Sacks-Spiral-OpenSCAD/sacks-spiral.scad at master · GeoMaciolek/Sacks-Spiral-OpenSCAD · GitHub

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/*
    Sacks Spiral
    2019-10-01
    https://github.com/GeoffMaciolek/????
    https://thingiverse.com/whatever (geo profile)

    An archimedes spiral highlighting prime numbers.  The Sacks Spiral
    is based on the Ulam spiral.
    https://en.wikipedia.org/wiki/Ulam_spiral

    See README.md for details of creating additional
    files, such as prime_table.scad etc
*/

/*
    Settings
*/

// Base Width - how large do you want this to be, in mm?
// base_width=300;
// Overall Height Ratio - how much of a 'pancake' vs a soda can? 0.1 = Height is 1/10th the width
overall_height_ratio=0.1;
// Max Number - How high do you want to count?
max_num=2500; //scale needs fixing for 'width/num ratio'


include <prime_table.scad>
//primes = [0,1,2,3];

//$fn=160; // Circle face number (can be defined per object)

/*
    GLOBALS
*/

base_width=max_num; //*0.173; // Happens to work out this way IF max_num is 300. Fiddling?


overall_height=base_width*overall_height_ratio;
section_height=overall_height/4;

/*
    MODULES
*/


module base() {
    $fn=160;

    cylinder(
        h = section_height*2,
        r = base_width
    );
}

module middle(base_width=200) {
    $fn=160;
    overall_height=base_width*overall_height_ratio;
    translate([0, 0, overall_height])
        cylinder(
            h = overall_height,
            r = base_width*0.8
            // y = 0 + overall_height*overall_height_ratio
        );
}

module littlespot(x,y,type) { } // TODO

module arch_spiral() {
    dia=base_width/60; // to be set up based on max num.
    spacing_factor=128;

    for(i = [0:max_num]) {
        // time = i / 20 * PI;
        //x= (4 + (20 * time)) * cos(time);
        //y= (4 + (20 * time)) * sin(time);

        //x=(-1 * cos(sqrt(i)*2*PI)*sqrt(i))*400;
        //y=(sin(sqrt(i)*2*PI)*sqrt(i))*400;

        r = sqrt(i);
        //echo("I: ", i, "   R: ", r);
        theta = r * 2 * PI;

        x = cos(theta*(180/PI))*(r*spacing_factor);
        y = sin(theta*(180/PI))*(r*spacing_factor);

        //primeoffset=1
        primeoffset= isPrime(i) ? 30 : 0;
            //primeoffset=4;
        // if it's prime, set above to 2

        translate([x,y,overall_height])
            cylinder(
                r=dia+((primeoffset-1)*1.5), //1.5 here is the 'larger factor' for prime spots
                h=section_height//*primeoffset
            );
            //cube([5,5,5]);
    }

    /* sachs type:

    theta = sqrt(i) * 2 * pi
    r = sqrt(i),

    and thus its x,y co-ordinates are given by:

    x = -cos(sqrt(i)*2*pi)*sqrt(i)
    y = sin(sqrt(i)*2*pi)*sqrt(i)


    standard:
    for i in range(200):
        t = i / 20 * pi
        x = (1 + 5 * t) * cos(t)
        y = (1 + 5 * t) * sin(t)
        plot(x, y)

    */

}

function isPrime(num) = (
    // Note: "primes" is loaded from prime_table.scad - see for details
    search(num,primes) != []

);


/*
    BEGIN MAIN EXECUTION
*/

//base();

arch_spiral();
//middle();
/*
// test prime table
for(testy = [1:15]) {
    echo(testy, "is prime? ",isPrime(testy));
}
*/