + root)/(2*p2);
double sol2x = (-p1 - root)/(2*p2);
double sol1y = a*sol1x - a*currentPoint.getX() + currentPoint.getY();
double sol2y = a*sol1x - a*currentPoint.getX() + currentPoint.getY();
//The line will intersect twice with the circle, we want the solution
//with the shortest distance to currentPoint (x0,y0)
double distSol1 = Math.sqrt(Math.pow(currentPoint.getX()- sol1x, 2) +
Math.pow(currentPoint.getY() - sol1y, 2));
double distSol2 = Math.sqrt(Math.pow(currentPoint.getX()- sol2x, 2) +
Math.pow(currentPoint.getY() - sol2y, 2));
//The collision point is the point that the line hits first
if(distSol1 < distSol2) {
collision.setXY(sol1x, sol1y);
}
else {
collision.setXY(sol2x, sol2y);
}
//newAngle returns a vector with the form (magnitude, angle)
newDirection = newAngle(currentPoint, gridPoint, collision, radius);
currentPoint = collision;
//The new line after the collision is defined here
m = Math.tan(-newDirection.getY());
a = m;
b = -m*collision.getX() + (collision.getY());
collisionList.add(collision);
System.out.println("A collision has been calculated successfully: " + collision.toString());
//If a collision
noCollision= false;
}
}
//If no collisions have been detected at the end of the for loop exit the while loop
if(i == pointList.size() - 1 && noCollision == true) {
repeat = false;
}
}
//If no collision has been calculated with the circles this
//calculates the collision with the limits of the window
if(noCollision == true && repeat == false) {
if(angle<angle11 || angle > angle1_1) {
collision.setXY(x, m*x + b);
}
else if(angle > angle11 && angle < angle_11){
collision.setXY((0 - b)/m, 0);
}
else if(angle > angle_11 && angle < angle_1_1) {
collision.setXY(0, m*0 + b);
}
else if(angle> angle_1_1 && angle < angle1_1) {
collision.setXY((y - b)/m, y);
}
collisionList.add(collision);
}
}
System.out.println("Number of collisions: " + (int)(collisionList.size() - 1));
}
My main problem is that the shortest distance to a circle doesn't seem to be calculated properly, which directly difficults if the rest of the code works properly.
I've tried different methods to find the shortest distance and this is the one that I liked the most as I find it easy to understand, however the implementation doesn't work properly. I've thought that this could be because of JavaFX coordinate system (x increases to the right and y to the bottom) but I'm not sure, I'm a bit lost at this point.
Thanks for your time.
Edit:
As suggested I am adding some extra code to facilitate reproducibility.
The Point and Vector classes are defined as follows:
public class Point {
private double x;
private double y;
public Point(double x, double y) {
this.x = x;
this.y = y;}
public double getX() {
return x;}
public double getY() {
return y;}
public void setX(double x) {
this.x = x;}
public void setY(double y) {
this.y = y;}
public void setXY(double x, double y) {
this.x = x;
this.y = y;}
#Override
public String toString() {
return("(" + this.x + "," + this.y + ")");
}
public static Point copy(Point a) {
return new Point(a.getX(), a.getY());
}
}
public class Vector {
private double vx;
private double vy;
private double ptoApX;
private double ptoApY;
private double angle;
private double modulo;
public Vector(double vx, double vy) {
this.vx = vx;
this.vy = vy;
this.ptoApX = 0;
this.ptoApY = 0;
this.angle = angle(vx,vy);
this.modulo = modulo(vx,vy);
}
//Getters
public double getVx() {
return this.vx;
}
public double getVy() {
return this.vy;
}
public double getPtoApX() {
return this.ptoApX;
}
public double getPtoApY() {
return this.ptoApY;
}
public double getAngle() {
return this.angle;
}
public double getModulo() {
return this.modulo;
}
//Setters
public void setVx(double vx) {
this.vx = vx;
}
public void setVy(double vy) {
this.vy = vy;
}
public void setPtoApX(double ptoApX) {
this.ptoApX = ptoApX;
}
public void setPtoApY(double ptoApY) {
this.ptoApY = ptoApY;
}
public void setAngle(double angle) {
this.angle = angle;
}
public void setModulo(double modulo) {
this.modulo = modulo;
}
//To String
#Override
public String toString() {
return "("+this.getVx()+","+this.getVy()+")";
}
public static double dotProduct(Vector a, Vector b) {
return a.getVx()*b.getVx() + a.getVy()*b.getVy();
}
public static Vector escalarProduct(Vector v, double n) {
return new Vector(n*v.getVx(), n*v.getVy());
}
public static Vector vectorWith2Points(Point a, Point b) {
Point p = Point.resta(a,b);
return new Vector(p.getX(),p.getY());
}
public static Vector vectorPointAngle(Point a, double angle, double modulo) {
double angleRadians = Math.toRadians(angle);
Point b = new Point(Math.cos(angleRadians)*modulo, Math.sin(angleRadians)*modulo);
return vectorWith2Points(a,b);
}
public static double modulo(double vx, double vy) {
return Math.sqrt(vx*vx + vy*vy);
}
public static double angle(double vx, double vy) {
return Math.atan2(vy, vx);
}
public static Vector normalize(Vector v) {
return new Vector(v.getVx()/v.getModulo(),v.getVy()/v.getModulo());
}
public static double angle2vectors(Vector u, Vector v) {
double argument = dotProduct(u,v)/(u.getModulo()*v.getModulo());
return Math.acos(argument);
}
public static Point polar2cart(double r, double angle) {
return new Point(r*Math.cos(angle), r*Math.sin(angle));
}
public static Point cart2polar(Point p) {
return new Point(modulo(p.getX(), p.getY()), angle(p.getX(), p.getY()));
}
}
And the method to obtain the new angle after a collision:
private Point newAngle(Point origin, Point center, Point c, double radius) {
//Normal vector
Vector n = Vector.vectorWith2Points(c, center);
Vector nNorm = Vector.normalize(n);
//Incident vector
Vector d = Vector.vectorWith2Points(c, origin);
//Tangent vector
Vector tg = new Vector(-nNorm.getVy(), nNorm.getVx());
//Reflected vector
double product = Vector.dotProduct(d,tg);
Vector r = new Vector(d.getVx()-2*product*tg.getVx(),
d.getVy() - 2*product*tg.getVy());
return new Point(r.getModulo(), r.getAngle());
}
An example of the code of different angles where a collision should be detected:
double x = 600;
double y = 400;
double radius = 10;
Point origin = new Point(x/2, y/2);
ArrayList<Point> pointList = new ArrayList<>();
pointList.add(new Point(40,40));
pointList.add(new Point(500,100));
pointList.add(new Point(40,330));
pointList.add(new Point(450,300));
//This should return a solution
extendPoint(0.4363323129985824, origin, x, y, radius, pointList);
extendPoint(2.6179938779914944, origin, x, y, radius, pointList);
//this returns a solution when it should not
extendPoint(1.5707963267948966, origin, x, y, radius, pointList);
extendPoint(-1.5707963267948966, origin, x, y, radius, pointList);
I wrote an class with everything needed to run the code here: https://pastebin.com/wMjUh9pZ
I think you should create a class that represents an intersection by a ray.
class Intersection{
double distance;
Point loc;
double normal;
}
That way, distance is along the ray and normal is the normal of the object intersected.
Then I would have a method for finding the intersetion of a circle and a point.
List<Intersection> lineAndCircle( Point org, double angle, Point center, double radius){...}
You seem to have a similar method but you're doing more work in it.
Then you also want to check the edge of the screen.
Intersection lineAndBoundary( Point org, double angle){ ... }
You have a very similar method, but you seem to be doing a lot more work in the method. . This way you are testing separate methods. Then your algorithm works as.
1 go through circles and find intersections.
2 get the intersection with the boundary.
3 find the closest intersection ( the smallest distance greater than 0 )
Doing it this way makes it a bit more extensible. First our ray is re-used a lot. Lets make a class.
class Ray{
Point origin;
double angle;
}
Then we collide a ray with multiple objects.
interface Interceptable{
List<Intersection> intercepts(Ray r);
}
Then we can use different classes.
class Circle implements Interceptable{
Point pos;
double radius;
#Override
List<Intersection> collides(Ray r){
...
}
}
Now you can right collides and testable.
Circle a = new Circle( new Point( 40, 40 ), 5 );
List<Intersection> yes = a.collides( new Ray( new Point(0, 0), 3.14/4 ) );
List<Intersection> no = a.collides( new Ray( new Point(0, 0), 0) ) );
Then you can narrow your example down to. "How do I write a collide method?" or "Why doesn't my collide method work for this ray/circle pair? I expect it to hit at two points, but it misses." etc.
Here is a complete runnable example that creates a swing window. I kinda enjoy making toy programs like this.
Note that I used an interface for the Intersectable. So now it is circles, but it could be anything that returns a list of Intersection
import javax.swing.*;
import java.awt.Graphics;
import java.awt.Dimension;
import java.awt.Color;
import java.awt.event.*;
import java.util.*;
public class RayAndCircle{
public static void main(String[] args){
List<Intersectable> circles = new ArrayList<>();
for(int i = 0; i<250; i++){
double r = Math.random()*50 + 50;
double x = 2048*Math.random();
double y = 2048*Math.random();
circles.add( new Circle( r, new double[]{x,y}));
}
List<LineSegment> segments = new ArrayList<>();
JFrame frame = new JFrame("Ray caster");
JPanel panel = new JPanel(){
#Override
public Dimension getPreferredSize(){
return new Dimension(2048, 2048);
}
#Override
public void paintComponent( Graphics g){
g.setColor(Color.RED);
for( Intersectable c: circles ){
c.draw(g);
}
g.setColor(Color.BLACK);
for( LineSegment segment: segments){
g.drawLine( (int) segment.a[0], (int) segment.a[1],(int)segment.b[0], (int)segment.b[1]);
}
}
};
panel.addMouseListener( new MouseAdapter(){
#Override
public void mouseClicked( MouseEvent evt ){
double x = evt.getPoint().getX();
double y = evt.getPoint().getY();
double theta = Math.random() * Math.PI * 2;
double dx = Math.cos( theta );
double dy = Math.sin( theta );
Ray ray = new Ray( new double[] {x, y}, new double[]{ dx, dy } );
int count = 500;
Intersectable last = null;
while( ray != null && count > 0 ){
Intersection hit = null;
Intersectable next = null;
for(Intersectable c: circles){
if(c == last){
continue;
}
List<Intersection> intersections = c.intersects(ray);
for(Intersection i : intersections){
if( hit == null ){
hit = i;
next = c;
} else{
if( hit.s > i.s ){
hit = i;
next = c;
}
}
}
}
if(hit != null){
last = next;
segments.add( new LineSegment( ray.origin, new double[]{ hit.pos[0], hit.pos[1] } ) );
count--;
//reflected portion of ray.
double dot = hit.normal[0]*ray.direction[0] + hit.normal[1]*ray.direction[1];
double rx = ray.direction[0] - 2 * hit.normal[0]*dot;
double ry = ray.direction[1] - 2 * hit.normal[1]*dot;
double z = Math.sqrt(rx*rx + ry*ry);
ray = new Ray(hit.pos, new double[] { rx/z, ry/z});
} else{
ray = null;
}
}
panel.repaint();
}
});
frame.setContentPane(panel);
frame.pack();
frame.setVisible(true);
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
}
}
class Ray{
double[] origin; double[] direction;
public Ray( double[] origin, double[] direction){
this.origin = new double[]{origin[0], origin[1]};
this.direction = new double[]{direction[0], direction[1]};
}
}
class Intersection{
double s;
double[] pos;
double[] normal;
Circle b;
public Intersection(double s, double[] pos, double[] normal){
this.s = s;
this.pos = pos;
setNormal(normal);
}
public void setNormal(double[] normal){
double m = Math.sqrt(normal[0]*normal[0] + normal[1]*normal[1]);
if( Double.isNaN(m) || m == 0) throw new RuntimeException("Invalid normal! Magnitude of" + m);
this.normal = new double[] { normal[0]/m , normal[1]/m };
}
}
interface Intersectable{
List<Intersection> intersects(Ray ray);
void draw(Graphics g);
}
class Circle implements Intersectable{
double[] origin;
double radius;
public Circle( double radius, double[] origin){
this.radius = radius;
this.origin = new double[]{origin[0], origin[1]};
}
Intersection intersectionAt(Ray ray, double s){
//intersection.
double locx = ray.origin[0] + s*ray.direction[0];
double locy = ray.origin[1] + s*ray.direction[1];
double nx = (locx - origin[0])/radius;
double ny = (locy - origin[1])/radius;
return new Intersection( s, new double[]{ locx, locy }, new double[]{nx, ny} );
}
public List<Intersection> intersects(Ray ray){
double rx = origin[0] - ray.origin[0];
double ry = origin[1] - ray.origin[1];
double m2 = rx*rx + ry*ry;
double m = Math.sqrt(m2);
//position along ray that is closest to circles origin.
double s = rx*ray.direction[0] + ry*ray.direction[1];
//closest distance to circle.
double approach = Math.sqrt(m2 - s*s);
List<Intersection> result = new ArrayList<>();
if( approach < radius ){
//two intersections at points on circle.
//radius is hypotenuse and approach is one of the lengths.
double l = Math.sqrt( radius*radius - approach*approach);
double s1 = s - l;
if(s1 > 0){
result.add( intersectionAt(ray, s1) );
}
double s2 = s + l;
if(s2 > 0){
//intersection!
result.add(intersectionAt(ray, s2) );
}
} else if(approach == radius){
//one intersection tangent.
if( s > 0 ){
result.add( intersectionAt(ray, s) );
}
} else{
//miss.
}
return result;
}
public void draw(Graphics g){
g.fillOval(
(int)(origin[0] - radius),
(int)(origin[1] - radius),
(int)radius*2,
(int)radius*2
);
}
}
class LineSegment{
double[] a, b;
public LineSegment( double[] a, double[] b){
this.a = new double[]{a[0], a[1]};
this.b = new double[]{b[0], b[1]};
}
}
You'll probably be most interested in the intersects method of the Circle class, and the small chunk of code burried in the mouseClicked method that calculates the reflected ray.
If you only want to know if the line intersects if a given circle, create a second line which originates at the center of the given circle and the direction is the direction of your initial line rotated by 90 degrees. Then compute the intersection of the two lines. If then the distance between the intersection point and the center of the circle is smaller then the radius, both intersect.
A while ago I wrote a small Geometry lib, I striped out the sections which are relevant for you, here is my code:
Line class
public class Line {
final Vector2D positionVector;
final Vector2D directionVector;
public Line(final Vector2D positionVector, final Vector2D directionVector) {
this.positionVector = positionVector;
this.directionVector = directionVector;
}
public OptionalDouble computeIntersection(final Line line) {
final double numerator = line.getPositionVector().subtract(this.positionVector).cross(this.directionVector);
final double denominator = this.directionVector.cross(line.directionVector);
if (Math.abs(numerator) < 1e-10 && Math.abs(denominator) < 1e-10) {
// collinear
return OptionalDouble.of(Double.POSITIVE_INFINITY);
} else if (Math.abs(denominator) < 1e-10) {
// parallel
return OptionalDouble.empty(); // Lines are parallel.
}
final double t = line.getPositionVector().subtract(this.positionVector).cross(line.directionVector) / denominator;
return OptionalDouble.of(t);
}
public Vector2D getPositionVector() {
return positionVector;
}
public Vector2D getDirectionVector() {
return directionVector;
}
public Point2D getClosestPointOnLine(final Point2D point) {
final Line line = new Line(new Vector2D(point.getX(), point.getY()), this.directionVector.turn90DegreeClockwise());
final OptionalDouble intersection = this.computeIntersection(line);
final Vector2D result = this.positionVector.add(this.directionVector.lerp(intersection.getAsDouble()));
return new Point2D(result.getX(), result.getY());
}
}
intersection function
public static PointResult intersection(final Line l1, final Circle c1) {
final Point2D intersection = l1.getClosestPointOnLine(c1.getCenter());
final double dist = intersection.distance(c1.getCenter());
if (Math.abs(dist - c1.getRadius()) < 1e-10) {
final List<Point2D> result = new LinkedList<>();
result.add(intersection);
return new PointResult(Collections.unmodifiableList(result));
} else if (dist < c1.getRadius()) {
// we have two points
final double adjacentLeg = Math.sqrt(c1.getRadius() * c1.getRadius() - dist * dist);
final Point2D pt1 = intersection.pointAt(l1.getDirectionVector().angle(), adjacentLeg);
final Point2D pt2 = intersection.pointAt(l1.getDirectionVector().angle() + Math.PI, adjacentLeg);
final List<Point2D> result = new LinkedList<>();
result.add(pt1);
result.add(pt2);
return new PointResult(Collections.unmodifiableList(result));
}
return new PointResult();
}
TestCase
#Test
void testIntersectionLineCircleTwoPoints() {
final Point2D ptCircleCenter = new Point2D(2.0, 5.0);
final Point2D ptLineCircleIntersection = new Point2D(5.0, 2.0);
final Point2D pt1 = new Point2D(3.0, 0.0);
final Point2D pt2 = new Point2D(7.0, 4.0);
final double a = Math.sqrt((2.0 * 2.0) + (2.0 * 2.0));
final double b = ptCircleCenter.diff(ptLineCircleIntersection).norm();
final double radius = Math.sqrt((a * a) + (b * b));
final Line l1 = new Line(pt1, pt2);
final Circle circle = new Circle(ptCircleCenter, radius);
PointResult intersection = GeometryOperation.intersection(l1, circle);
assertTrue(intersection.getPoints().isPresent());
assertEquals(2, intersection.getPoints().get().size());
assertEquals(7.0, intersection.getPoints().get().get(0).getX(), 1e-10);
assertEquals(4.0, intersection.getPoints().get().get(0).getY(), 1e-10);
assertEquals(3.0, intersection.getPoints().get().get(1).getX(), 1e-10);
assertEquals(0.0, intersection.getPoints().get().get(1).getY(), 1e-10);
}
I did not add the Circle, Vector2D and Point2D class because they are trivial. And the class PointResult is just a list.
I have a few restrictions type of a ax+by>=c (1) and x>=z and y>=k (2). Restrictions (1) and (2) make a regions. I need to find the intersection of this regions and fill that other color. How can I do it in JavaFX? Can I use Canvas for solve this?
Sure, just fill everything with the polygon color and then for each area fill everything not in the area with the background color.
Note that this way you fill the whole Canvas except for the polygon with the background color.
public class Area {
private final double x;
private final double y;
private final double threshold;
private final int minCorner;
public Area(double x, double y, double threshold, boolean greater) {
if (x == 0 && y == 0) {
throw new IllegalArgumentException();
}
if (greater) {
x *= -1;
y *= -1;
threshold *= -1;
}
this.x = x;
this.y = y;
this.threshold = threshold;
boolean yPos = y > 0;
// find corner with minimum result for evaluate
this.minCorner = x < 0 ? (yPos ? 1 : 2) : (yPos ? 0 : 3);
}
public Area(double x, double y, double threshold) {
this(x, y, threshold, false);
}
private static final int[][] CORNER_FACTORS = {
{0, 0},
{1, 0},
{1, 1},
{0, 1}
};
public boolean contains(double x, double y) {
return evaluate(x, y) <= threshold;
}
public double hLineIntersection(double y) {
if (x == 0) {
return this.y * y == threshold ? Double.POSITIVE_INFINITY : Double.NaN;
} else {
return (threshold - this.y * y) / this.x;
}
}
public double vLineIntersection(double x) {
if (y == 0) {
return this.x * x == threshold ? Double.POSITIVE_INFINITY : Double.NaN;
} else {
return (threshold - this.x * x) / this.y;
}
}
private double evaluate(double x, double y) {
return this.x * x + this.y * y;
}
public void fillCleanArea(GraphicsContext gc, double w, double h) {
double[] xcoords = new double[5];
double[] ycoords = new double[5];
int[] factors = CORNER_FACTORS[minCorner];
boolean inside = contains(factors[0] * w, factors[1] * h);
int ptIndex = 0;
for (int i = minCorner, max = minCorner + 4; i < max; i++) {
factors = CORNER_FACTORS[i % 4];
double x = factors[0] * w;
double y = factors[1] * h;
boolean nowInside = contains(x, y);
if (inside != nowInside) {
// add intersection point with side
if ((i & 1) == 0) {
ycoords[ptIndex] = vLineIntersection(x);
xcoords[ptIndex++] = x;
} else {
xcoords[ptIndex] = hLineIntersection(y);
ycoords[ptIndex++] = y;
}
inside = nowInside;
// stop, if the end point is inside the area again
if (inside) {
break;
}
}
// add corners outside the bounds to polygon
if (!inside) {
xcoords[ptIndex] = x;
ycoords[ptIndex++] = y;
}
}
// draw polygon
if (ptIndex > 0) {
gc.fillPolygon(xcoords, ycoords, ptIndex);
}
}
}
public static void draw(Canvas canvas, Paint fill, Paint background, Area... areas) {
GraphicsContext gc = canvas.getGraphicsContext2D();
double w = canvas.getWidth();
double h = canvas.getHeight();
// fill everything with polygon color
gc.setFill(fill);
gc.fillRect(0, 0, w, h);
// fill everything outside the polygon with background color
gc.setFill(background);
for (Area area : areas) {
area.fillCleanArea(gc, w, h);
}
}
#Override
public void start(Stage primaryStage) {
Canvas canvas = new Canvas(400, 400);
draw(canvas, Color.BLUE, Color.WHITE,
new Area(1, 1, 400), new Area(1, -1, 100), new Area(1, -1, -100, true), new Area(1, 2, 250, true));
StackPane root = new StackPane(canvas);
Scene scene = new Scene(root);
primaryStage.setScene(scene);
primaryStage.show();
}
This won't give you the polygon's corner points though...
I am looking for touch detection. The code showed below is what I did to set a circle in my app. I want detect touch on this circle and not around or on the entire texture. The strange thing is that touch isn't detected, in nowhere I can detect it
Circle class:
public class Circle_Obj extends Actor{
private Vector2 position;
private float radius;
private com.badlogic.gdx.math.Circle circle;
private Texture texture;
public Circle_Obj(float x, float y, float radius) {
position = new Vector2(x,y);
this.radius = radius;
circle = new com.badlogic.gdx.math.Circle(x,y,radius);
texture = new Texture(Gdx.files.internal("texture.png"));
addListener(new InputListener(){
#Override
public boolean touchDown(InputEvent event, float x, float y, int pointer, int button) {
Gdx.app.log("TOUCHED", " TOUCHED ");
return true;
}
});
}
#Override
public void draw(Batch batch, float parentAlpha) {
batch.draw(texture,0, 0);
}
}
Screen class :
public class GameScreen implements Screen {
private Stage stage;
private Circle_Obj circle_obj;
public GameScreen() {
circle_obj = new Circle_Obj(Static_values.Width/2, Static_values.Height/2, Static_values.Width / 100 * 10);
stage = new Stage(new FitViewport(Static_values.Width/3, Static_values.Height/3));
stage.addActor(circle_obj);
Gdx.input.setInputProcessor(stage);
}
#Override
public void render(float delta) {
Gdx.gl.glClear(GL20.GL_COLOR_BUFFER_BIT);
stage.draw();
}
#Override
public void dispose() {
stage.dispose();
}
/** other methods **/
}
You can use libgdx's touch detection in a circle class.Only touched circle will affected.
public boolean is_touched() {
if (Gdx.input.justTouched()) {
float xx = Gdx.input.getX();
float yy = Gdx.input.getY();
float x = position.x;
float y = position.y;
return (xx - x) * (xx - x) + (yy - y) * (yy - y) < radius * radius;
}
}
If you are using a lot of circles so it is better for performance to take touch position as a parameter.
in the circle class
public boolean is_touched(float xx,float yy) {
float x = position.x;
float y = position.y;
return (xx - x) * (xx - x) + (yy - y) * (yy - y) < radius * radius;
}
}
and in another class
if (Gdx.input.justTouched()) {
float xx = Gdx.input.getX();
float yy = Gdx.input.getY();
if (circle0.is_touched(xx, yy)) {
// do something about circle0
}
if (circle1.is_touched(xx, yy)) {
// do something about circle1
}
if (circle2.is_touched(xx, yy)) {
// do something about circle2
}
}
You can also ignore one of the touched circles when two circles overlaps and user touchs the overlapping area.
if (Gdx.input.justTouched()) {
float xx = Gdx.input.getX();
float yy = Gdx.input.getY();
if (circle0.is_touched(xx, yy)) {
// do something about circle0
}
else if (circle1.is_touched(xx, yy)) {
// do something about circle1
}
else if (circle2.is_touched(xx, yy)) {
// do something about circle2
}
}
To detect the touch on an actor added in a Stage, the method hit of the actor is called (hit detection in the documentation)
public Actor hit (float x, float y, boolean touchable) {
if (touchable && getTouchable() != Touchable.enabled) return null;
return x >= 0 && x < width && y >= 0 && y < height ? this : null;
}
You have not set a size to your Circle_Obj actor, so hit will always return null.
Now, your actor is a circle, so you probably want to override hit so that it checks if the given coordinates ares in the circle instead of the default implementation that checks if the coordinates are in a box of the size of the actor.
Something like:
#Override
public Actor hit (float x, float y, boolean touchable) {
if (touchable && getTouchable() != Touchable.enabled) return null;
return (x - position.x)*(x- position.x) + (y - position.y)*(y - position.y) < radius*radius ? this : null;
}
If you inherit from Actor, you need to set the bounds or it will not be click/touch-able!.
Simply set the bounds to match the texture your Actor contains.
//add this Set bounds the x, y, width, and height
circle_obj.setBounds(0, 0,texture.getWidth(), texture.getHeight());
Anyone has a good algorithm for how to get a smooth but predictable movement from point a -> b in 2D in any language?
I need to have one function setting the velocity each frame:
function GetVel(current_pos : Vector2, dest_pos : Vector2, current_vel : Vector2)
{
var new_vel : Vector2d;
.......
return new_vel;
}
and a corresponding:
function GetDestTime(current_pos : Vector2, dest_pos : Vector2, current_vel : Vector2 )
{
var duration : float;
.......
return duration;
}
Simply using acceleration leads up to lots of sliding so some good smoothDamp algorithm that can be predicted the exact dest time is what I need.
Any ideas?
Let's assume v(0) = 0 and v(T) = 0 and, v(t) is a quadratic function which the maximum value at t = T/2.
Accordingly, we can assume the form,
Since the point moves L within T seconds, integrating v(t) from 0 to T must give L. So, we can get another equation,
Solving these equations gives,
Using these a and b, you can compute the current velocity.
It is rather long, but I made a Java toy to realize this. Please check it!
import java.awt.*;
import javax.swing.*;
public class MovePoint extends Canvas implements Runnable {
public static void main(String... args) {
Thread thread = new Thread(new MovePoint());
thread.start();
}
private static final int WIDTH = 500;
private static final int HEIGHT = 500;
public MovePoint() {
super();
this.setBackground(Color.WHITE);
this.setForeground(Color.BLACK);
this.setSize(WIDTH, HEIGHT);
JFrame f = new JFrame("Move Point");
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.add(this);
f.pack();
f.setVisible(true);
}
private Point V;
private Point S = new Point(50, 50);
private Point E = new Point(450, 450);
private double duration = 5.0;
private double dt = 0.03;
private Image buffer;
private Graphics gBuf;
public void run() {
double t = 0.0;
V = S.copy();
while (t < duration) {
V = Point.add(V, calcVelocity(V, S, E, t, duration).scale(dt));
t += dt;
repaint();
try {
Thread.sleep(30);
} catch (InterruptedException e) {
e.printStackTrace();
}
}
System.exit(0);
}
public void paint(Graphics g) {
if (gBuf == null) {
buffer = createImage(WIDTH, HEIGHT);
gBuf = buffer.getGraphics();
}
gBuf.setColor(Color.WHITE);
gBuf.fillRect(0, 0, WIDTH, HEIGHT);
gBuf.setColor(Color.BLACK);
gBuf.fillOval((int)(V.x - 5), (int)(V.y - 5), 11, 11);
g.drawImage(buffer, 0, 0, this);
}
public void update(Graphics g) {
paint(g);
}
public Point calcVelocity(Point current, Point start, Point goal, double t, double T) {
double L = Point.distance(start, goal);
double a = -6.0 / (T * T * T);
double b = 3.0 / (2.0 * T);
double s = (t - 0.5 * T);
double v = a * s * s + b;
return Point.subtract(goal, start).scale(v);
}
}
class Point {
public double x;
public double y;
public Point(double x, double y) {
this.x = x;
this.y = y;
}
public Point copy() {
return new Point(x, y);
}
public static double distance(Point p, Point q) {
double dx = p.x - q.x;
double dy = p.y - q.y;
return Math.sqrt(dx * dx + dy * dy);
}
public static Point add(Point p, Point q) {
return new Point(p.x + q.x, p.y + q.y);
}
public static Point subtract(Point p, Point q) {
return new Point(p.x - q.x, p.y - q.y);
}
public Point scale(double s) {
return new Point(x * s, y * s);
}
}
I absolutely love maths (or 'math' as most of you would say!) but I haven't done it to a level where I know the answer to this problem. I have a main circle which could have a centre point at any x and y on a display. Other circles will move around the display at will but at any given call to a render method I want to render not only those circles that intersect the main circle, but also only render the segment of that circle that is visible inside the main circle. An analogy would be a shadow cast on a real life object, and I only want to draw the part of that object that is 'illuminated'.
I want to do this preferably in Java, but if you have a raw formula that would be appreciated. I wonder how one might draw the shape and fill it in Java, I'm sure there must be some variation on a polyline with arcs or something?
Many thanks
Let A and B be the 2 intersection points (you can ignore it when there is no, or 1 intercetion point).
Then calculate the length of the circular line segment between A and B.
With this information, you should be able to draw the arc using Graphics' drawArc(...) method (if I'm not mistaken...).
EDIT
Well, you don't even need the length of the circular line segment. I had the line-intersection code laying around, so I built a small GUI around it how you could paint/view the ARC of such intersecting circles (there are a bit of comments in the code):
import javax.swing.*;
import java.awt.*;
import java.awt.event.*;
import java.awt.geom.Arc2D;
/**
* #author: Bart Kiers
*/
public class GUI extends JFrame {
private GUI() {
super("Circle Intersection Demo");
initGUI();
}
private void initGUI() {
super.setSize(600, 640);
super.setDefaultCloseOperation(EXIT_ON_CLOSE);
super.setLayout(new BorderLayout(5, 5));
final Grid grid = new Grid();
grid.addMouseMotionListener(new MouseMotionAdapter() {
#Override
public void mouseDragged(MouseEvent e) {
Point p = new Point(e.getX(), e.getY()).toCartesianPoint(grid.getWidth(), grid.getHeight());
grid.showDraggedCircle(p);
}
});
grid.addMouseListener(new MouseAdapter() {
#Override
public void mouseReleased(MouseEvent e) {
Point p = new Point(e.getX(), e.getY()).toCartesianPoint(grid.getWidth(), grid.getHeight());
grid.released(p);
}
#Override
public void mousePressed(MouseEvent e) {
Point p = new Point(e.getX(), e.getY()).toCartesianPoint(grid.getWidth(), grid.getHeight());
grid.pressed(p);
}
});
super.add(grid, BorderLayout.CENTER);
super.setVisible(true);
}
public static void main(String[] args) {
SwingUtilities.invokeLater(new Runnable() {
#Override
public void run() {
new GUI();
}
});
}
private static class Grid extends JPanel {
private Circle c1 = null;
private Circle c2 = null;
private Point screenClick = null;
private Point currentPosition = null;
public void released(Point p) {
if (c1 == null || c2 != null) {
c1 = new Circle(screenClick, screenClick.distance(p));
c2 = null;
} else {
c2 = new Circle(screenClick, screenClick.distance(p));
}
screenClick = null;
repaint();
}
public void pressed(Point p) {
if(c1 != null && c2 != null) {
c1 = null;
c2 = null;
}
screenClick = p;
repaint();
}
#Override
public void paintComponent(Graphics g) {
Graphics2D g2d = (Graphics2D) g;
g2d.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
g2d.setColor(Color.WHITE);
g2d.fillRect(0, 0, super.getWidth(), super.getHeight());
final int W = super.getWidth();
final int H = super.getHeight();
g2d.setColor(Color.LIGHT_GRAY);
g2d.drawLine(0, H / 2, W, H / 2); // x-axis
g2d.drawLine(W / 2, 0, W / 2, H); // y-axis
if (c1 != null) {
g2d.setColor(Color.RED);
c1.drawOn(g2d, W, H);
}
if (c2 != null) {
g2d.setColor(Color.ORANGE);
c2.drawOn(g2d, W, H);
}
if (screenClick != null && currentPosition != null) {
g2d.setColor(Color.DARK_GRAY);
g2d.setComposite(AlphaComposite.getInstance(AlphaComposite.SRC_OVER, 0.5f));
Circle temp = new Circle(screenClick, screenClick.distance(currentPosition));
temp.drawOn(g2d, W, H);
currentPosition = null;
}
if (c1 != null && c2 != null) {
g2d.setColor(Color.BLUE);
g2d.setComposite(AlphaComposite.getInstance(AlphaComposite.SRC_OVER, 0.4f));
Point[] ips = c1.intersections(c2);
for (Point ip : ips) {
ip.drawOn(g, W, H);
}
g2d.setComposite(AlphaComposite.getInstance(AlphaComposite.SRC_OVER, 0.2f));
if (ips.length == 2) {
g2d.setStroke(new BasicStroke(10.0f));
c1.highlightArc(g2d, ips[0], ips[1], W, H);
}
}
g2d.dispose();
}
public void showDraggedCircle(Point p) {
currentPosition = p;
repaint();
}
}
private static class Circle {
public final Point center;
public final double radius;
public Circle(Point center, double radius) {
this.center = center;
this.radius = radius;
}
public void drawOn(Graphics g, int width, int height) {
// translate Cartesian(x,y) to Screen(x,y)
Point screenP = center.toScreenPoint(width, height);
int r = (int) Math.rint(radius);
g.drawOval((int) screenP.x - r, (int) screenP.y - r, r + r, r + r);
// draw the center
Point screenCenter = center.toScreenPoint(width, height);
r = 4;
g.drawOval((int) screenCenter.x - r, (int) screenCenter.y - r, r + r, r + r);
}
public void highlightArc(Graphics2D g2d, Point p1, Point p2, int width, int height) {
double a = center.degrees(p1);
double b = center.degrees(p2);
// translate Cartesian(x,y) to Screen(x,y)
Point screenP = center.toScreenPoint(width, height);
int r = (int) Math.rint(radius);
// find the point to start drawing our arc
double start = Math.abs(a - b) < 180 ? Math.min(a, b) : Math.max(a, b);
// find the minimum angle to go from `start`-angle to the other angle
double extent = Math.abs(a - b) < 180 ? Math.abs(a - b) : 360 - Math.abs(a - b);
// draw the arc
g2d.draw(new Arc2D.Double((int) screenP.x - r, (int) screenP.y - r, r + r, r + r, start, extent, Arc2D.OPEN));
}
public Point[] intersections(Circle that) {
// see: http://mathworld.wolfram.com/Circle-CircleIntersection.html
double d = this.center.distance(that.center);
double d1 = ((this.radius * this.radius) - (that.radius * that.radius) + (d * d)) / (2 * d);
double h = Math.sqrt((this.radius * this.radius) - (d1 * d1));
double x3 = this.center.x + (d1 * (that.center.x - this.center.x)) / d;
double y3 = this.center.y + (d1 * (that.center.y - this.center.y)) / d;
double x4_i = x3 + (h * (that.center.y - this.center.y)) / d;
double y4_i = y3 - (h * (that.center.x - this.center.x)) / d;
double x4_ii = x3 - (h * (that.center.y - this.center.y)) / d;
double y4_ii = y3 + (h * (that.center.x - this.center.x)) / d;
if (Double.isNaN(x4_i)) {
// no intersections
return new Point[0];
}
// create the intersection points
Point i1 = new Point(x4_i, y4_i);
Point i2 = new Point(x4_ii, y4_ii);
if (i1.distance(i2) < 0.0000000001) {
// i1 and i2 are (more or less) the same: a single intersection
return new Point[]{i1};
}
// two unique intersections
return new Point[]{i1, i2};
}
#Override
public String toString() {
return String.format("{center=%s, radius=%.2f}", center, radius);
}
}
private static class Point {
public final double x;
public final double y;
public Point(double x, double y) {
this.x = x;
this.y = y;
}
public double degrees(Point that) {
double deg = Math.toDegrees(Math.atan2(that.y - this.y, that.x - this.x));
return deg < 0.0 ? deg + 360 : deg;
}
public double distance(Point that) {
double dX = this.x - that.x;
double dY = this.y - that.y;
return Math.sqrt(dX * dX + dY * dY);
}
public void drawOn(Graphics g, int width, int height) {
// translate Cartesian(x,y) to Screen(x,y)
Point screenP = toScreenPoint(width, height);
int r = 7;
g.fillOval((int) screenP.x - r, (int) screenP.y - r, r + r, r + r);
}
public Point toCartesianPoint(int width, int height) {
double xCart = x - (width / 2);
double yCart = -(y - (height / 2));
return new Point(xCart, yCart);
}
public Point toScreenPoint(int width, int height) {
double screenX = x + (width / 2);
double screenY = -(y - (height / 2));
return new Point(screenX, screenY);
}
#Override
public String toString() {
return String.format("(%.2f,%.2f)", x, y);
}
}
}
If you start the GUI above and then type 100 0 130 -80 55 180 in the text box and hit return, you'll see the following: ...
Changed the code so that circles can be drawn by pressing- and dragging the mouse. Screenshot:
Assuming you know the center point and the radius of the two circles:
Calculate the points where the circles intersect. This can easily be done with trigonometry. There may be no intersection (distance between the center points is longer than the sum of the radiuses, ignorable in your case), one point (distance between center points is equal to the sum of the radiuses, ignorable), or two. Special cases: the circles are identical, or the moving circle ist smaller and completely inside the main circle.
If there are two intersection points: take the center point from the moving circle and draw an arc between those points.
(I have no code for you, but since you love maths... ;-)