EN
JavaScript - how to calculate intersection point of two lines for given 4 points?
6
points
Intersection point formula for given two points on each line should be calculated in the following way:
Where:
L1andL2represent points on line 1 and line 2 calculated with linear parametric equation. Points(x1, y1)and(x2, y2)are located on line 1,(x3, y3)and(x4, y4)are located on line 2.
Practical example:
Using JavaScript it is possible to calculate intersection points using the above formula in the following way:
// ONLINE-RUNNER:browser;
function calculateIntersection(p1, p2, p3, p4) {
// down part of intersection point formula
var d1 = (p1.x - p2.x) * (p3.y - p4.y); // (x1 - x2) * (y3 - y4)
var d2 = (p1.y - p2.y) * (p3.x - p4.x); // (y1 - y2) * (x3 - x4)
var d = (d1) - (d2);
if(d == 0) {
throw new Error('Number of intersection points is zero or infinity.');
}
// upper part of intersection point formula
var u1 = (p1.x * p2.y - p1.y * p2.x); // (x1 * y2 - y1 * x2)
var u4 = (p3.x * p4.y - p3.y * p4.x); // (x3 * y4 - y3 * x4)
var u2x = p3.x - p4.x; // (x3 - x4)
var u3x = p1.x - p2.x; // (x1 - x2)
var u2y = p3.y - p4.y; // (y3 - y4)
var u3y = p1.y - p2.y; // (y1 - y2)
// intersection point formula
var px = (u1 * u2x - u3x * u4) / d;
var py = (u1 * u2y - u3y * u4) / d;
var p = { x: px, y: py };
return p;
}
// Usage example:
// line 1
var p1 = { x: 85, y: 45 }; // P1: (x1, y1)
var p2 = { x: 260, y: 180 }; // P2: (x2, y2)
// line 2
var p3 = { x: 225, y: 75 }; // P3: (x4, y4)
var p4 = { x: 65, y: 260 }; // P4: (x4, y4)
var p = calculateIntersection(p1, p2, p3, p4); // intersection point
console.log('P=(' + p.x + '; ' + p.y + ')');
1. Intersection point + drawing result example
In this section, we can see example calculations and visualization of a cross point on the canvas.
An Animated version of this article has been presented here.
// ONLINE-RUNNER:browser;
<!doctype html>
<html>
<head>
<style>
#my-canvas { border: 1px solid gray; }
</style>
</head>
<body>
<canvas id="my-canvas" width="350" height="300"></canvas>
<script>
// -----------------------------------------------------------------------
// Intersection formula:
function calculateIntersection(p1, p2, p3, p4) {
// down part of intersection point formula
var d1 = (p1.x - p2.x) * (p3.y - p4.y); // (x1 - x2) * (y3 - y4)
var d2 = (p1.y - p2.y) * (p3.x - p4.x); // (y1 - y2) * (x3 - x4)
var d = (d1) - (d2);
if(d == 0) {
throw new Error('Number of intersection points is zero or infinity.');
}
// upper part of intersection point formula
var u1 = (p1.x * p2.y - p1.y * p2.x); // (x1 * y2 - y1 * x2)
var u4 = (p3.x * p4.y - p3.y * p4.x); // (x3 * y4 - y3 * x4)
var u2x = p3.x - p4.x; // (x3 - x4)
var u3x = p1.x - p2.x; // (x1 - x2)
var u2y = p3.y - p4.y; // (y3 - y4)
var u3y = p1.y - p2.y; // (y1 - y2)
// intersection point formula
var px = (u1 * u2x - u3x * u4) / d;
var py = (u1 * u2y - u3y * u4) / d;
var p = { x: px, y: py };
return p;
}
// Usage example:
// line 1
var p1 = { x: 85, y: 45 }; // P1: (x1, y1)
var p2 = { x: 260, y: 180 }; // P2: (x2, y2)
// line 2
var p3 = { x: 225, y: 75 }; // P3: (x4, y4)
var p4 = { x: 65, y: 260 }; // P4: (x4, y4)
var p = calculateIntersection(p1, p2, p3, p4); // intersection point
console.log('P1=(' + p1.x + '; ' + p1.y + ')');
console.log('P2=(' + p2.x + '; ' + p2.y + ')');
console.log('P3=(' + p3.x + '; ' + p3.y + ')');
console.log('P4=(' + p4.x + '; ' + p4.y + ')');
console.log('P=(' + p.x + '; ' + p.y + ')');
// -----------------------------------------------------------------------
// Drawing results:
function drawLine(context, p1, p2, color) {
context.strokeStyle = color;
context.beginPath();
context.moveTo(p1.x, p1.y);
context.lineTo(p2.x, p2.y);
context.stroke();
}
// https://dirask.com/posts/JavaScript-how-to-draw-point-on-canvas-element-PpOBLD
//
function drawPoint(context, x, y, label, color, size) {
if (color == null) {
color = '#000';
}
if (size == null) {
size = 5;
}
// to increase smoothing for numbers with decimal part
var pointX = Math.round(x);
var pointY = Math.round(y);
context.beginPath();
context.fillStyle = color;
context.arc(pointX, pointY, size, 0 * Math.PI, 2 * Math.PI);
context.fill();
if (label) {
var textX = pointX;
var textY = Math.round(pointY - size - 3);
var text = label + '=(' + x + '; ' + y + ')';
context.font = 'Italic 14px Arial';
context.fillStyle = color;
context.textAlign = 'center';
context.fillText(text, textX, textY);
}
}
var canvas = document.querySelector('#my-canvas');
var context = canvas.getContext('2d');
drawLine(context, p1, p2, 'red');
drawPoint(context, p1.x, p1.y, 'P1', 'red', 5);
drawPoint(context, p2.x, p2.y, 'P2', 'red', 5);
drawLine(context, p3, p4, 'blue');
drawPoint(context, p3.x, p3.y, 'P3', 'blue', 5);
drawPoint(context, p4.x, p4.y, 'P4', 'blue', 5);
drawPoint(context, p.x, p.y, 'P', 'green', 5);
</script>
</body>
</html>