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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<title>n-gon viewer</title>
<style>
#container{
margin: 10px;
padding: 10px;
}
.canvasContainer{
display: inline-block;
border: solid;
margin: 5px;
padding: 10px;
border-radius: 5px;
}
</style>
</head>
<body>
<div id="container">
<div id="parameters">
<p>Value of n:</p>
<input id="input_n" type="number" min="7" step="1" value="7"></input>
<p>Must be on the form 4|n or 4|n+1</p>
</div>
<div id="graphics">
<div class="canvasContainer">
<h2>Smallest</h2>
<p id="smallestComment"></p>
<canvas id="smallest" width="600" height="400"></canvas>
</div>
<div class="canvasContainer">
<h2>Largest</h2>
<p id="largestComment"></p>
<canvas id="largest" width="600" height="400"></canvas>
</div>
</div>
</div>
<script>
const solutions = {
7: {
minimum: 14,
minimum_vertices: [{"x":0,"y":0},{"x":7,"y":0},{"x":7,"y":-2},{"x":10,"y":-2},{"x":6,"y":-5},{"x":6,"y":-1},{"x":0,"y":-1},{"x":0,"y":0}],
minimum_proven: true,
maximum: 48,
maximum_vertices: [{"x":0,"y":0},{"x":7,"y":0},{"x":7,"y":-4},{"x":4,"y":-8},{"x":1,"y":-8},{"x":1,"y":-6},{"x":0,"y":-6},{"x":0,"y":0}],
maximum_proven: true
},
8: {
minimum: 16,
minimum_vertices: [{"x":0,"y":0},{"x":8,"y":0},{"x":8,"y":-6},{"x":10,"y":-6},{"x":10,"y":-9},{"x":7,"y":-5},{"x":7,"y":-1},{"x":0,"y":-1},{"x":0,"y":0}],
minimum_proven: true,
maximum: 75,
maximum_vertices: [{"x":0,"y":0},{"x":8,"y":0},{"x":8,"y":4},{"x":5,"y":8},{"x":5,"y":10},{"x":-1,"y":10},{"x":-1,"y":3},{"x":0,"y":3},{"x":0,"y":0}],
maximum_proven: true
},
11: {
minimum: 27,
minimum_vertices: [{"x":0,"y":0},{"x":11,"y":0},{"x":15,"y":-3},{"x":15,"y":-5},{"x":18,"y":-5},{"x":10,"y":1},{"x":1,"y":1},{"x":1,"y":5},{"x":8,"y":5},{"x":8,"y":6},{"x":0,"y":6},{"x":0,"y":0}],
maximum: 271,
maximum_vertices: [{"x":0,"y":0},{"x":11,"y":0},{"x":17,"y":-8},{"x":17,"y":-15},{"x":14,"y":-15},{"x":10,"y":-18},{"x":1,"y":-18},{"x":1,"y":-14},{"x":-1,"y":-14},{"x":-1,"y":-6},{"x":0,"y":-6},{"x":0,"y":0}]
},
12: {
minimum: 37,
minimum_vertices: [{"x":0,"y":0},{"x":3,"y":4},{"x":3,"y":8},{"x":13,"y":8},{"x":13,"y":-1},{"x":6,"y":-1},{"x":6,"y":-2},{"x":14,"y":-2},{"x":14,"y":9},{"x":2,"y":9},{"x":2,"y":3},{"x":0,"y":3},{"x":0,"y":0}],
maximum: 378,
maximum_vertices: [{"x":0,"y":0},{"x":12,"y":0},{"x":15,"y":4},{"x":15,"y":12},{"x":14,"y":12},{"x":14,"y":19},{"x":8,"y":19},{"x":8,"y":21},{"x":-3,"y":21},{"x":-3,"y":17},{"x":-6,"y":17},{"x":-6,"y":8},{"x":0,"y":0}]
},
15: {
minimum: 49,
minimum_vertices: [{"x":0,"y":0},{"x":-6,"y":-8},{"x":-10,"y":-11},{"x":-8,"y":-11},{"x":1,"y":1},{"x":1,"y":13},{"x":12,"y":13},{"x":12,"y":6},{"x":6,"y":6},{"x":6,"y":9},{"x":5,"y":9},{"x":5,"y":5},{"x":13,"y":5},{"x":13,"y":14},{"x":0,"y":14},{"x":0,"y":0}],
maximum: 955,
maximum_vertices: [{"x":0,"y":0},{"x":14,"y":0},{"x":20,"y":8},{"x":20,"y":19},{"x":19,"y":19},{"x":19,"y":27},{"x":7,"y":36},{"x":-2,"y":36},{"x":-6,"y":33},{"x":-10,"y":33},{"x":-10,"y":27},{"x":-12,"y":27},{"x":-12,"y":15},{"x":-7,"y":3},{"x":0,"y":3},{"x":0,"y":0}]
},
16: {
minimum: 59,
minimum_vertices: [{"x":0,"y":0},{"x":-12,"y":-9},{"x":-12,"y":0},{"x":-15,"y":0},{"x":-11,"y":3},{"x":-11,"y":-8},{"x":-3,"y":-2},{"x":-3,"y":5},{"x":13,"y":5},{"x":13,"y":-3},{"x":0,"y":-3},{"x":0,"y":-2},{"x":12,"y":-2},{"x":12,"y":4},{"x":-2,"y":4},{"x":-2,"y":0},{"x":0,"y":0}],
maximum: 1221,
maximum_vertices: [{"x":0,"y":0},{"x":-11,"y":0},{"x":-11,"y":-3},{"x":-17,"y":-3},{"x":-17,"y":-10},{"x":-20,"y":-14},{"x":-20,"y":-26},{"x":-11,"y":-38},{"x":3,"y":-38},{"x":3,"y":-37},{"x":12,"y":-37},{"x":18,"y":-29},{"x":18,"y":-13},{"x":16,"y":-13},{"x":16,"y":-5},{"x":12,"y":-5},{"x":0,"y":0}]
},
19: {
minimum: 84,
minimum_vertices: [{"x":0,"y":0},{"x":-6,"y":-8},{"x":-10,"y":-11},{"x":-8,"y":-11},{"x":1,"y":1},{"x":1,"y":18},{"x":17,"y":18},{"x":17,"y":6},{"x":6,"y":6},{"x":6,"y":13},{"x":12,"y":13},{"x":12,"y":10},{"x":13,"y":10},{"x":13,"y":14},{"x":5,"y":14},{"x":5,"y":5},{"x":18,"y":5},{"x":18,"y":19},{"x":0,"y":19},{"x":0,"y":0}],
maximum: 2386,
maximum_vertices: [{"x":0,"y":0},{"x":2,"y":0},{"x":2,"y":11},{"x":8,"y":11},{"x":16,"y":17},{"x":32,"y":17},{"x":44,"y":12},{"x":51,"y":12},{"x":51,"y":4},{"x":54,"y":4},{"x":54,"y":-14},{"x":53,"y":-14},{"x":53,"y":-26},{"x":41,"y":-35},{"x":22,"y":-35},{"x":7,"y":-27},{"x":3,"y":-27},{"x":3,"y":-18},{"x":0,"y":-14},{"x":0,"y":0}]
},
20: {
minimum: 92,
minimum_vertices: [{"x":0,"y":0},{"x":0,"y":4},{"x":2,"y":4},{"x":-14,"y":16},{"x":-14,"y":10},{"x":-17,"y":10},{"x":-13,"y":7},{"x":-13,"y":15},{"x":-1,"y":6},{"x":-1,"y":-1},{"x":18,"y":-1},{"x":18,"y":17},{"x":4,"y":17},{"x":4,"y":4},{"x":14,"y":4},{"x":14,"y":5},{"x":5,"y":5},{"x":5,"y":16},{"x":17,"y":16},{"x":17,"y":0},{"x":0,"y":0}],
maximum: 2994,
maximum_vertices: [{"x":0,"y":0},{"x":9,"y":12},{"x":9,"y":18},{"x":20,"y":18},{"x":20,"y":21},{"x":36,"y":21},{"x":36,"y":20},{"x":50,"y":20},{"x":62,"y":4},{"x":62,"y":-14},{"x":59,"y":-18},{"x":59,"y":-27},{"x":44,"y":-35},{"x":36,"y":-35},{"x":36,"y":-37},{"x":17,"y":-37},{"x":9,"y":-31},{"x":5,"y":-31},{"x":5,"y":-24},{"x":0,"y":-12},{"x":0,"y":0}]
},
23: {
minimum: 127,
minimum_vertices: [{"x":0,"y":0},{"x":-6,"y":-8},{"x":-10,"y":-11},{"x":-8,"y":-11},{"x":1,"y":1},{"x":1,"y":22},{"x":21,"y":22},{"x":21,"y":5},{"x":5,"y":5},{"x":5,"y":17},{"x":16,"y":17},{"x":16,"y":11},{"x":9,"y":11},{"x":9,"y":14},{"x":8,"y":14},{"x":8,"y":10},{"x":17,"y":10},{"x":17,"y":18},{"x":4,"y":18},{"x":4,"y":4},{"x":22,"y":4},{"x":22,"y":23},{"x":0,"y":23},{"x":0,"y":0}],
maximum: 5002,
maximum_vertices: [{"x":0,"y":0},{"x":6,"y":8},{"x":6,"y":19},{"x":15,"y":19},{"x":27,"y":24},{"x":49,"y":24},{"x":49,"y":20},{"x":61,"y":20},{"x":73,"y":11},{"x":73,"y":-7},{"x":76,"y":-7},{"x":76,"y":-28},{"x":68,"y":-43},{"x":62,"y":-43},{"x":62,"y":-50},{"x":54,"y":-50},{"x":50,"y":-53},{"x":27,"y":-53},{"x":27,"y":-51},{"x":13,"y":-51},{"x":1,"y":-35},{"x":1,"y":-19},{"x":0,"y":-19},{"x":0,"y":0}]//[{"x":0,"y":0},{"x":1,"y":0},{"x":1,"y":18},{"x":13,"y":34},{"x":25,"y":34},{"x":25,"y":37},{"x":44,"y":37},{"x":56,"y":32},{"x":67,"y":32},{"x":73,"y":24},{"x":73,"y":10},{"x":77,"y":10},{"x":77,"y":-11},{"x":74,"y":-15},{"x":74,"y":-31},{"x":66,"y":-31},{"x":51,"y":-39},{"x":28,"y":-39},{"x":28,"y":-37},{"x":19,"y":-37},{"x":7,"y":-28},{"x":7,"y":-22},{"x":0,"y":-22},{"x":0,"y":0}]//[{"x":0,"y":0},{"x":4,"y":0},{"x":4,"y":14},{"x":10,"y":14},{"x":26,"y":26},{"x":45,"y":26},{"x":45,"y":25},{"x":63,"y":25},{"x":75,"y":16},{"x":75,"y":4},{"x":77,"y":4},{"x":77,"y":-19},{"x":74,"y":-23},{"x":74,"y":-34},{"x":67,"y":-34},{"x":67,"y":-42},{"x":52,"y":-50},{"x":30,"y":-50},{"x":18,"y":-45},{"x":9,"y":-45},{"x":3,"y":-37},{"x":3,"y":-21},{"x":0,"y":-21},{"x":0,"y":0}]
},
24: {
minimum: 137,
minimum_vertices: [{"x":0,"y":0},{"x":2,"y":0},{"x":-14,"y":12},{"x":-14,"y":6},{"x":-17,"y":6},{"x":-13,"y":3},{"x":-13,"y":11},{"x":-1,"y":2},{"x":-1,"y":-5},{"x":23,"y":-5},{"x":23,"y":18},{"x":4,"y":18},{"x":4,"y":0},{"x":18,"y":0},{"x":18,"y":13},{"x":8,"y":13},{"x":8,"y":12},{"x":17,"y":12},{"x":17,"y":1},{"x":5,"y":1},{"x":5,"y":17},{"x":22,"y":17},{"x":22,"y":-4},{"x":0,"y":-4},{"x":0,"y":0}],
maximum: 5832,
maximum_vertices: [{"x":0,"y":0},{"x":3,"y":0},{"x":3,"y":16},{"x":15,"y":25},{"x":23,"y":25},{"x":35,"y":30},{"x":59,"y":30},{"x":74,"y":22},{"x":74,"y":13},{"x":81,"y":13},{"x":81,"y":-5},{"x":82,"y":-5},{"x":82,"y":-27},{"x":78,"y":-27},{"x":78,"y":-39},{"x":62,"y":-51},{"x":43,"y":-51},{"x":43,"y":-53},{"x":20,"y":-53},{"x":20,"y":-47},{"x":9,"y":-47},{"x":3,"y":-39},{"x":3,"y":-25},{"x":0,"y":-21},{"x":0,"y":0}]
},
27: {
minimum: 178,
minimum_vertices: [{"x":0,"y":0},{"x":-6,"y":-8},{"x":-10,"y":-11},{"x":-8,"y":-11},{"x":1,"y":1},{"x":1,"y":26},{"x":25,"y":26},{"x":25,"y":5},{"x":5,"y":5},{"x":5,"y":22},{"x":21,"y":22},{"x":21,"y":10},{"x":10,"y":10},{"x":10,"y":17},{"x":16,"y":17},{"x":16,"y":14},{"x":17,"y":14},{"x":17,"y":18},{"x":9,"y":18},{"x":9,"y":9},{"x":22,"y":9},{"x":22,"y":23},{"x":4,"y":23},{"x":4,"y":4},{"x":26,"y":4},{"x":26,"y":27},{"x":0,"y":27},{"x":0,"y":0}],
maximum: 9547,
maximum_vertices: [{"x":0,"y":0},{"x":2,"y":0},{"x":2,"y":23},{"x":8,"y":31},{"x":8,"y":43},{"x":14,"y":43},{"x":34,"y":58},{"x":53,"y":58},{"x":53,"y":57},{"x":69,"y":57},{"x":81,"y":48},{"x":95,"y":48},{"x":105,"y":24},{"x":105,"y":2},{"x":102,"y":-2},{"x":102,"y":-23},{"x":97,"y":-35},{"x":81,"y":-47},{"x":63,"y":-47},{"x":63,"y":-50},{"x":36,"y":-50},{"x":21,"y":-42},{"x":12,"y":-42},{"x":12,"y":-35},{"x":4,"y":-35},{"x":4,"y":-24},{"x":0,"y":-24},{"x":0,"y":0}]
},
28: {
minimum: 190,
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min_y = Math.min(min_y,corner.y);
max_y = Math.max(max_y,corner.y);
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canvas.beginPath();
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canvas.strokeStyle = "black";
canvas.moveTo(
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10 + (vertices[0].y - min_y)/zoom,
);
for(let i=1;i<vertices.length;i++){
canvas.lineTo(
10 + (vertices[i].x - min_x)/zoom,
10 + (vertices[i].y - min_y)/zoom,
)
}
canvas.closePath();
canvas.stroke()
canvas.fill();
if(vertices.length < 40){
canvas.fillStyle = "black";
for(let i=1;i<vertices.length;i++){
canvas.fillText(
Math.hypot(vertices[i].x - vertices[i - 1].x,vertices[i].y - vertices[i - 1].y),
10 + ((vertices[i].x + vertices[i - 1].x)/2 - min_x)/zoom + 2,
10 + ((vertices[i].y + vertices[i - 1].y)/2 - min_y)/zoom - 2
)
}
smallest_canvas.fillStyle = "azure";
largest_canvas.fillStyle = "coral";
}
}
function gcd(a,b){
if(!b){
return a
}
return gcd(b, a % b);
}
function lower_bound(n){
let sum = 0;
for(let i=1;i<=n;i++){
let bestCD = i;
for(let j=1;j<Math.sqrt(i);j++){
for(let k=1;k<j;k++){
let squareSum = j*j + k*k;
if(squareSum > i){
break
}
if(i % squareSum === 0){
bestCD = Math.min(
bestCD,
gcd(
j*j - k*k,
2*j*k
)*i/squareSum
)
}
}
}
sum += bestCD;
}
return Math.floor(sum/2 - 1)
}
function upper_bound(n){
return Math.floor(n/Math.tan(Math.PI/n)*Math.pow((n+1)/4,2))
//return Math.floor(Math.pow(n*(n+1)/2,2)/(4*Math.PI))
}
function polygon_area(vertices){
let psum = 0;
let nsum = 0;
for(let i=0;i<vertices.length;i++){
let sindex = (i + 1) % vertices.length;
let prod = vertices[i].x * vertices[sindex].y;
psum += prod
}
for(let i=0;i<vertices.length;i++){
let sindex = (i + 1) % vertices.length;
let prod = vertices[sindex].x * vertices[i].y;
nsum += prod
}
return Math.abs((psum - nsum)/2)
}
function generate_quadratic_snake(n){
if(n % 4 === 0){
let k = Math.floor((n - 20)/20);
let numbers = [];
for(let i=1;i<=n;i++){
numbers.push(i)
}
let removeNumber = function(num){
numbers.splice(numbers.findIndex(e => e === num),1)
}
removeNumber(1);
removeNumber(2);
removeNumber(3);
removeNumber(4);
removeNumber(5);
removeNumber(6);
removeNumber(7);
removeNumber(8);
removeNumber(9);
removeNumber(10);
removeNumber(11);
removeNumber(12);
removeNumber(15);
removeNumber(20);
for(let i=1;i<=k;i++){
removeNumber(5*i + 8);
removeNumber(5*i + 9);
removeNumber(5*i + 11);
removeNumber(5*i + 12);
removeNumber(20*i + 5);
removeNumber(20*i + 10);
removeNumber(20*i + 15);
removeNumber(20*i + 20);
}
let tail1 = 5*k + 13;
let tail2 = 5*k + 14;
removeNumber(tail1);
removeNumber(tail2);
let bodyPairs = [];
for(let i=0;i<numbers.length;i+=4){
bodyPairs.push([numbers[i],numbers[i + 2]]);
bodyPairs.push([numbers[i + 1],numbers[i + 3]]);
}
bodyPairs = bodyPairs.reverse();
let repeatingPairs = bodyPairs.splice(0,2*k);
repeatingPairs = repeatingPairs.reverse();
let vertices = [
{x:0,y:0},
{x:0,y:9},
{x:10,y:9},
{x:10,y:5},
{x:8,y:5},
{x:24,y:-7},
{x:24,y:-1},
{x:27,y:-1},
{x:23,y:2},
{x:23,y:-6},
{x:11,y:3},
{x:11,y:10},
{x:-1,y:10},
{x:-1,y:-1}
];
let addVertice = function(x,y){
vertices.push({
x: vertices[vertices.length - 1].x + x,
y: vertices[vertices.length - 1].y + y
})
}
for(let i=1;i<=k;i++){
addVertice(
-3*(20*i + 15)/5,
-4*(20*i + 15)/5
);
addVertice(-5*i - 12,0);
addVertice(
-3*(20*i + 5)/5,
4*(20*i + 5)/5
);
addVertice(0,5*i + 11);
if(i === k){
bodyPairs.push(repeatingPairs[2*k - 2])
bodyPairs.push(repeatingPairs[2*k - 1])
bodyPairs.sort((b,a) => a[0] - b[0])
}
else{
addVertice(-repeatingPairs[2*i - 2][1],0);
addVertice(0,-repeatingPairs[2*i - 1][1]);
}
}
let direction = 2;
for(let i=0;i<bodyPairs.length;i++){
if(direction % 4 === 0){
addVertice(bodyPairs[i][1],0);
}
else if(direction % 4 === 1){
addVertice(0,bodyPairs[i][1]);
}
else if(direction % 4 === 2){
addVertice(-bodyPairs[i][1],0);
}
else if(direction % 4 === 3){
addVertice(0,-bodyPairs[i][1]);
}
direction++
}
if(direction % 4 === 2){
addVertice(-tail2,0);
addVertice(0,-1);
addVertice(tail1,0);
}
else if(direction % 4 === 0){
addVertice(tail2,0);
addVertice(0,1);
addVertice(-tail1,0);
}
bodyPairs = bodyPairs.reverse();
for(let i=0;i<bodyPairs.length;i++){
if(direction % 4 === 0){
addVertice(0,bodyPairs[i][0]);
}
else if(direction % 4 === 1){
addVertice(bodyPairs[i][0],0);
}
else if(direction % 4 === 2){
addVertice(0,-bodyPairs[i][0]);
}
else if(direction % 4 === 3){
addVertice(-bodyPairs[i][0],0);
}
direction++
}
for(let i=k;i>0;i--){
if(i !== k){
addVertice(0,repeatingPairs[2*i - 1][0]);
addVertice(repeatingPairs[2*i - 2][0],0);
}
addVertice(0,-5*i - 9);
addVertice(
3*(20*i + 10)/5,
-4*(20*i + 10)/5
);
addVertice(5*i + 8,0);
addVertice(
3*(20*i + 20)/5,
4*(20*i + 20)/5
);
}
return vertices;
}
else if(n % 4 === 3){
let k = Math.floor((n - 15)/20);
let numbers = [];
for(let i=1;i<=n;i++){
numbers.push(i)
}
let removeNumber = function(num){
numbers.splice(numbers.findIndex(e => e === num),1)
}
removeNumber(1);
removeNumber(2);
removeNumber(5);
removeNumber(10);
removeNumber(15);
for(let i=1;i<=k;i++){
removeNumber(5*i - 1);
removeNumber(5*i + 1);
removeNumber(5*i - 2);
removeNumber(5*i + 2);
removeNumber(20*i);
removeNumber(20*i + 5);
removeNumber(20*i + 10);
removeNumber(20*i + 15);
}
let tail1 = 5*k + 3;
let tail2 = 5*k + 4;
removeNumber(tail1);
removeNumber(tail2);
let bodyPairs = [];
for(let i=0;i<numbers.length;i+=4){
bodyPairs.push([numbers[i],numbers[i + 2]]);
bodyPairs.push([numbers[i + 1],numbers[i + 3]]);
}
let repeatingPairs = bodyPairs.splice(0,2*k);
let vertices = [
{x:0,y:0},
{x:2,y:0},
{x:11,y:12}
];
let addVertice = function(x,y){
vertices.push({
x: vertices[vertices.length - 1].x + x,
y: vertices[vertices.length - 1].y + y
})
}
for(let i=1;i<=k;i++){
addVertice(0,5*i - 1);
addVertice(repeatingPairs[2*i - 2][0],0);
addVertice(0,-repeatingPairs[2*i - 1][0]);
addVertice(
3*(20*i + 5)/5,
-4*(20*i + 5)/5
);
addVertice(5*i - 2,0);
addVertice(
3*(20*i + 15)/5,
4*(20*i + 15)/5
);
}
let direction = 0;
bodyPairs = bodyPairs.reverse();
for(let i=0;i<bodyPairs.length;i++){
if(direction % 4 === 0){
addVertice(0,bodyPairs[i][0]);
}
else if(direction % 4 === 1){
addVertice(bodyPairs[i][0],0);
}
else if(direction % 4 === 2){
addVertice(0,-bodyPairs[i][0]);
}
else if(direction % 4 === 3){
addVertice(-bodyPairs[i][0],0);
}
direction++
}
if(direction % 4 === 1){
addVertice(tail1,0);
addVertice(0,1);
addVertice(-tail2,0);
}
else if(direction % 4 === 2){
addVertice(0,-tail1);
addVertice(1,0);
addVertice(0,tail2);
}
else if(direction % 4 === 3){
addVertice(-tail1,0);
addVertice(0,-1);
addVertice(tail2,0);
}
else if(direction % 4 === 0){
addVertice(0,tail1);
addVertice(-1,0);
addVertice(0,-tail2);
}
bodyPairs = bodyPairs.reverse();
for(let i=0;i<bodyPairs.length;i++){
if(direction % 4 === 0){
addVertice(bodyPairs[i][1],0);
}
else if(direction % 4 === 1){
addVertice(0,bodyPairs[i][1]);
}
else if(direction % 4 === 2){
addVertice(-bodyPairs[i][1],0);
}
else if(direction % 4 === 3){
addVertice(0,-bodyPairs[i][1]);
}
direction++
}
for(let i=k;i>0;i--){
addVertice(
-3*(20*i + 10)/5,
-4*(20*i + 10)/5
);
addVertice(-5*i - 2,0);
addVertice(
-3*(20*i)/5,
4*(20*i)/5
);
addVertice(0,repeatingPairs[2*i - 1][1]);
addVertice(-repeatingPairs[2*i - 2][1],0);
addVertice(0,-5*i - 1);
}
vertices.push({x:4,y:3})
vertices.push({x:0,y:0})
return vertices;
}
else{
throw "invalid input for generate_quadratic_snake"
}
}
function generate_big_square2(n){
let rest = n % 40;
if(rest === 0 || rest === 7){
let k = (n - rest)/40;
let vertices = [
{x:0,y:0}
];
let addVertice = function(x,y){
vertices.push({
x: vertices[vertices.length - 1].x + x,
y: vertices[vertices.length - 1].y + y
})
}
let vertLegs = [];
let horiLegs = [];
let dias = [];
for(let i=1;i<=k;i++){
let vertical = true;
for(let j=0;j<5;j++){
let lengthy = 40*i + rest - j;
if(lengthy % 5 === 0){
dias.push(lengthy);
continue
}
if(vertical){
vertLegs.push(lengthy);
}
else{
horiLegs.push(lengthy);
}
vertical = !vertical
}
}
for(let i=1;i<=k;i++){
let vertical = true;
for(let j=0;j<5;j++){
let lengthy = 40*i + rest - j - 35;
if(lengthy % 5 === 0){
dias.push(lengthy);
continue
}
if(vertical){
vertLegs.push(lengthy);
}
else{
horiLegs.push(lengthy);
}
vertical = !vertical
}
}
vertLegs.sort((a,b) => a - b);
horiLegs.sort((b,a) => a - b);
dias.sort((b,a) => a - b);
for(let i=1;i<=2*k;i++){
if(i === 1){
addVertice(0,-vertLegs.pop());
addVertice(horiLegs.pop(),0);
addVertice(0,-vertLegs.pop());
let diaLength = dias.pop();
addVertice(diaLength * 4/5,-diaLength * 3/5);
if(i === k){
dias = dias.reverse()
}
addVertice(0,-vertLegs.pop());
}
else if(i === 2*k){
addVertice(0,-vertLegs.pop());
addVertice(horiLegs.pop(),0);
addVertice(0,-vertLegs.pop());
addVertice(horiLegs.pop(),0);
let diaLength = dias.pop();
addVertice(diaLength * 4/5,-diaLength * 3/5);
if(i === k){
dias = dias.reverse()
}
}
else{
addVertice(horiLegs.pop(),0);
addVertice(0,-vertLegs.pop());
addVertice(horiLegs.pop(),0);
let diaLength = dias.pop();
addVertice(diaLength * 4/5,-diaLength * 3/5);
if(i === k){
dias = dias.reverse()
}
if(i === 2*k - 1){
addVertice(horiLegs.pop(),0);
}
else{
addVertice(0,-vertLegs.pop());
}
}
}
for(let i=1;i<=k;i++){
let vertical = false;
for(let j=0;j<5;j++){
let lengthy = 40*i + rest - j - 5;
if(lengthy % 5 === 0){
dias.push(lengthy);
continue
}
if(vertical){
vertLegs.push(lengthy);
}
else{
horiLegs.push(lengthy);
}
vertical = !vertical
}
}
for(let i=1;i<=k;i++){
let vertical = false;
for(let j=0;j<5;j++){
let lengthy = 40*i + rest - j - 30;
if(lengthy % 5 === 0){
dias.push(lengthy);
continue
}
if(vertical){
vertLegs.push(lengthy);
}
else{
horiLegs.push(lengthy);
}
vertical = !vertical
}
}
vertLegs.sort((b,a) => a - b);
horiLegs.sort((a,b) => a - b);
dias.sort((b,a) => a - b);
if(rest === 7){
addVertice(0,-2);
}
for(let i=1;i<=2*k;i++){
if(i === 1){
addVertice(horiLegs.pop(),0);
addVertice(0,vertLegs.pop());
addVertice(horiLegs.pop(),0);
let diaLength = dias.pop();
addVertice(diaLength * 3/5,diaLength * 4/5);
if(i === k){
dias = dias.reverse()
}
addVertice(horiLegs.pop(),0);
}
else if(i === 2*k){
addVertice(horiLegs.pop(),0);
addVertice(0,vertLegs.pop());
addVertice(horiLegs.pop(),0);
addVertice(0,vertLegs.pop());
let diaLength = dias.pop();
addVertice(diaLength * 3/5,diaLength * 4/5);
if(i === k){
dias = dias.reverse()
}
}
else{
addVertice(0,vertLegs.pop());
addVertice(horiLegs.pop(),0);
addVertice(0,vertLegs.pop());
let diaLength = dias.pop();
addVertice(diaLength * 3/5,diaLength * 4/5);
if(i === k){
dias = dias.reverse()
}
if(i === 2*k - 1){
addVertice(0,vertLegs.pop());
}
else{
addVertice(horiLegs.pop(),0);
}
}
}
for(let i=1;i<=k;i++){
let vertical = true;
for(let j=0;j<5;j++){
let lengthy = 40*i + rest - j - 10;
if(lengthy % 5 === 0){
dias.push(lengthy);
continue
}
if(vertical){
vertLegs.push(lengthy);
}
else{
horiLegs.push(lengthy);
}
vertical = !vertical
}
}
for(let i=1;i<=k;i++){
let vertical = true;
for(let j=0;j<5;j++){
let lengthy = 40*i + rest - j - 25;
if(lengthy % 5 === 0){
dias.push(lengthy);
continue
}
if(vertical){
vertLegs.push(lengthy);
}
else{
horiLegs.push(lengthy);
}
vertical = !vertical
}
}
vertLegs.sort((a,b) => a - b);
horiLegs.sort((b,a) => a - b);
dias.sort((b,a) => a - b);
if(rest === 7){
addVertice(3,0);
addVertice(3,4);
}
for(let i=1;i<=2*k;i++){
if(i === 1){
addVertice(0,vertLegs.pop());
addVertice(-horiLegs.pop(),0);
addVertice(0,vertLegs.pop());
let diaLength = dias.pop();
addVertice(-diaLength * 4/5,diaLength * 3/5);
if(i === k){
dias = dias.reverse()
}
addVertice(0,vertLegs.pop());
}
else if(i === 2*k){
addVertice(0,vertLegs.pop());
addVertice(-horiLegs.pop(),0);
addVertice(0,vertLegs.pop());
addVertice(-horiLegs.pop(),0);
let diaLength = dias.pop();
addVertice(-diaLength * 4/5,diaLength * 3/5);
if(i === k){
dias = dias.reverse()
}
}
else{
addVertice(-horiLegs.pop(),0);
addVertice(0,vertLegs.pop());
addVertice(-horiLegs.pop(),0);
let diaLength = dias.pop();
addVertice(-diaLength * 4/5,diaLength * 3/5);
if(i === k){
dias = dias.reverse()
}
if(i === 2*k - 1){
addVertice(-horiLegs.pop(),0);
}
else{
addVertice(0,vertLegs.pop());
}
}
}
for(let i=1;i<=k;i++){
let vertical = false;
for(let j=0;j<5;j++){
let lengthy = 40*i + rest - j - 15;
if(lengthy % 5 === 0){
dias.push(lengthy);
continue
}
if(vertical){
vertLegs.push(lengthy);
}
else{
horiLegs.push(lengthy);
}
vertical = !vertical
}
}
for(let i=1;i<=k;i++){
let vertical = false;
for(let j=0;j<5;j++){
let lengthy = 40*i + rest - j - 20;
if(lengthy % 5 === 0){
dias.push(lengthy);
continue
}
if(vertical){