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1020 lines (960 loc) · 44.6 KB
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<script type="text/javascript">
var gk_isXlsx = false;
var gk_xlsxFileLookup = {};
var gk_fileData = {};
function filledCell(cell) {
return cell !== '' && cell != null;
}
function loadFileData(filename) {
if (gk_isXlsx && gk_xlsxFileLookup[filename]) {
try {
var workbook = XLSX.read(gk_fileData[filename], { type: 'base64' });
var firstSheetName = workbook.SheetNames[0];
var worksheet = workbook.Sheets[firstSheetName];
// Convert sheet to JSON to filter blank rows
var jsonData = XLSX.utils.sheet_to_json(worksheet, { header: 1, blankrows: false, defval: '' });
// Filter out blank rows (rows where all cells are empty, null, or undefined)
var filteredData = jsonData.filter(row => row.some(filledCell));
// Heuristic to find the header row by ignoring rows with fewer filled cells than the next row
var headerRowIndex = filteredData.findIndex((row, index) =>
row.filter(filledCell).length >= filteredData[index + 1]?.filter(filledCell).length
);
// Fallback
if (headerRowIndex === -1 || headerRowIndex > 25) {
headerRowIndex = 0;
}
// Convert filtered JSON back to CSV
var csv = XLSX.utils.aoa_to_sheet(filteredData.slice(headerRowIndex)); // Create a new sheet from filtered array of arrays
csv = XLSX.utils.sheet_to_csv(csv, { header: 1 });
return csv;
} catch (e) {
console.error(e);
return "";
}
}
return gk_fileData[filename] || "";
}
</script><!DOCTYPE html>
<html lang="uk">
<head>
<meta charset="UTF-8">
<title>Симулятор мереж Штейнера</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/1.4.2/p5.min.js"></script>
<style>
body {
display: flex;
flex-direction: column;
align-items: center;
font-family: Arial, sans-serif;
margin: 20px;
}
canvas {
border: 1px solid black;
}
.textured-canvas-wrapper {
background-image: url('background.png');
background-repeat: repeat;
background-color: transparent;
}
#totalCost {
margin: 10px 0;
font-size: 16px;
}
.button-container {
display: flex;
gap: 10px;
flex-wrap: wrap;
margin-bottom: 10px;
align-items: center;
}
.button-container button, .button-container label button {
padding: 8px 16px;
font-size: 14px;
cursor: pointer;
background-color: #4da8da;
color: white;
border: none;
border-radius: 5px;
min-width: 120px;
text-align: center;
}
.button-container button:hover, .button-container label button:hover {
background-color: #3b8fc1;
}
#loadInput {
display: none;
}
.checkbox-container {
display: flex;
align-items: center;
gap: 10px;
font-size: 14px;
}
#bridgeMultiplier {
width: 60px;
padding: 5px;
font-size: 14px;
border: 1px solid #ccc;
border-radius: 3px;
}
details {
width: 800px;
margin: 10px 0;
font-size: 14px;
}
summary {
cursor: pointer;
font-weight: bold;
padding: 5px;
}
details[open] summary {
margin-bottom: 5px;
}
details p, details ul {
margin: 0;
padding: 0 10px 10px;
}
details ul {
list-style-type: disc;
padding-left: 20px;
}
</style>
</head>
<body>
<details>
<summary>Гарячі клавіші</summary>
<ul>
<li><strong>Лівий клік</strong>: Додати точку графа (якщо не ближче 20 пікселів до інших) або точку перешкоди (в режимі перешкоди).</li>
<li><strong>Shift + клік</strong>: Виділити/зняти виділення точки графа (до 3-х) або точки перешкоди (помаранчеві, якщо видно).</li>
<li><strong>Shift відпускання (2 точки графа)</strong>: Додати ребро.</li>
<li><strong>Shift відпускання (3 точки графа)</strong>: Додати точку Ферма та ребра.</li>
<li><strong>Ctrl + клік на точці</strong>: Видалити точку графа/перешкоди (для перешкоди ≥4 точки, якщо видно).</li>
<li><strong>Ctrl + клік на ребрі</strong>: Видалити ребро.</li>
<li><strong>Ctrl + Z</strong>: Скасувати останню дію.</li>
<li><strong>Клік + перетягування червоної/помаранчевої точки</strong>: Перемістити виділені точки.</li>
</ul>
</details>
<div class="button-container">
<button id="connectButton">З'єднати</button>
<button id="optimizeButton">Оптимізувати</button>
<button id="disconnectButton">Роз'єднати</button>
<button id="clearButton">Очистити канву</button>
<button id="obstacleButton">Створити перешкоду</button>
<button id="saveButton">Зберегти</button>
<label for="loadInput">
<button id="loadBtn">Завантажити</button>
</label>
<input type="file" id="loadInput" accept=".json">
<div class="checkbox-container">
<input type="checkbox" id="allowBridges">
<label for="allowBridges">Дозволити мости</label>
<label for="bridgeMultiplier">Множник вартості:</label>
<input type="number" id="bridgeMultiplier" value="2" min="1" step="0.01">
</div>
</div>
<div id="totalCost">Вартість: 0</div>
<details>
<summary>Про задачу Торічеллі та мережі Штейнера</summary>
<p>Задача Торічеллі полягає у знаходженні точки (Ферма-Торічеллі), яка мінімізує суму відстаней до трьох точок. Ця точка утворює кути 120°, якщо всі кути трикутника <120°. Якщо кут ≥120°, точка збігається з вершиною.</p>
<p>Мережі Штейнера розширюють ідею, будуючи дерево мінімальної довжини з додаванням точок Штейнера, зменшуючи загальну суму.</p>
<p><strong>Застосування:</strong></p>
<ul>
<li>Телекомунікації: оптимізація кабелів.</li>
<li>Транспорт: планування доріг/залізниць.</li>
<li>Електромережі: проектування ліній.</li>
<li>Комп'ютерні мережі: розташування серверів.</li>
</ul>
<p><strong>Складність:</strong> Задача NP-складна через експоненціальне зростання комбінацій точок Штейнера.</p>
</details>
<script>
let points = [];
let edges = [];
let selectedPoints = [];
let totalLength = 0;
let history = [];
const POINT_RADIUS = 10;
const MIN_DISTANCE = POINT_RADIUS * 2; // 20px
let isDragging = false;
let dragOffsets = [];
let obstacleMode = false;
let obstaclePoints = [];
let selectedObstaclePoints = [];
let obstacleActive = false;
let showObstaclePoints = false;
let allowBridges = false;
let bridgeMultiplier = 2;
function setup() {
let canvas = createCanvas(800, 600);
canvas.class('textured-canvas-wrapper');
select('#connectButton').mousePressed(runKruskal);
select('#optimizeButton').mousePressed(optimizeWithFermat);
select('#disconnectButton').mousePressed(disconnect);
select('#clearButton').mousePressed(clearCanvas);
select('#obstacleButton').mousePressed(toggleObstacleMode);
select('#saveButton').mousePressed(saveConfig);
select('#loadBtn').mousePressed(() => select('#loadInput').elt.click());
select('#loadInput').changed(loadConfig);
select('#allowBridges').elt.onchange = () => {
allowBridges = select('#allowBridges').elt.checked;
updateTotalLength();
redraw();
};
select('#bridgeMultiplier').elt.oninput = () => {
bridgeMultiplier = parseFloat(select('#bridgeMultiplier').elt.value) || 2;
console.log('Множник змінено на:', bridgeMultiplier);
updateTotalLength();
redraw();
};
}
function draw() {
clear();
if (obstacleActive && obstaclePoints.length >= 3) {
fill(0, 0, 255, 100);
noStroke();
beginShape();
for (let p of obstaclePoints) {
curveVertex(p.x, p.y);
}
curveVertex(obstaclePoints[0].x, obstaclePoints[0].y);
curveVertex(obstaclePoints[1].x, obstaclePoints[1].y);
curveVertex(obstaclePoints[2].x, obstaclePoints[2].y);
endShape();
}
if (showObstaclePoints) {
for (let p of obstaclePoints) {
fill(p.selected ? 'orange' : 'yellow');
circle(p.x, p.y, POINT_RADIUS);
}
}
for (let p of points) {
if (p.selected) {
fill('red');
} else if (p.isFermat) {
fill('green');
} else {
fill('black');
}
circle(p.x, p.y, POINT_RADIUS);
}
for (let e of edges) {
let isBridge = intersectsObstacle(e.p1.x, e.p1.y, e.p2.x, e.p2.y, false);
if (isBridge) {
console.log('Малюємо міст:', e.p1, e.p2);
stroke(200, 0, 200);
} else {
stroke(0, 0, 255);
}
line(e.p1.x, e.p1.y, e.p2.x, e.p2.y);
}
}
function toggleObstacleMode() {
obstacleMode = !obstacleMode;
if (obstacleMode) {
showObstaclePoints = true;
if (obstacleActive) {
// Редагування існуючої перешкоди
} else {
obstaclePoints = [];
obstacleActive = false;
}
} else {
if (obstaclePoints.length >= 3) {
obstacleActive = true;
showObstaclePoints = false;
} else {
obstaclePoints = [];
obstacleActive = false;
showObstaclePoints = false;
}
}
saveState();
}
function mousePressed() {
if (mouseY < 0 || mouseY > height || mouseX < 0 || mouseX > width) return;
if (obstacleMode) {
let closestObstaclePoint = findClosestObstaclePoint(mouseX, mouseY);
if (keyIsDown(SHIFT) && closestObstaclePoint && dist(mouseX, mouseY, closestObstaclePoint.x, closestObstaclePoint.y) < POINT_RADIUS / 2) {
if (!closestObstaclePoint.selected) {
closestObstaclePoint.selected = true;
selectedObstaclePoints.push(closestObstaclePoint);
} else {
closestObstaclePoint.selected = false;
selectedObstaclePoints = selectedObstaclePoints.filter(p => p !== closestObstaclePoint);
}
saveState();
return;
}
if (keyIsDown(CONTROL) && closestObstaclePoint && dist(mouseX, mouseY, closestObstaclePoint.x, closestObstaclePoint.y) < POINT_RADIUS / 2 && obstaclePoints.length > 3) {
obstaclePoints = obstaclePoints.filter(p => p !== closestObstaclePoint);
selectedObstaclePoints = selectedObstaclePoints.filter(p => p !== closestObstaclePoint);
obstacleActive = obstaclePoints.length >= 3;
saveState();
return;
}
if (!keyIsDown(SHIFT) && !keyIsDown(CONTROL) && showObstaclePoints && closestObstaclePoint && closestObstaclePoint.selected && dist(mouseX, mouseY, closestObstaclePoint.x, closestObstaclePoint.y) < POINT_RADIUS / 2) {
isDragging = true;
dragOffsets = selectedObstaclePoints.map(p => ({
point: p,
dx: p.x - mouseX,
dy: p.y - mouseY,
isObstacle: true
}));
return;
}
if (!keyIsDown(SHIFT) && !keyIsDown(CONTROL)) {
let tooClose = obstaclePoints.some(p => dist(mouseX, mouseY, p.x, p.y) < MIN_DISTANCE) ||
points.some(p => dist(mouseX, mouseY, p.x, p.y) < MIN_DISTANCE);
if (!tooClose) {
obstaclePoints.push({ x: mouseX, y: mouseY, selected: false });
saveState();
} else {
console.log('Точка перешкоди занадто близько, пропускаємо');
}
return;
}
}
let closestPoint = findClosestPoint(mouseX, mouseY);
let closestEdge = findClosestEdge(mouseX, mouseY);
if (keyIsDown(CONTROL)) {
if (closestPoint && dist(mouseX, mouseY, closestPoint.x, closestPoint.y) < POINT_RADIUS / 2) {
points = points.filter(p => p !== closestPoint);
edges = edges.filter(e => e.p1 !== closestPoint && e.p2 !== closestPoint);
selectedPoints = selectedPoints.filter(p => p !== closestPoint);
saveState();
} else if (closestEdge && closestEdge.dist < 10) {
edges = edges.filter(e => e !== closestEdge.edge);
saveState();
}
} else if (keyIsDown(SHIFT)) {
if (closestPoint && dist(mouseX, mouseY, closestPoint.x, closestPoint.y) < POINT_RADIUS / 2) {
if (!closestPoint.selected && selectedPoints.length < 3) {
closestPoint.selected = true;
selectedPoints.push(closestPoint);
} else if (closestPoint.selected) {
closestPoint.selected = false;
selectedPoints = selectedPoints.filter(p => p !== closestPoint);
}
saveState();
}
} else {
if (closestPoint && closestPoint.selected && dist(mouseX, mouseY, closestPoint.x, closestPoint.y) < POINT_RADIUS / 2) {
isDragging = true;
dragOffsets = selectedPoints.map(p => ({
point: p,
dx: p.x - mouseX,
dy: p.y - mouseY,
isObstacle: false
}));
} else {
let tooClose = points.some(p => dist(mouseX, mouseY, p.x, p.y) < MIN_DISTANCE) ||
obstaclePoints.some(p => dist(mouseX, mouseY, p.x, p.y) < MIN_DISTANCE);
if (!tooClose) {
let newPoint = { x: mouseX, y: mouseY, selected: false, isFermat: false };
points.push(newPoint);
saveState();
} else {
console.log('Нова точка занадто близько, пропускаємо');
}
}
}
updateTotalLength();
}
function mouseDragged() {
if (isDragging && mouseY >= 0 && mouseY <= height && mouseX >= 0 && mouseX <= width) {
for (let offset of dragOffsets) {
let newX = mouseX + offset.dx;
let newY = mouseY + offset.dy;
let tooClose = false;
if (offset.isObstacle) {
tooClose = obstaclePoints.some(p => p !== offset.point && dist(newX, newY, p.x, p.y) < MIN_DISTANCE) ||
points.some(p => dist(newX, newY, p.x, p.y) < MIN_DISTANCE);
} else {
tooClose = points.some(p => p !== offset.point && dist(newX, newY, p.x, p.y) < MIN_DISTANCE) ||
obstaclePoints.some(p => dist(newX, newY, p.x, p.y) < MIN_DISTANCE);
}
if (!tooClose) {
offset.point.x = newX;
offset.point.y = newY;
}
}
updateTotalLength();
}
}
function mouseReleased() {
if (isDragging) {
isDragging = false;
dragOffsets = [];
saveState();
}
}
function keyReleased() {
if (keyCode === SHIFT) {
if (selectedPoints.length === 2) {
addEdge(selectedPoints[0], selectedPoints[1]);
clearSelection();
saveState();
} else if (selectedPoints.length === 3) {
addFermatPoint(selectedPoints[0], selectedPoints[1], selectedPoints[2]);
clearSelection();
saveState();
}
}
}
function keyPressed() {
if (keyIsDown(CONTROL) && keyCode === 90) {
undo();
}
}
function findClosestPoint(x, y) {
let minDist = Infinity;
let closest = null;
for (let p of points) {
let d = dist(x, y, p.x, p.y);
if (d < minDist) {
minDist = d;
closest = p;
}
}
return closest;
}
function findClosestObstaclePoint(x, y) {
if (!obstacleMode) return null;
let minDist = Infinity;
let closest = null;
for (let p of obstaclePoints) {
let d = dist(x, y, p.x, p.y);
if (d < minDist) {
minDist = d;
closest = p;
}
}
return closest;
}
function findClosestEdge(x, y) {
let minDist = Infinity;
let closestEdge = null;
for (let e of edges) {
let d = pointToLineDistance(x, y, e.p1.x, e.p1.y, e.p2.x, e.p2.y);
if (d < minDist) {
minDist = d;
closestEdge = e;
}
}
return { edge: closestEdge, dist: minDist };
}
function pointToLineDistance(px, py, x1, y1, x2, y2) {
let A = px - x1;
let B = py - y1;
let C = x2 - x1;
let D = y2 - y1;
let dot = A * C + B * D;
let len_sq = C * C + D * D;
let param = len_sq !== 0 ? dot / len_sq : -1;
let xx, yy;
if (param < 0) {
xx = x1;
yy = y1;
} else if (param > 1) {
xx = x2;
yy = y2;
} else {
xx = x1 + param * C;
yy = y1 + param * D;
}
let dx = px - xx;
let dy = py - yy;
return Math.sqrt(dx * dx + dy * dy);
}
function approximateCurvePoints() {
if (obstaclePoints.length < 3) return [];
let curvePoints = [];
let steps = 10; // Кількість точок на сегмент кривої
let closedPoints = [...obstaclePoints, obstaclePoints[0], obstaclePoints[1], obstaclePoints[2]];
function catmullRom(t, p0, p1, p2, p3) {
let t2 = t * t;
let t3 = t2 * t;
let x = 0.5 * ((2 * p1.x) +
(-p0.x + p2.x) * t +
(2 * p0.x - 5 * p1.x + 4 * p2.x - p3.x) * t2 +
(-p0.x + 3 * p1.x - 3 * p2.x + p3.x) * t3);
let y = 0.5 * ((2 * p1.y) +
(-p0.y + p2.y) * t +
(2 * p0.y - 5 * p1.y + 4 * p2.y - p3.y) * t2 +
(-p0.y + 3 * p1.y - 3 * p2.y + p3.y) * t3);
return { x, y };
}
for (let i = 0; i < obstaclePoints.length; i++) {
let p0 = closedPoints[i];
let p1 = closedPoints[i + 1];
let p2 = closedPoints[i + 2];
let p3 = closedPoints[i + 3];
for (let t = 0; t <= 1; t += 1 / steps) {
let point = catmullRom(t, p0, p1, p2, p3);
curvePoints.push(point);
}
}
return curvePoints;
}
function isPointInsideObstacle(px, py) {
if (!obstacleActive || obstaclePoints.length < 3) return false;
let curvePoints = approximateCurvePoints();
if (curvePoints.length < 3) return false;
let inside = false;
for (let i = 0, j = curvePoints.length - 1; i < curvePoints.length; j = i++) {
let xi = curvePoints[i].x, yi = curvePoints[i].y;
let xj = curvePoints[j].x, yj = curvePoints[j].y;
let intersect = ((yi > py) !== (yj > py)) &&
(px < (xj - xi) * (py - yi) / (yj - yi) + xi);
if (intersect) inside = !inside;
}
return inside;
}
function intersectsObstacle(x1, y1, x2, y2, forOptimization = false) {
if (!obstacleActive || obstaclePoints.length < 3) return false;
function segmentsIntersect(ax, ay, bx, by, cx, cy, dx, dy) {
function orientation(px, py, qx, qy, rx, ry) {
let val = (qy - py) * (rx - qx) - (qx - px) * (ry - qy);
if (Math.abs(val) < 1e-10) return 0;
return val > 0 ? 1 : 2;
}
let o1 = orientation(ax, ay, bx, by, cx, cy);
let o2 = orientation(ax, ay, bx, by, dx, dy);
let o3 = orientation(cx, cy, dx, dy, ax, ay);
let o4 = orientation(cx, cy, dx, dy, bx, by);
if (o1 !== o2 && o3 !== o4) return true;
return false;
}
// Якщо обидві точки ребра всередині перешкоди, це не міст
if (isPointInsideObstacle(x1, y1) && isPointInsideObstacle(x2, y2)) {
console.log('Ребро всередині перешкоди, не міст:', { x1, y1 }, { x2, y2 });
return false;
}
let curvePoints = approximateCurvePoints();
if (curvePoints.length < 2) return false;
let intersects = false;
for (let i = 0; i < curvePoints.length - 1; i++) {
let p1 = curvePoints[i];
let p2 = curvePoints[i + 1];
if (segmentsIntersect(x1, y1, x2, y2, p1.x, p1.y, p2.x, p2.y)) {
intersects = true;
console.log('Ребро перетинає криву:', { x1, y1 }, { x2, y2 }, 'at', p1, p2);
if (forOptimization || !allowBridges) return true;
}
}
return allowBridges ? intersects : false;
}
function addEdge(p1, p2) {
if (p1 === p2 || edges.some(e => (e.p1 === p1 && e.p2 === p2) || (e.p1 === p2 && e.p2 === p1))) {
console.log('Ребро вже існує або некоректне, пропускаємо');
return;
}
let isBridge = intersectsObstacle(p1.x, p1.y, p2.x, p2.y, false);
if (isBridge && !allowBridges) {
console.log('Ребро перетинає перешкоду, пропускаємо');
return;
}
edges.push({ p1, p2, isUserBridge: isBridge });
updateTotalLength();
}
function clearSelection() {
for (let p of points) {
p.selected = false;
}
for (let p of obstaclePoints) {
p.selected = false;
}
selectedPoints = [];
selectedObstaclePoints = [];
}
function runKruskal() {
let userBridges = edges.filter(e => e.isUserBridge);
let possibleEdges = [];
for (let i = 0; i < points.length; i++) {
for (let j = i + 1; j < points.length; j++) {
let p1 = points[i];
let p2 = points[j];
let isBridge = intersectsObstacle(p1.x, p1.y, p2.x, p2.y, false);
if (!isBridge || allowBridges) {
let d = dist(p1.x, p1.y, p2.x, p2.y);
if (isBridge) d *= bridgeMultiplier;
possibleEdges.push({ p1, p2, weight: d, isUserBridge: false });
}
}
}
userBridges.forEach(e => {
let d = dist(e.p1.x, e.p1.y, e.p2.x, e.p2.y) * bridgeMultiplier;
possibleEdges.push({ p1: e.p1, p2: e.p2, weight: d, isUserBridge: true });
});
possibleEdges.sort((a, b) => a.weight - b.weight);
let parent = new Map();
function find(v) {
if (!parent.has(v)) parent.set(v, v);
if (parent.get(v) !== v) parent.set(v, find(parent.get(v)));
return parent.get(v);
}
function union(v1, v2) {
parent.set(find(v1), find(v2));
}
edges = [];
for (let e of possibleEdges) {
if (find(e.p1) !== find(e.p2)) {
edges.push({ p1: e.p1, p2: e.p2, isUserBridge: e.isUserBridge });
union(e.p1, e.p2);
}
}
let root = points.length > 0 ? find(points[0]) : null;
let isConnected = points.every(p => !root || find(p) === root);
if (!isConnected && !allowBridges && obstacleActive) {
console.log('Мережа незв’язна без мостів');
alert('Неможливо з’єднати мережу без мостів через перешкоду');
}
updateTotalLength();
saveState();
}
function optimizeWithFermat() {
let improved = true;
while (improved) {
improved = false;
let minAngle = 120 * Math.PI / 180;
let bestTriangle = null;
for (let i = 0; i < edges.length; i++) {
for (let j = i + 1; j < edges.length; j++) {
let e1 = edges[i];
let e2 = edges[j];
if (e1.isUserBridge || e2.isUserBridge) continue;
let commonPoint = null;
let p1, p2, p3;
if (e1.p1 === e2.p1) {
commonPoint = e1.p1;
p1 = e1.p2;
p2 = e2.p2;
} else if (e1.p1 === e2.p2) {
commonPoint = e1.p1;
p1 = e1.p2;
p2 = e2.p1;
} else if (e1.p2 === e2.p1) {
commonPoint = e1.p2;
p1 = e1.p1;
p2 = e2.p2;
} else if (e1.p2 === e2.p2) {
commonPoint = e1.p2;
p1 = e1.p1;
p2 = e2.p1;
}
if (commonPoint) {
p3 = commonPoint;
let angle = calculateAngle(p1, p3, p2);
if (angle < minAngle) {
let fermat = findFermatPoint(p1, p2, p3);
if (fermat && !intersectsObstacle(p1.x, p1.y, fermat.x, fermat.y, true) &&
!intersectsObstacle(p2.x, p2.y, fermat.x, fermat.y, true) &&
!intersectsObstacle(p3.x, p3.y, fermat.x, fermat.y, true) &&
!isPointInsideObstacle(fermat.x, fermat.y)) {
minAngle = angle;
bestTriangle = { p1, p2, p3, e1, e2, fermat };
}
}
}
}
}
if (bestTriangle) {
let { p1, p2, p3, e1, e2, fermat } = bestTriangle;
let oldLength = dist(p1.x, p1.y, p3.x, p3.y) + dist(p2.x, p2.y, p3.x, p3.y);
let newLength = dist(p1.x, p1.y, fermat.x, fermat.y) +
dist(p2.x, p2.y, fermat.x, fermat.y) +
dist(p3.x, p3.y, fermat.x, fermat.y);
if (newLength < oldLength) {
points.push({ x: fermat.x, y: fermat.y, selected: false, isFermat: true });
edges = edges.filter(e => e !== e1 && e !== e2);
addEdge(p1, points[points.length - 1]);
addEdge(p2, points[points.length - 1]);
addEdge(p3, points[points.length - 1]);
runKruskal();
improved = true;
saveState();
}
}
}
updateTotalLength();
}
function calculateAngle(p1, p2, p3) {
let v1x = p1.x - p2.x;
let v1y = p1.y - p2.y;
let v2x = p3.x - p2.x;
let v2y = p3.y - p2.y;
let dot = v1x * v2x + v1y * v2y;
let mag1 = Math.sqrt(v1x * v1x + v1y * v1y);
let mag2 = Math.sqrt(v2x * v2x + v2y * v2y);
if (mag1 === 0 || mag2 === 0) return 0;
let cosTheta = dot / (mag1 * mag2);
return Math.acos(Math.max(-1, Math.min(1, cosTheta)));
}
function findFermatPoint(p1, p2, p3) {
let angleA = calculateAngle(p2, p1, p3);
let angleB = calculateAngle(p1, p2, p3);
let angleC = calculateAngle(p1, p3, p2);
if (angleA >= 120 * Math.PI / 180) return { x: p1.x, y: p1.y };
if (angleB >= 120 * Math.PI / 180) return { x: p2.x, y: p2.y };
if (angleC >= 120 * Math.PI / 180) return { x: p3.x, y: p3.y };
let x = (p1.x + p2.x + p3.x) / 3;
let y = (p1.y + p2.y + p3.y) / 3;
let step = 10;
let maxIterations = 1000;
let tolerance = 0.01;
function totalDistance(px, py) {
return dist(px, py, p1.x, p1.y) + dist(px, py, p2.x, p2.y) + dist(px, py, p3.x, p3.y);
}
for (let i = 0; i < maxIterations; i++) {
let currentDist = totalDistance(x, y);
let bestDist = currentDist;
let bestX = x;
let bestY = y;
let directions = [
{ dx: step, dy: 0 },
{ dx: -step, dy: 0 },
{ dx: 0, dy: step },
{ dx: 0, dy: -step }
];
for (let dir of directions) {
let newX = x + dir.dx;
let newY = y + dir.dy;
let newDist = totalDistance(newX, newY);
if (newDist < bestDist) {
bestDist = newDist;
bestX = newX;
bestY = newY;
}
}
if (bestDist < currentDist) {
x = bestX;
y = bestY;
} else {
step *= 0.5;
if (step < tolerance) break;
}
}
let distances = [
dist(x, y, p1.x, p1.y),
dist(x, y, p2.x, p2.y),
dist(x, y, p3.x, p3.y)
];
let tooCloseToExisting = points.some(p => dist(x, y, p.x, p.y) < MIN_DISTANCE && p !== p1 && p !== p2 && p !== p3) ||
obstaclePoints.some(p => dist(x, y, p.x, p.y) < MIN_DISTANCE);
if (distances.some(d => d < MIN_DISTANCE) || tooCloseToExisting) {
return null;
}
function isPointInTriangle(px, py, ax, ay, bx, by, cx, cy) {
let v0x = cx - ax, v0y = cy - ay;
let v1x = bx - ax, v1y = by - ay;
let v2x = px - ax, v2y = py - ay;
let dot00 = v0x * v0x + v0y * v0y;
let dot01 = v0x * v1x + v0y * v1y;
let dot02 = v0x * v2x + v0y * v2y;
let dot11 = v1x * v1x + v1y * v1y;
let dot12 = v1x * v2x + v1y * v2y;
let invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
let u = (dot11 * dot02 - dot01 * dot12) * invDenom;
let v = (dot00 * dot12 - dot01 * dot02) * invDenom;
return u >= 0 && v >= 0 && u + v <= 1;
}
if (!isPointInTriangle(x, y, p1.x, p1.y, p2.x, p2.y, p3.x, p3.y)) {
x = (p1.x + p2.x + p3.x) / 3;
y = (p1.y + p2.y + p3.y) / 3;
}
return { x, y };
}
function addFermatPoint(p1, p2, p3) {
let fermat = findFermatPoint(p1, p2, p3);
if (!fermat) {
console.log('Точка Ферма неможлива, пропускаємо');
return;
}
if (isPointInsideObstacle(fermat.x, fermat.y)) {
console.log('Точка Ферма всередині перешкоди, пропускаємо');
alert('Неможливо з’єднати точкою Ферма: точка потрапляє всередину перешкоди');
return;
}
if (intersectsObstacle(p1.x, p1.y, fermat.x, fermat.y, true) ||
intersectsObstacle(p2.x, p2.y, fermat.x, fermat.y, true) ||
intersectsObstacle(p3.x, p3.y, fermat.x, fermat.y, true)) {
console.log('Ребра до точки Ферма перетинають перешкоду, пропускаємо');
return;
}
points.push({ x: fermat.x, y: fermat.y, selected: false, isFermat: true });
addEdge(p1, points[points.length - 1]);
addEdge(p2, points[points.length - 1]);
addEdge(p3, points[points.length - 1]);
}
function disconnect() {
points = points.filter(p => !p.isFermat);
edges = [];
selectedPoints = points.filter(p => p.selected);
saveState();
updateTotalLength();
}
function updateTotalLength() {
totalLength = 0;
for (let e of edges) {
let d = dist(e.p1.x, e.p1.y, e.p2.x, e.p2.y);
if (e.isUserBridge) {
d *= bridgeMultiplier;
console.log('Міст:', e.p1, e.p2, 'Довжина:', d);
}
totalLength += d;
}
select('#totalCost').html(`Вартість: ${totalLength.toFixed(2)}`);
}
function saveState() {
history.push({
points: points.map(p => ({ ...p })),
edges: edges.map(e => ({ p1: { x: e.p1.x, y: e.p1.y, selected: e.p1.selected, isFermat: e.p1.isFermat }, p2: { x: e.p2.x, y: e.p2.y, selected: e.p2.selected, isFermat: e.p2.isFermat }, isUserBridge: e.isUserBridge })),
selectedPoints: selectedPoints.map(p => ({ ...p })),
obstaclePoints: obstaclePoints.map(p => ({ ...p })),
selectedObstaclePoints: selectedObstaclePoints.map(p => ({ ...p })),
obstacleActive: obstacleActive,
obstacleMode: obstacleMode,
showObstaclePoints: showObstaclePoints,
allowBridges: allowBridges,
bridgeMultiplier: bridgeMultiplier
});
}
function undo() {
if (history.length > 0) {
let state = history.pop();
points = state.points.map(p => ({ ...p }));
edges = state.edges.map(e => ({
p1: points.find(p => p.x === e.p1.x && p.y === e.p1.y),
p2: points.find(p => p.x === e.p2.x && p.y === e.p2.y),
isUserBridge: e.isUserBridge
}));
selectedPoints = state.selectedPoints.map(p => points.find(pt => pt.x === p.x && pt.y === p.y)).filter(p => p);
obstaclePoints = state.obstaclePoints.map(p => ({ ...p }));
selectedObstaclePoints = state.selectedObstaclePoints.map(p => obstaclePoints.find(pt => pt.x === p.x && pt.y === p.y)).filter(p => p);
obstacleActive = state.obstacleActive;
obstacleMode = state.obstacleMode;
showObstaclePoints = state.showObstaclePoints;
allowBridges = state.allowBridges;
bridgeMultiplier = state.bridgeMultiplier;
select('#allowBridges').elt.checked = allowBridges;
select('#bridgeMultiplier').elt.value = bridgeMultiplier;
updateTotalLength();
}
}
function clearCanvas() {
points = [];
edges = [];
selectedPoints = [];
obstaclePoints = [];
selectedObstaclePoints = [];
obstacleActive = false;
obstacleMode = false;
showObstaclePoints = false;
allowBridges = false;
bridgeMultiplier = 2;
select('#allowBridges').elt.checked = false;
select('#bridgeMultiplier').elt.value = 2;
history = [];
updateTotalLength();
select('#loadInput').elt.value = '';
}
function saveConfig() {
const config = {
points: points.map(p => ({ x: p.x, y: p.y, isFermat: p.isFermat })),
edges: edges.map(e => ({
p1: points.indexOf(e.p1),
p2: points.indexOf(e.p2),
isUserBridge: e.isUserBridge
})),
obstaclePoints: obstaclePoints.map(p => ({ x: p.x, y: p.y })),
allowBridges: allowBridges,
bridgeMultiplier: bridgeMultiplier,
showObstaclePoints: showObstaclePoints
};
const dataStr = "data:text/json;charset=utf-8," + encodeURIComponent(JSON.stringify(config));
const downloadAnchor = document.createElement('a');
downloadAnchor.setAttribute("href", dataStr);
downloadAnchor.setAttribute("download", "steiner_config.json");
document.body.appendChild(downloadAnchor);
downloadAnchor.click();
downloadAnchor.remove();
}
function loadConfig(event) {
const file = event.target.files[0];
if (!file) {
console.log('Файл не вивірений');
alert('Файл не вибрано');
return;
}
console.log('Завантаження файлу:', file.name);
const reader = new FileReader();
reader.onload = function(e) {
console.log('Файл прочитано:', e.target.result);
try {
const config = JSON.parse(e.target.result);
console.log('JSON розпарсено:', config);
if (!config.points || !Array.isArray(config.points) || !config.edges || !Array.isArray(config.edges)) {
throw new Error("Некоректний формат JSON: потрібні масиви points та edges");
}
clearCanvas();
points = config.points.map((p, i) => {
if (typeof p.x !== 'number' || typeof p.y !== 'number') {
throw new Error(`Некоректні координати точки ${i}`);
}
return {
x: parseFloat(p.x),
y: parseFloat(p.y),
selected: false,
isFermat: p.isFermat || false
};
});
edges = config.edges
?.filter((e, i) => {
if (!Number.isInteger(e.p1) || !Number.isInteger(e.p2) ||
e.p1 < 0 || e.p1 >= points.length ||
e.p2 < 0 || e.p2 >= points.length) {
console.warn(`Некоректне ребро ${i}: p1=${e.p1}, p2=${e.p2}`);
return false;
}
return true;
})
.map(e => ({
p1: points[e.p1],
p2: points[e.p2],
isUserBridge: e.isUserBridge || false
}));
obstaclePoints = config.obstaclePoints ?
config.obstaclePoints.map((p, i) => {
if (typeof p.x !== 'number' || typeof p.y !== 'number') {
throw new Error(`Некоректні координати точки перешкоди ${i}`);
}
return { x: parseFloat(p.x), y: parseFloat(p.y), selected: false };
}) : [];
obstacleActive = obstaclePoints.length >= 3;
obstacleMode = false;
showObstaclePoints = config.showObstaclePoints || false;
selectedPoints = [];
selectedObstaclePoints = [];
allowBridges = config.allowBridges || false;
bridgeMultiplier = parseFloat(config.bridgeMultiplier) || 2;
select('#allowBridges').elt.checked = allowBridges;
select('#bridgeMultiplier').elt.value = bridgeMultiplier;