/**
 * Bernstein polynomials
 * By Raphael Rouvinov-Kats
 * 
 * Create curves using bernstein polynomials
 * https://en.wikipedia.org/wiki/Bernstein_polynomial
 * E.g. if you have 3 points P1 P2 P3 and you're calculating a curve
 * C(t) where 0 <= t <= 1
 * 
 * C(t) = (1-x)^2 P1 + 2x(1-x) P2 + x^2 P3
 * */

var num_vertices = 4;
var vertex_diam = 10;
var t_step = 0.05;

var vertices = [];
for (var i = 0; i < num_vertices; i++) {
    vertices.push([random(0, 400), random(0, 400)]);
}

var selected_vertex = -1;

// return n choose k using dynamic programming
var binom_coeff_memo = {};
var binom_coeff = function(n, k) {
    binom_coeff_memo[n] = binom_coeff_memo[n] || {};
    if (n in binom_coeff_memo && k in binom_coeff_memo[n]) {
        return binom_coeff_memo[n][k];
    }
    
    if (k === 0) {
        binom_coeff_memo[n][k] = 1;
    }
    else if (k === 1 || n === 1) {
        binom_coeff_memo[n][k] = n;
    }
    else if (k > n) {
        println("ahh @ line 31");
        return undefined;
    }
    else if (k > n/2) {
        binom_coeff_memo[n][k] = binom_coeff(n, n-k);
    } 
    else {
        binom_coeff_memo[n][k] = n/k * binom_coeff(n-1, k-1);
    }
    
    return binom_coeff_memo[n][k];
};

// returns whether mouse is over vertex i
var over_vertex = function(i) {
    return dist(mouseX, mouseY, vertices[i][0], vertices[i][1]) < vertex_diam/2;
};

var draw = function() {
    background(255, 255, 255);
    
    // draw line
    var old_x = vertices[0][0], old_y = vertices[0][1];
    for (var t = 0; t <= 1.0001; t += t_step) {
        
        // calculate coordinates at step t
        var new_x = 0, new_y = 0;
        for (var i = 0; i < vertices.length; i++) {
            new_x += binom_coeff(vertices.length-1, i) * 
                     pow(t, i) *
                     pow(1-t, vertices.length-i-1) * vertices[i][0];
            new_y += binom_coeff(vertices.length-1, i) * 
                     pow(t, i) *
                     pow(1-t, vertices.length-i-1) * vertices[i][1];
        }
        
        stroke(map(t,0,1,0,255), 0, 0);
        line(old_x, old_y, new_x, new_y);
        old_x = new_x;
        old_y = new_y;
    }
    
    // draw points, stroke if hovered over or selected
    for (var i = 0; i < vertices.length; i++) {
        fill(map(i, 0, vertices.length-1, 0, 255), 0, 0);
        noStroke();
        
        if (selected_vertex === i) {
            stroke(0, 255, 89);
        }
        else if (selected_vertex === -1 && over_vertex(i)) {
            stroke(60, 0, 255);
        }
        
        ellipse(vertices[i][0], vertices[i][1], vertex_diam, vertex_diam);
    }
    
    // move selected vertex
    if (selected_vertex !== -1) {
        vertices[selected_vertex][0] = mouseX;
        vertices[selected_vertex][1] = mouseY;
    }
    
};

var mousePressed = function() {
    for (var i = 0; i < vertices.length; i++) {
        if (over_vertex(i)) {
            selected_vertex = i;
        }
    }
};

var mouseReleased = function() {
    selected_vertex = -1;
};