// Forked from "Deployable kirigami" by JooWoho
// https://turtletoy.net/turtle/6a37b2a9f7

Canvas.setpenopacity(1);

const turtle = new Turtle();
let scale = 1; // adjust to fit canvas

// ----------------------
// PARAMETERS
// ----------------------
const part = 8;          // number of sections
const circle_number = 30; // total circles
let r0 = 15;              // starting radius
let w = 2;                // base width

// Initial epsilon for first circle
let epsilon0 = 5;

// ----------------------
// Examples slope functions

//constant slope
//function epsilon_slope(n) { return epsilon0}

// linear increase
//function epsilon_slope(n) { return epsilon0 + n*0.2; }

// linear decrease
//function epsilon_slope(n) { return epsilon0 - n*0.1; }

// sinusoidal variation
function epsilon_slope(n) { return epsilon0 * (1 + 0.3 * Math.sin(n/5)); }


// ----------------------
// DRAW ARC FUNCTION
// ----------------------
function draw_arc(radius, start, end, epsilon) {
    const steps = 20;
    const step = (end - start) / steps;

    for (let k = 0; k <= steps; k++) {
        let angle = start + k * step;
        let x = scale * radius * Math.cos(angle);
        let y = scale * radius * Math.sin(angle);

        if (k === 0) {
            turtle.penup();
            turtle.goto(x, y);
            turtle.pendown();
        } else {
            turtle.goto(x, y);
        }
    }
}

// ----------------------
// WALK FUNCTION
// ----------------------
function walk(i) {
    if (i > 0) return false; // draw only once

    let r = r0;

    for (let n = 0; n < circle_number; n++) {

        // Compute epsilon for this circle
        let epsilon = epsilon_slope(n);

        // Compute radius increment from slope equation
        if (n === 0) delta_r = 0; // first circle doesn't grow

        let start = 0;
        let end = start + 2 * Math.PI / part;
        let start2 = end;
        let end2 = start2 + 2 * Math.PI / part;

        for (let j = 1; j <= part; j++) {
            if (n % 2 === 0) {
                draw_arc(r, start - epsilon / r, end + epsilon / r, epsilon);
            } else {
                draw_arc(r, start2 - epsilon / r, end2 + epsilon / r, epsilon);
            }

            start = end + 2 * Math.PI / part;
            end = start + 2 * Math.PI / part;
            start2 = end2 + 2 * Math.PI / part;
            end2 = start2 + 2 * Math.PI / part;
        }

        // Update radius according to slope equation
        r += w;
    }

    return false;
}