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draw images with random rotation java + processing

I'm drawing arrows using Java and I can draw them straight but now I need to have the arrows pointing in different directions.
In my current code, I draw a triangle and then a square.
Is there a way to group the two after they've been drawn and then rotate them at a random angle?
Right now I'm only able to rotate the triangle and square separately, causing some messy thing.
void setup() {
size(400, 400);
}
void draw() {
float r = random(24, 64);
background(255);
drawArrow(r);
//drawPlus(r);
saveFrame("dataArrow/plus####.png");
if (frameCount == 100) {
exit();
}
}
void drawArrow(float r){
float base = r * 2;
float xStart = random(1, width-base - 1);
float xEnd = xStart + base;
float k = 0.5 * base;
float y = random(k, width-k);
float middleBase = base/2 + xStart;
float rectSide = 0.5 * base;
float rectX1 = middleBase - rectSide/2;
float rectX2 = middleBase + rectSide/2;
fill(0);
triangle(xStart, y, xEnd, y, middleBase, y - k);
rect(rectX1, y, rectSide, rectSide);
}

not sure if this exactly what you mean but here is how to move things around
push and pop matrix allows you to organize things that should have the same translations
https://processing.org/reference/pushMatrix_.html
https://processing.org/reference/rotate_.html
https://processing.org/reference/translate_.html
basic example
pushMatrix();//start of new translation and rotation things
translate(xAmount,yAmount);//this moves the origin
rotate(angle);//this rotates around origin
//drawing around the point of rotation 0,0 here
//drawing...
popMatrix();//reset all translations and rotations to before

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);
}
}
}

Rectangle with Double Values vs Int Values

I am making a game in java and my player can be rotated 360 degrees. I have to make a hitbox that rotates and moves with the player. I used a Rectangle to do this, however, it uses int values instead of double values and as a result, the hitbox's positioning is a little off (because I add double values to integers). How do I fix this?
I've already tried Rectangle2D.Double but I can't modify the x and y values.
Here is the relevant code:
Declaration:
private Rectangle hitbox;
private Shape transformed;
Initialization
hitbox = new Rectangle((int) x, (int) y + 20, currentImg.getWidth(), currentImg.getHeight()/2 + 20);
transformed = hitbox;
Movement
hitbox.x += xM * Math.sin(Math.toRadians(angle));
hitbox.y += yM * Math.cos(Math.toRadians(angle));
Rotation
AffineTransform transform = new AffineTransform();
transform.rotate(Math.toRadians(this.angle), hitbox.x + hitbox.getWidth()/2, hitbox.y + hitbox.getHeight()/2);
transformed = transform.createTransformedShape(hitbox);

Rendering an isometric map in java with individual rectangles

I've been researching for the past hour or so and I can't seem to render an isometric map. I want to achieve something like this.
But I am getting this.... I am storing my map as tiles in a 1 dimensional array like so:
private final int width, height;
private final int tileWidth, length;
private int[] tiles;
public Level(int width, int height) {
this.width = width;
this.height = height;
tiles = new int[width * height];
tileWidth = 68;
length = 48;
}
I am passing through 10, 10 as the parameters for width and height. And I render the map like so:
public void render(Graphics g) {
for (int x = 0; x < width; x++) {
for (int y = 0; y < height; y++) {
g.setColor(Color.red);
if (x % 2 == 0)
g.drawRect(x * tileWidth, y * length / 2, tileWidth, length);
else
g.fillRect((x * tileWidth) + (tileWidth / 2), (y * length / 2), width, length);
}
}
}
Any help would be really appreciated, I've wanted to learn to make isometric games but have been stuck with flat 2D for a while.

For just tiles, you could use a shear transform:
Graphics2D g2d = (Graphics2D) g;
AffineTransform at = AffineTransform.getShearInstance(1, 0);
g2d.transform(at);
// rest of your drawing code here
You may also want to set the shear anchor point:
double sa_x = 100, sa_y = 100; // or whatever
AffineTransform at = new AffineTransform();
// S3: Move back to original origin
at.translate(sa_x, sa_y);
// S2: Shear
at.shear(1, 0);
// S1: Set origin
at.translate(-sa_x, -sa_y);
You can vary the shear factor 1 to get different amounts of shear.

Instead of drawing rects, you need to draw lines at isometric angles.
The angles in isometric geometry are 30 degrees, 90 degrees, 150 degrees, 210 degrees and 270 degrees (in radians: pi/6, pi/2, 5pi/6, 7pi/6, 3pi/2, 11pi/6.).
cos(pi/6) is sqrt(3)/2 or 0.866... and sin(pi/6) is 1/2 or 0.5. (This is meaningful because of http://en.wikipedia.org/wiki/File:Sin-cos-defn-I.png )
This means that if you want to draw a line at the angle pi/6 that is D pixels long starting at x1,y1:
x2 = x1+cos(pi/6)*D e.g. x1+D*sqrt(3)/2
y2 = y1+sin(pi/6)*D e.g. y1+D/2
and draw from x1,y1 to x2,y2.
All the other angles are either reflections of this (one dimension or both are made negative) or straight up and down (trivial to draw).
To calculate where on the screen to draw an isometric object, consider that isometric geometry has three dimensions: X, Y, Z. Movement by Z will just make you draw D higher or D lower. Movement by X or Y will move you in one isometric angled direction or the other, by the same x and y as the distance of drawing one tile line in that direction (so similar formula to the above).

Translate Java 3D coordinates to 2D screen coordinates

I'm working with a Java 3D application called "Walrus" that is used to display directed graphs. The code already has a feature to highlight a node and draw label adjacent in graph given its screen coordinates.
Upon rotating the screen, the node is no more highlighted.
What I have is the node coordinates in 3D. I need to draw label to it.
Code for highlight using 3D coordinates
Point3d p = new Point3d();
m_graph.getNodeCoordinates(node, p);
PointArray array = new PointArray(1, PointArray.COORDINATES);
array.setCoordinate(0, p);
m_parameters.putModelTransform(gc);
gc.setAppearance(m_parameters.getPickAppearance());
How can I draw Label with 3D coordinates( Raster graphics throws error Renderer: Error creating immediate mode Canvas3D graphics context )
How can I convert 3D coordinates to 2D screen and use existing code to draw label at 2D screen point
Thanks,
Dakshina

I have an algorithm/method for converting [x,y,z] into [x,y] with the depth parameter:
The x value is : (int) (x - (z / depth * x))
The y value is : (int) (y - (z / depth * y))
Essentially, the depth is the focal point. The vanishing point will be at [0,0,depth].

Here's what i used to convert my 3D coordinates into perspective 2D, x2 and y2 being the 2dimensional coordinates, xyz being the 3D coordinates.
use these formulas:
x2 = cos(30)*x - cos(30)*y
y2 = sin(30)*x + sin(30)*y + z
I picked the angle 30 as it is easy for perspective purposes, also used in Isometric grids for drawing 3D on 2D papers. As the z axe will be the vertical one, x and y are the ones at 60 degrees from it right and left. Isometric Grid Picture.
I'm still working on rotation, but without altering the axes, just coordinate rotation in 3D.
Enjoy.

I found the solution.
This is the function to display Text3D at image 2D coordinates
public void drawLabel(GraphicsContext3D gc, double x, double y, int zOffset, String s) {
boolean frontBufferRenderingState = gc.getFrontBufferRendering();
gc.setBufferOverride(true);
gc.setFrontBufferRendering(true);
Point3d eye = getEye();
double labelZ = zOffset * LABEL_Z_OFFSET_SCALE
+ LABEL_Z_SCALE * eye.z + LABEL_Z_OFFSET;
double xOffset = LABEL_X_OFFSET * m_pixelToMeterScale;
double yOffset = LABEL_Y_OFFSET * m_pixelToMeterScale;
Point3d p = new Point3d(x + xOffset, y + yOffset, 0.0);
{
// Project given (x, y) coordinates to the plane z=labelZ.
// Convert from image-plate to eye coordinates.
p.x -= eye.x;
p.y -= eye.y;
double inversePerspectiveScale = 1.0 - labelZ / eye.z;
p.x *= inversePerspectiveScale;
p.y *= inversePerspectiveScale;
// Convert from eye to image-plate coordinates.
p.x += eye.x;
p.y += eye.y;
}
Transform3D scale = new Transform3D();
scale.set(LABEL_SCALE);
Vector3d t = new Vector3d(p.x, p.y, labelZ);
Transform3D translation = new Transform3D();
translation.set(t);
translation.mul(scale);
Transform3D transform = new Transform3D(m_imageToVworld);
transform.mul(translation);
gc.setModelTransform(transform);
//-----------------
int fontSize=(int)(10*m_magnification);
if(fontSize>20)
fontSize=20;
//---------------
// XXX: Courier may not be available on all systems.
Text2D text = new Text2D(s, new Color3f(1.0f, 1.0f, 1.0f),
"Courier", fontSize, Font.BOLD);
gc.draw(text);
gc.flush(true);
// NOTE: Resetting the model transform here is very important.
// For some reason, not doing this causes the immediate
// following frame to render incorrectly (but subsequent
// frames will render correctly). In some ways, this
// makes sense, because most rendering code assumes that
// GraphicsContext3D has been set to some reasonable
// transform.
gc.setModelTransform(m_objectTransform);
gc.setFrontBufferRendering(frontBufferRenderingState);
}
This is the function to take 3D coordinates and convert them to image 2D coordinates and render using above function
private boolean displayOnScreenLabel(int node, String label) {
boolean success = false;
try {
Transform3D transform = m_parameters.getObjectToEyeTransform();
Point3d nodeC = new Point3d();
m_graph.getNodeCoordinates(node, nodeC);
transform.transform(nodeC);
Point3d eye = m_parameters.getEye();
double perspectiveScale = 1.0 / (1.0 - nodeC.z / eye.z);
double centerX = eye.x + nodeC.x * perspectiveScale;
double centerY = eye.y + nodeC.y * perspectiveScale;
GraphicsContext3D gc = m_canvas.getGraphicsContext3D();
m_parameters.drawLabel(gc, centerX, centerY, m_labelZOffsetCounter++, label);
success = true;
} catch (final java.lang.OutOfMemoryError error) {
JOptionPane.showMessageDialog(m_frame, "The 3D Graphics is unable to find enough memory on your system. Kill the application!", "Out Of Memory!", JOptionPane.ERROR_MESSAGE);
} catch (Exception e) {
success = false;
}
return success;
}