# modeling/src/maths/utils/intersect.js

``````/**
* Calculate the intersect point of the two line segments (p1-p2 and p3-p4), end points included.
* Note: If the line segments do NOT intersect then undefined is returned.
* @see http://paulbourke.net/geometry/pointlineplane/
* @param {vec2} p1 - first point of first line segment
* @param {vec2} p2 - second point of first line segment
* @param {vec2} p3 - first point of second line segment
* @param {vec2} p4 - second point of second line segment
* @returns {vec2} intersection point of the two line segments, or undefined
* @alias module:modeling/maths/utils.intersect
*/
const intersect = (p1, p2, p3, p4) => {
// Check if none of the lines are of length 0
if ((p1[0] === p2[0] && p1[1] === p2[1]) || (p3[0] === p4[0] && p3[1] === p4[1])) {
return undefined
}

const denominator = ((p4[1] - p3[1]) * (p2[0] - p1[0]) - (p4[0] - p3[0]) * (p2[1] - p1[1]))

// Lines are parallel
if (Math.abs(denominator) < Number.MIN_VALUE) {
return undefined
}

const ua = ((p4[0] - p3[0]) * (p1[1] - p3[1]) - (p4[1] - p3[1]) * (p1[0] - p3[0])) / denominator
const ub = ((p2[0] - p1[0]) * (p1[1] - p3[1]) - (p2[1] - p1[1]) * (p1[0] - p3[0])) / denominator

// is the intersection along the segments
if (ua < 0 || ua > 1 || ub < 0 || ub > 1) {
return undefined
}

// Return the x and y coordinates of the intersection
const x = p1[0] + ua * (p2[0] - p1[0])
const y = p1[1] + ua * (p2[1] - p1[1])

return [x, y]
}

module.exports = intersect
``````