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How to draw lines pointing to mouse in Processing

I am trying to make a program where there are lines in a grid pointing towards the mouse like magnets. I am a beginner in Processing, can someone point me towards a tutorial on how to do that or give me some code and explain what it does?
int x1 = 0;
int x2 = 0;
int y1 = 0;
int y2 = 0;
void setup() {
size(200, 200);
}
void draw() {
background(255, 255, 0);
x1 = (mouseX + 100) / 2;
y1 = (mouseY + 100) / 2;
x2 = -1 * x1 + 200;
y2 = -1 * y1 + 200;
line(x1, y1, x2, y2);
}

There's plenty of solutions for this project. One of the easiest is to use Processing's PVector class.
The PVector class can be used for two or three dimensional vectors. A vector is an entity that has both magnitude and direction. The PVector class, however, stores the components of the vector (x,y for 2D, and x,y,z for 3D). The magnitude and direction are calculated from the components and can be accessed via the methods mag() and heading().
A two dimensional vector in Processing is defined through x and y components:
PVector v = new PVector(xComponent, yComponent);
With some mathematical formulae, you can determine magnitude and direction using the x- and y-components. But we don't need to determine these.
Below, I've attached completed solution code. Most of it should make sense to you. But it's worth understanding what is going on with PVector.
A nested for loop within void draw() contains x and y variables that represent the coordinates of each grid vertex.
We first define PVector v as a vector given by an x-component of mouseX - x, or the difference between the x-positions of the mouse and each grid point. Similarly, the y-component given by mouseY - y has the same difference.
Creating a variable PVector u initialized from v.setMag(15) holds a PVector that has the same direction as v, but with a length of just 15.
Now to draw the lines. Vectors represent an offset, not a position (in this case), so drawing a line from a grid point to an offset of a grid point is key.
Hence line(x, y, x + u.x, y + u.y), where u.x and u.y are the x- and y-components of the vector u.
void setup() {
size(600, 600); // Set the size of the canvas to 600x600.
}
void draw() {
background(255);
stroke(200); // Set the stroke color to black
int distVertLine = width / 10; // This variable defines the distance between each subsequent vertical line.
for(int i = 0; i < width; i += distVertLine) {
line(i, 0, i, height); // Draw a line at x=i starting at the top of the canvas (y=0) and going to the bottom (y=height)
}
int distHorizLine = height / 10; // This variable defines the distance between each subsequent vertical line.
for(int i = 0; i < width; i += distHorizLine) {
line(0, i, width, i); // Draw a line at y=i starting at the left of the canvas (x=0) and going to the right (x=width)
}
stroke(0); // Set the stroke to black.
// Use a nested for loop to iterate through all grid vertices.
for(int x = 0; x <= width; x += width/10) {
for(int y = 0; y <= height; y += height/10) {
PVector v = new PVector(mouseX - x, mouseY - y); // Define a vector that points in the direction of the mouse from each grid point.
PVector u = v.setMag(15); // Make the vector have a length of 15 units.
line(x, y, x + u.x, y + u.y); // Draw a line from the grid vertex to the terminal point given by the vector.
}
}
}

The answer already given by Ben Myers is excellent! The code below has a few small modifications:
the two for loops for the grid lines have been combined (since width and height are equal);
the construction of the vector is combined with setting the magnitude;
some minor changes to colors and comments.
Modified code:
void setup() {
// Set the size of the canvas to 600x600 pixels.
size(600, 600);
}
void draw() {
// There are 10x10 grid cells that each have a size of 60x60 pixels.
int gridSize = width / 10;
// Set the background color to anthracite and the stroke color to orange.
background(56, 62, 66);
stroke(235, 113, 52);
// Draw vertical and horizontal grid lines.
for (int lineIndex = 0; lineIndex < gridSize; lineIndex++) {
line(lineIndex * gridSize, 0, lineIndex * gridSize, height);
line(0, lineIndex * gridSize, width, lineIndex * gridSize);
}
// Set the stroke color to blue.
stroke(0, 139, 225);
// Use a nested for loop to iterate through all grid cells.
for (int x = 0; x <= width; x += gridSize) {
for (int y = 0; y <= height; y += gridSize) {
// Define a vector that points in the direction of the mouse from
// each grid point and set the vector length to 15 units.
PVector vector = new PVector(mouseX - x, mouseY - y).setMag(15);
// Draw a line from the grid point to the end point using the vector.
line(x, y, x + vector.x, y + vector.y);
}
}
}

Making a moving circle disappear after being clicked on, Processing

I have written a program in which a UFO (in essence, a gray ellipse) appears from the center of the screen and flies to the edge. There is a laser that appears when the mouse is pressed, and disappears when the mouse is released. I want to make it so that the UFO disappears when the mouse clicks on it/the laser touches it.
I've made it as far as to make the UFO class and create variables that determine its movements and speed, and I was able to get the laser to appear directly on the cursor. I thought of making an 'if' statement to check if the cursor is within the radius (or diameter) of the UFO, and placing it inside of the for loop I created for the UFOs. However, I am not sure how to achieve the proper syntax to make it happen.
Note: You may need to wait a few seconds for the first circle to appear after you play the sketch.
UFO[] ufos = new UFO[3];
void setup() {
size(700, 700);
for (int j = 0; j < ufos.length; j++) {
ufos[j] = new UFO();
}
}
//UFO class
//Class setup ends on line 61
class UFO {
float a;
float b;
float c;
float sa;
float sb;
float d;
UFO() {
//declare float a/b/c value
a = random(-width/2, width/2);
b = random(-height/2, width/2);
c = random(width);
}
//UFO movement
void update() {
//float c will serve as a speed determinant of UFOs
c = c - 1;
if (c < 5) {
c = width;
}
}
//UFO setup
void show() {
//moving x/y coordinates of UFO
float sa = map(a / c, 0, 1, 0, width);
float sb = map(b / c, 0, 1, 0, height);
float d = map(c, 0, width, 50, 0);
//UFO drawing shapes
//ellipse is always sa (or sb) / c to allow UFO to appear
//as if it is moving through space
fill(200);
ellipse((sa / c), (sb / c), d + 5, d+5);
//Hides UFO way off the screen
//and replaces it with a black-filled ellipse until
//it forms into a full circle
//When radius d becomes 50, the UFO flies from the
//center of the screen to off of the screen
if (d < 50) {
fill(0);
ellipse(-5, -10, 90, 90);
sa = 10000;
sb = 10000;
}
}
}
void draw() {
//Background
background(0);
//Translated the screen so that the UFOs appear to fly from
//the center of the screen
translate(width/2, height/2);
//UFO draw loop, make UFO visible on screen
for (int j = 0; j < ufos.length; j++) {
ufos[j].update();
ufos[j].show();
//mouse-click laser
if (mousePressed == true) {
fill(200,0,0);
ellipse(mouseX - 352,mouseY - 347,50,50);
}
}
}

Like I said on the Happy Coding forum:
Basically, if your UFO is a series of circles, then you just need to use the dist() function to check whether the distance from the mouse to the center of the circle is less than the radius of the circle. If it is, then the mouse is inside the circle. Here's a small example:
float circleX = 50;
float circleY = 50;
float circleDiameter = 20;
boolean showCircle = true;
void draw(){
background(0);
if(showCircle){
ellipse(circleX, circleY, circleDiameter, circleDiameter);
}
}
void mousePressed(){
if(dist(mouseX, mouseY, circleX, circleY) < circleDiameter/2){
showCircle = false;
}
}
If your UFO is multiple circles, then you need to apply this logic to each circle. Please try something and post a small example like this one (not your whole sketch) if you get stuck. Good luck.

Rotating Polygon Objects

Rotating Asteroids ( Polygons )
I am trying to rotate asteroids(polygons) so that they look nice. I am doing this through multiple mathematical equations. To start I give the individual asteroid a rotation velocity:
rotVel = ((Math.random()-0.5)*Math.PI/16);
Then I create the polygon shape,
this.shape = new Polygon();
Followed by generating the points,
for (j = 0; j < s; j++) {
theta = 2 * Math.PI / s * j;
r = MIN_ROCK_SIZE + (int) (Math.random() * (MAX_ROCK_SIZE - MIN_ROCK_SIZE));
x = (int) -Math.round(r * Math.sin(theta)) + asteroidData[0];
y = (int) Math.round(r * Math.cos(theta)) + asteroidData[1];
shape.addPoint(x, y);
}
Finally, in a loop a method is being called in which it attempts to move the polygon and its points down as well as rotating them. (I'm just pasting the rotating part as the other one is working)
for (int i = 0; i < shape.npoints; i++) {
// Subtract asteroid's x and y position
double x = shape.xpoints[i] - asteroidData[0];
double y = shape.ypoints[i] - asteroidData[1];
double temp_x = ((x * Math.cos(rotVel)) - (y * Math.sin(rotVel)));
double temp_y = ((x * Math.sin(rotVel)) + (y * Math.cos(rotVel)));
shape.xpoints[i] = (int) Math.round(temp_x + asteroidData[0]);
shape.ypoints[i] = (int) Math.round(temp_y + asteroidData[1]);
}
now, the problem is that when it prints to the screen the asteroids appear to 'warp' or rather the x and y positions on some of the polygon points 'float' off course.
I've noticed that when I make 'rotVel' be a whole number the problem is solved however the asteroid will rotate at mach speeds. So I've concluded that the problem has to be in the rounding but no matter what I do I can't seem to find a way to get it to work as the Polygon object requires an array of ints.
Does anyone know how to fix this?

Currently your asteroids rotate around (0 , 0) as far as i can see. Correct would be to rotate them around the center of the shape, which would be (n , m), where n is the average of all x-coordinates of the shape, and m is the average of all y-coordinates of the shape.

Your problem is definitely caused by rounding to int! The first improvement is to make all shape coordinates to be of type double. This will solve most of your unwanted 'effects'.
But even with double you might experience nasty rounding errors in case you do a lot of very small updates of the coordinates. The solution is simple: Just avoid iterative updates of the asteroid points. Every time, you update the coordinates based on the previous coordinates, the rounding error will get worse.
Instead, add a field for the rotation angle to the shape and increment it instead of the points themselves. Not until drawing the shape, you compute the final positions by applying the rotation to the points. Note that this will never change the points themselves.
You can extend this concept to other transformations (e.g. translation) too. What you get is some kind of local coordinate system for every shape/object. The points of the shape are defined in the local coordinate system. By moving and rotating this system, you can reposition the entire object anywhere in space.
public class Shape {
// rotation and position of the local coordinate system
private double rot, x, y;
// points of the shape in local coordinate system
private double[] xp, yp;
private int npoints;
// points of the shape in world coordinates
private int[][] wxp, wyp;
private boolean valid;
public void setRotation(double r) { this.rot = r; valid = false; }
public void setPosition(double x, double y) { this.x = x; this.y = y; valid = false; }
public void addPoint(double x, double y) {
// TODO: add point to xp, yp
valid = false;
}
public void draw(...) {
if (!valid) {
computeWorldCoordinates(wxp, wyp);
valid = true;
}
// TODO: draw shape at world coordaintes wxp and wyp
}
protected void computeWorldCoordinates(int[] xcoord, int[] ycoord) {
for (int i = 0; i < npoints; i++) {
double temp_x = xp[i] * Math.cos(rot) - yp[i] * Math.sin(rot);
double temp_y = xp[i] * Math.sin(rot) + yp[i] * Math.cos(rot);
xcoord[i] = (int) Math.round(x + temp_x);
ycoord[i] = (int) Math.round(y + temp_y);
}
}
}

Converting an Ellipse2D to Polygon

I have a Java swing application where I can draw hot spots. I am allowing user to draw Rectangle , Polygon and Circle.
For Circle I am using Ellipse2D
Ellipse2D.Double ellipseDouble = new Ellipse2D.Double(x,y,width,height);
g.draw(ellipseDouble);
Above works fine and it does draw an ellipse/circle.
Now the problems when I want the region to be used in HTML Image map.
Html Image map doesn't support Ellipse so I was thinking to use polygon for Ellipse2D but really don't know how would I convert it.
Does anyone know how would I go about it converting an Ellipse2D to Polygon ponits?

Use FlatteningPathIterator.
See e.g. http://java-sl.com/tip_flatteningpathiterator_moving_shape.html where point moves following custom Shape.
You can get list of Points and create Polygon.

Maybe someone will find this one useful: this is pdfbox ellipse or circle (width=height) draw function inside rectangle, it make ellipse as polygon initially to draw.
Code based on math function of ellipse at poin [0 , 0]: x^2/a^2 + y^2/b^2 = 1
private PdfBoxPoligon draw_Ellipse_or_Circle_as_poligon_with_PDFBOX (
PDPageContentStream content, float bottomLeftX, float bottomLeftY,
float width, float height, boolean draw) throws IOException {
PdfBoxPoligon result = new PdfBoxPoligon();
float a = width/2;
float b = height/2;
int points = (int) (a*b/20);
if (DEBUG) {
System.out.println("points=" + points);
}
//top arc
for (float x = -a; x < a; x = x + a / points) {
result.x.add(bottomLeftX + a + x);
float y = (float) Math.sqrt((1-(x*x)/(a*a))*(b*b));
result.y.add(bottomLeftY+b+y);
}
//bottom arc
for (float x = a; x >= -a; x = x - a / points) {
result.x.add(bottomLeftX + a + x);
float y = -(float) Math.sqrt((1-(x*x)/(a*a))*(b*b));
result.y.add(bottomLeftY+b+y);
}
result.x.add(result.x.get(0));
result.y.add(result.y.get(0));
if (draw) {
for (int i=1; i < result.x.size(); i++) {
content.addLine(result.x.get(i-1), result.y.get(i-1), result.x.get(i), result.y.get(i));
}
}
return result;
}

How to avoid overlapping polygon

I created a program to draw many polygons automatically everytimes user presses a button. The points of the polygon are generated automatically using the random function. The problem is that, since the points of the polygon were randomly generated, some of the polygon are overlap with other polygon. How can I avoid this, so that every polygon shown without being overlapped?
.....
List<Polygon> triangles = new LinkedList<Polygon>();
Random generator = new Random();
public void paintComponent(Graphics g) {
for(int i = 0; i < 10; i++) {
double xWidth = generator.nextDouble() * 40.0 + 10.0;
double yHeight = generator.nextDouble() * 40.0 + 10.0;
xCoord[0] = generator.nextInt(MAX_WIDTH);
yCoord[0] = generator.nextInt(MAX_HEIGHT);
xCoord[1] = (int) (xCoord[0] - xWidth);
xCoord[2] = (int) (xCoord[1] + (xWidth/2));
yCoord[1] = yCoord[0];
yCoord[2] = (int) (yCoord[1] - yHeight);
triangles.add( new Polygon(xCoord,yCoord, 3));
}
Graphics2D g2 = (Graphics2D) g;
g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
g2.setStroke(new BasicStroke(1));
g2.setComposite(AlphaComposite.getInstance(AlphaComposite.SRC_OVER, 1.00f));
g2.setPaint(Color.black);//set the polygon line
for (Polygon triangle : triangles) g2.drawPolygon(triangle);
Polygon[] triArray = triangles.toArray(new Polygon[triangles.size()]);
for (Polygon p:triArray) triangles.remove (p);
}

Check out the game programming wiki on Polygon Collision:
http://gpwiki.org/index.php/Polygon_Collision

You could break your canvas into 10 regions and constrain your polygons each to their own region. To do this, you could use your i value and a %100 (or other suitable magnitude) of your randomly generated value and apply them to your x coordinates and y coordinates as applicable. The result would be a grid of similarly constrained(no larger than the grid cell), but randomly shaped, Polygons.
EDIT:
Taking another look and fooling around a bit, I took the general concept as I described above and made a stab at an implementation:
public void paintComponent(Graphics g) {
int[] xCoord = new int[3];
int[] yCoord = new int[3];
int colCnt = 5;
int rowCnt = 2;
int maxCellWidth = getWidth() / colCnt;
int maxCellHeight = getHeight() / rowCnt;
for (int i = 0; i < (colCnt * rowCnt); i++) {
int xMultiple = i % colCnt;
int yMultiple = i / colCnt;
for (int j = 0; j < 3; j++) {
xCoord[j] = generator.nextInt(maxCellWidth)
+ (maxCellWidth * xMultiple);
yCoord[j] = generator.nextInt(maxCellHeight)
+ (maxCellHeight * yMultiple);
}
triangles.add(new Polygon(xCoord, yCoord, 3));
}
//... the rest of your method
}
As you can see, all of the Polygons have all points randomly generated, as opposed to your method of generating the first point and then making the rest relative to the first. There is a sense of randomness that is lost, however, as the Polygons are laid out in a grid-like pattern.

Create Area objects from your new polygon as well as for all existing polygons.
Subtract the new polygon's area from the existing ones. If the subtract changed the area, the polygons overlap.
Area newArea = new Area(newPolygon);
Area existingArea = new Area(existingPolygon);
Area existingAreaSub = new Area(existingPolygon); existingAreaSub.subtract(newArea);
boolean intersects = existingAreaSub.equals(existingArea);

You could implement a method Polycon.containsPoint( x, y ) and repeat your random generation until this method returns false for all drawn Polygons.

I have achieved this in Android Using Kotlin (See github project) by using JTS see here
Step-1:
Add JTS library to your project
implementation group: 'org.locationtech.jts', name: 'jts-core', version: '1.15.0'
Step-2:
Create JTS polygon objects for both polygon
// create polygons One
var polygoneOneArray: ArrayList<Coordinate> = ArrayList()
for (points in polygonOnePointsList) {
polygoneOneArray.add(Coordinate(points.latitude(), points.longitude()))
}
val polygonOne: org.locationtech.jts.geom.Polygon = GeometryFactory().createPolygon(
polygoneOneArray.toTypedArray()
)
// create polygons Two
var polygoneTwoArray: ArrayList<Coordinate> = ArrayList()
for (points in polygoneTwoPointsList) {
polygoneTwoArray.add(Coordinate(points.latitude(), points.longitude()))
}
val polygonTwo: org.locationtech.jts.geom.Polygon = GeometryFactory().createPolygon(
polygoneTwo.toTypedArray()
)
Step-3:
Get Common Area of both Polygon
val intersection: org.locationtech.jts.geom.Geometry = polygonOne.intersection(polygonTwo)
Step-4:
Remove common Area from polygonTwo
val difference: org.locationtech.jts.geom.Geometry = polygonTwo.difference(intersection)
Step-5:
Merge Both polygonOne and update polygonTwo
val union: org.locationtech.jts.geom.Geometry = mergePolygonList.get(0).polygons.union(difference)
Step-5:
Now pick points from Geometry and draw a final merged Polygon
val array: ArrayList<Coordinate> = union.coordinates.toList() as ArrayList<Coordinate>
val pointList: ArrayList<Point> = ArrayList()
for (item in array) {
pointList.add(Point.fromLngLat(item.y, item.x))
}
var list: ArrayList<List<Point>> = ArrayList<List<Point>>()
list.add(pointList)
style.addSource(
GeoJsonSource(
"source-id${timeStamp}",
Feature.fromGeometry(Polygon.fromLngLats(list))
)
)