Creating Visualisations in Processing and Understanding Code

Question

I am trying to get into creative coding mainly for creating live visuals. I have recently stumbled upon this great website called https://www.openprocessing.org/ where people can share their creations.

I have attached code below for creating two moving circles but I am having trouble understanding how the creator went about doing so, If anyone could explain to me how the for loop is working as well as how the x += 0.006; y += 0.006; if (x > TWO_PI) {x = 0;} section works, it would be greatly appreciated. The use of sin, cos and the Two_PI functions has me puzzled. Here is a link to the original code:

https://www.openprocessing.org/sketch/467333

//comment
float x = 0;
float xx = 0;
float y = 0;
float yy = 0;
float sizecircle = 250;

void setup() {
    size (800, 650);
    frameRate (60);
    strokeWeight (1);
    stroke (223, 170, 22);
}

void draw() {
    background (51, 51, 51);

    for (float i = 0; i < TWO_PI; i += TWO_PI/100) {  
        line (350 + sin(x+i) * sizecircle, 275 + cos(y+i) * sizecircle, 450 + cos(xx+i) * sizecircle, 375 + sin(yy+i) * sizecircle);
    }

    x += 0.006;
    y += 0.006;
    if (x > TWO_PI) {
        x = 0;
    }
    if (y > TWO_PI) {
        y = 0;
    }

    xx += 0.002;
    yy += 0.002;
    if (xx > TWO_PI) {
        xx = 0;
    }
    if (yy > TWO_PI) {
        yy = 0;
    }
}

Answer 1

The unit of the angle for sin and cos is Radian. 360° are 2*PI, this is the reason for TWO_PI.
The variables x, y, xx and yy are incremented for 0.0 to 2*PI. If they reach 2*PI, they start form 0.0 again.

With the following code will draw lines from a center point (cx, cy) to 100 points around a circle with radius r.

for (float i = 0; i < TWO_PI; i += TWO_PI/100) {  
    line(cx, cy, cx + cos(i)*r, cy + sin(i)*r);
}  

The trick in the code of the question is that the lines are connection the points around 2 circles, which are rotating opposite direction:

line(cx1 + sin(i)*r, cy1 + cos(i)*r,
     cx2 + cos(i)*r, cy2 + sin(i)*r);

Note, that the order of sin and cos is swapped for the start point in compare to the end point, this causes that the circles are rotating opposite directions.
The different rotation speed is caused by the different constants 0.006 respectively 0.002.

---

By the way, the code can be simplified, because x == y and xx == yy. It is sufficient to use 2 angles in the range [0, TWO_PI]:

float a1 = 0;
float a2 = 0;
float sizecircle = 250;
void draw() {
    background (51, 51, 51);

    for (float i = 0; i < TWO_PI; i += TWO_PI/100) {  
        line (350 + sin(a1+i)*sizecircle, 275 + cos(a1+i)*sizecircle,
              450 + cos(a2+i)*sizecircle, 375 + sin(a2+i)*sizecircle);
    }

    a1 += 0.006;
    a2 += 0.002;
}

Since sin(x) == sin(x + TWO_PI*n) and cos(x) == cos(x + TWO_PI*n) (n is an integral number), it is not necessary to "reset" the angles.

Answer 2

It's more about math than about programming (well, both these things goes hand in hand).

He's doing the same thing twice, once for each circle, but one of the two will "move" faster than the other, hence the difference in x += 0.006; and xx += 0.002;.

There are 2 PI radians in a full circle (so 2 PI radians == 360 degrees). That's why he's using this measure.

This line

line (350 + sin(x+i) * sizecircle, 275 + cos(y+i) * sizecircle, 450 + cos(xx+i) * sizecircle, 375 + sin(yy+i) * sizecircle);

defines how each circle is "attached" to the other one by drawing a bunch of lines between them. The idea is that the author created a loop that updated the beginning point and the end point of a line, and this loop runs as long as there are lines to draw (it goes around the circle using the 2 PI number).

So in the for (float i = 0; i < TWO_PI; i += TWO_PI/100) loop he draws every line for this position of the circles.

Than he changes the "starting point" where he'll draw the first line by increasing variables x, y, xx, yy a little bit. As they are used in the context of radians, they "circle" around the circles.

Then the draw() loop start over again and he re-draws the whole thing, but a little different as the starting points changed. This makes the drawing look like it moves.

When the "starting points" variables x, y, xx, yy are finished doing a complete turn (so when they are over 2 PI radians), he resets them. As it's a full turn, it's not a huge reset. It's like rounding the time when the clock is one minute past the hour.

Hope it helps.