Question

The problem is to position dots in certain sectors of a circle starting in the center.

$dot[1] = secto12;
$dot[2] = secto6;
$dot[3] = secto8;
$dot[4] = secto2;
$dot[5] = secto8;
$dot[6] = secto3;
etc...

We could use PHP or javascript.

I can imagine a function to mimic a centripetal force. Or maybe some procedure of analytic geometry. Or whatever…

Any idea is welcome.
THX.-

Answer 1

The solution that I used is a little complicated. And is not generic. We need calculate certain things manually ($factor (variations of angles) and $dots (amount of dots to draw on certain radius)).

But I want to give the basic ideas for someone else that needs something similar:

1.- We use the equation that find a point given:
0.- a center point: ($x0, $y0)
1.- a radius: $r
2.- an angle: $angle

$x = floor($x0 + $r * sin($angle * pi() / 180));
$y = floor($y0 + $r * -cos($angle * pi() / 180));

2.-We plot dots (certain amount of dots) changing the radius and the angle
The amount of dots depends of the radius. More radius more dots. We will need define a function that draw dots sector by sector.

3.- We need calculate certain things manually ($factor (variations of angles) and $dots (amount of dots to draw on certain radius)). Here it is:

if ($r >= 90) {
    $dots = 4;
    $factor = 12.1;
}
if ($r >= 100) {
    $dots = 4;
    $factor = 12.4;
}
if ($r >= 110) {
    $dots = 5;
    $factor = 8.4;
}
if ($r >= 120) {
    $dots = 6;
    $factor = 6.2;
}
if ($r >= 130) {
    $dots = 7;
    $factor = 5.2;
}
if ($r >= 140) {
    $dots = 8;
    $factor = 4.4;
}
if ($r >= 150) {
    $dots = 9;
    $factor = 3.8;
}
if ($r >= 200) {
    $dots = 10;
    $factor = 3.40;
}
if ($r >= 220) {
    $dots = 11;
    $factor = 3.0;
}

Those are the main ideas to solve this, in this tricky way.

4.- Obviously this code (inside a function) must be called inside nested loops (3 in my case)

function plot($sector, $start) {
    ....
}

$start is the angle from start drawing: 0, 30, 60,…, 330

??? OK, here is the function. Enjoy:

function plot($sector, $start) {

    static $static;
    $x0 = 0;
    $y0 = 0;

    if ( ! isset($static[$sector])) {
        /*
         * factor: related to the amplitude of the arc on which dots are drawn. (11.1 -> 3.0)
         * dots: how many dots draw towards the right. (3 -> 10)
         * r: radius in pixels. (60 -> 240)
         * jstatic: save last position of dot drawn.
         *
         */
        $static[$sector]['factor'] = 11.1;
        $static[$sector]['dots'] = 4;
        $static[$sector]['r'] = 60;
        $static[$sector]['jstatic'] = 0;
    }

    $factor = $static[$sector]['factor'];
    $dots = $static[$sector]['dots'];
    $r = $static[$sector]['r'];
    $jstatic = $static[$sector]['jstatic'];

    for ($j = $jstatic; $j < $dots; $j ++ ) {
        if ($r >= 90) {
            $dots = 4;
            $factor = 12.1;
        }
        if ($r >= 100) {
            $dots = 4;
            $factor = 12.4;
        }
        if ($r >= 110) {
            $dots = 5;
            $factor = 8.4;
        }
        if ($r >= 120) {
            $dots = 6;
            $factor = 6.2;
        }
        if ($r >= 130) {
            $dots = 7;
            $factor = 5.2;
        }
        if ($r >= 140) {
            $dots = 8;
            $factor = 4.4;
        }
        if ($r >= 150) {
            $dots = 9;
            $factor = 3.8;
        }
        if ($r >= 200) {
            $dots = 10;
            $factor = 3.40;
        }
        if ($r >= 220) {
            $dots = 11;
            $factor = 3.0;
        }

        if ($j == $dots - 1) {
            $j = 0;
            $jstatic = 0;
            // increase radius (by 10 pixels --each dot have 7 pixel of diameter) to the next arc.
            $r = $r + 10;
        }

        // stop if circumference is reached.
        if ($r > 240)
            break;

        $angle = $factor * $j + $start;

        // (x, y) is...
        $x = floor($x0 + $r * sin($angle * pi() / 180));
        $y = floor($y0 + $r * -cos($angle * pi() / 180));

        $pos['x'] = $x;
        $pos['y'] = $y;

        $jstatic ++;

        // save all dat by each sector
        $static[$sector]['factor'] = $factor;
        $static[$sector]['dots'] = $dots;
        $static[$sector]['r'] = $r;
        $static[$sector]['jstatic'] = $jstatic;

        /*
         * only for debugging:
         * counting how many dots are drawn
          static $countDots = 0;
          global $countDots;
          $countDots++;
         */
        return $pos;
    }
}