# Coordinates (en)

deutsche Version

Processing uses a Cartesian coordinate system. It is important to note that the zero point is in the upper left corner in processing. The X axis is from left to right and the Y axis is from top to bottom. While this might seem odd, it comes from the tradition that bitmaps were always read in that order. In computer graphics the cartesian coordinate system is almost always used.

In processing we can simplify the drawing of objects in many cases by assigning them their own local coordinate system. Imagine an animation of a car moving across the screen. If you draw this in processing you could add a value to the the x and y coordinates for every detail of the car to move it across the screen. When it comes to the wheels, it would get complicated as we would not only change the position relative to the car, but rotate every detail in relation to the wheel axis! But if we modify the coordinate systems this becomes a lot simpler. Such coordinate system changes are called transformations. There are three basic types:

• Translation – shifting
• Rotation
• Scaling

It should be noted that such transformations are not commutative. That means the order that you make the transformations will effect the output. In processing, the commands look like this:

```translate(float x, float y)
rotate(float angle)
scale(float xScale, float yScale)```

If you work in 3D mode, there is a third parameter for the z axis.

Frequently, local and global coordinate systems will be used. The global coordinate system is the original coordinate system, in processing this is the one fixed to the upper left corner. If the original coordinate system is transformed, then the result is local coordinate system (in reference to the global). To switch between these coordinate systems, there are two commands from Processing:

• pushMatrix() – save the current coordinate system

These two commands work according to the stack principle. This is an very old form of working with computer memory. Just imagine a stack of graph paper: when you call pushMatrix, the stack is increased by one sheet. On this page we would describe the current data of our coordinate system. Now you can rotate, scale and transform as you want. If you now want to bring the coordinate system back to the position of the last pushMatrix call, you must call popMatrix.

With an example program, this should be easer to understand:

```void setup()
{
size(400,400);      // def. window size
strokeWeight(15);    // line thickness
}

void draw()
{
background(255);    // def. background colour
float radius = dist(mouseX,mouseY,width/2,height/2);  // calculate the distance from the mouse curser to the center of the screen

pushMatrix();
translate(200,200);
rotate(calcAngle());
smiley();          // function call
popMatrix();

pushMatrix();
translate(30,30);
scale(.2);
smiley();          // function call
popMatrix();
}

// funktion
void smiley()
{
noFill();

fill(0);
ellipse(0 - 30,0 - 30,20,20);  // left eye
ellipse(0 + 30,0 - 30,20,20);  // right eye

noFill();
}

// calculate the angle from the screen middle to the mouse cursor
// the angle is in radians
float calcAngle()
{
return -atan2(mouseX - (width / 2),mouseY - (height / 2));
}```

This example introduces a couple of new things starting on line 13:

Here the distance from the mouse pointer to the window centre is determined (see Pythagoras).

The original range is from 0 to the width of the window. The target range is from 1-4. Now radius is transformed from original range to the target range.

-atan2(mouseX - (width / 2),mouseY - (height / 2));

The atan2 function returns the angle in radians at a given coordinate from the 0 point. In this example we shift the 0 point to the centre of the screen by subtracting width/2 from X and height/2 from Y.

# `Image Credit: wikipedia`

# Exercise 8

Create a new program where a simple car follows the mouse on the screen from left to right. The car should be drawn from the side, and include wheels that rotate. You may use the example code to get started.

```int rotation;
void setup()
{
size(900, 400);      // def. window size
}

void draw()
{
rotation++;
}

void car(int x, int y) {
fill(100);
beginShape();
vertex(0, 0);
vertex(5, -50);
vertex(50, -50);
vertex(70, -80);
vertex(150, -80);
vertex(190, -50);
vertex(265, -45);
vertex(270, 0);
vertex(0, 0);
endShape();
wheel(60, 0);
wheel(210, 0);
}

void wheel(int x, int y) {
fill(150);
stroke(0);
strokeWeight(7);
strokeWeight(4);
noStroke();
}
```

Possible Solution:

Solution to exercise  Expand source
```int rotation;
boolean forward = true;
int xScale = 1;
void setup()
{
size(900, 400);
}

void draw()
{
background(255);
int mouseMovement = mouseX-pmouseX; //pmousex gives us our mouse x value from the last frame. Subtracting from the current position give us the distance moved per frame
if (mouseMovement<0) { // if the movement is negative, then we flip everthing backwards with a negative xcale
xScale = -1;
}
if (mouseMovement>0) { // if the movement is positive, then our xscale is positive
xScale = 1;
}
rotation+= abs(mouseMovement);
car(mouseX, height/2);
}

void car(int x, int y) {
pushMatrix();
translate(x, y);
scale(xScale, 1);
fill(100);
beginShape();
vertex(0, 0);
vertex(5, -50);
vertex(50, -50);
vertex(70, -80);
vertex(150, -80);
vertex(190, -50);
vertex(265, -45);
vertex(270, 0);
vertex(0, 0);
endShape();
wheel(60, 0);
wheel(210, 0);
popMatrix();
}

void wheel(int x, int y) {
fill(150);
stroke(0);
pushMatrix();
translate(x, y);