Calculating the distance between a point and a line segment in Three.js

Question

Calculating the distance between a point and a line segment in Three.js

When working with Three.js, I have mastered a straightforward technique for determining the distance between a point (representing my camera's location) and an infinitely extending line. However, my current challenge lies in calculating the distance between a point and a specific line segment created by connecting two points. It is crucial to keep in mind that Three.js operates within the three spatial dimensions: x, y, and z.

Below is the formula I am currently utilizing to address the point to line segment distance calculation in Three.js:

var A = lineVertex1.clone()
var B = lineVertex2.clone()

var D = B.clone().sub( A ).normalize();
var d = camera.position.clone().sub( A ).dot( D );
var X = A.clone().add( D.clone().multiplyScalar( d ) );

var distance = camera.position.distanceTo( X );

javascript three.js 3d distance line-segment

Answer 1

Answer №1

Approach 1 Using THREE.js

In order to calculate the distance between a point (A) and a line segment created by two other points (B and C), we can leverage the capabilities of THREE.Vector3. While it may not be a mesh, it serves as a geometric representation of a line.

The Vector3 class offers a convenient method called closestPointToPoint(), which allows us to determine the distance between point A and the line segment BC based on the result of this method.

const A = new Vector3(0, 0, 0);

const B = new Vector3(5, 2, 5); // coordinates of line endpoint 1
const C = new Vector3(5, -2, 5); // coordinates of line endpoint 2

const line = new Line3(B, C);
const distance = line.closestPointToPoint(A).distanceTo(A);

console.log(distance.toFixed(3)); // Output: 7.071 (which is equivalent to 5 × √2)

Approach 2 Employing Algebra

If we possess the coordinates of points A, B, and C, we can compute the distance between point A and the line BC using a mathematical formula provided at Math StackExchange.

Answer 2

Approach 1 Using THREE.js

In order to calculate the distance between a point (A) and a line segment created by two other points (B and C), we can leverage the capabilities of THREE.Vector3. While it may not be a mesh, it serves as a geometric representation of a line.

The Vector3 class offers a convenient method called closestPointToPoint(), which allows us to determine the distance between point A and the line segment BC based on the result of this method.

const A = new Vector3(0, 0, 0);

const B = new Vector3(5, 2, 5); // coordinates of line endpoint 1
const C = new Vector3(5, -2, 5); // coordinates of line endpoint 2

const line = new Line3(B, C);
const distance = line.closestPointToPoint(A).distanceTo(A);

console.log(distance.toFixed(3)); // Output: 7.071 (which is equivalent to 5 × √2)

Approach 2 Employing Algebra

If we possess the coordinates of points A, B, and C, we can compute the distance between point A and the line BC using a mathematical formula provided at Math StackExchange.

Answer 3

Answer №2

While I may not be an expert at coding, I believe I can offer you the algorithm you need.

Consider extending a segment into an infinite line and then calculating the distance from the camera point to that line. The challenge lies in determining if the perpendicular drawn from the camera to the line falls within or outside the original segment. To solve this, compute three distances: from the camera to each end of the segment and from the camera to the line itself. The shortest of these distances should give you the desired result.

I hope this explanation proves useful to you.

Answer 4

While I may not be an expert at coding, I believe I can offer you the algorithm you need.

Consider extending a segment into an infinite line and then calculating the distance from the camera point to that line. The challenge lies in determining if the perpendicular drawn from the camera to the line falls within or outside the original segment. To solve this, compute three distances: from the camera to each end of the segment and from the camera to the line itself. The shortest of these distances should give you the desired result.

I hope this explanation proves useful to you.

Answer 5

Answer №3

The use of line.closestPointToPoint mentioned earlier is now considered outdated. For the updated method, refer to Line3.closestPointToPoint. The revised code snippet should be:

const pointA = new Vector3(0, 0, 0);

const pointB = new Vector3(5, 2, 5); // defining line base point 1
const pointC = new Vector3(5, -2, 5); // establishing line base point 2

const line = new Line3(pointB, pointC);
const targetPoint = new Vector3();

line.closestPointToPoint(pointA, false, targetPoint);
const distance = targetPoint.distanceTo(pointA);

console.log(distance.toFixed(3)); // Output: 7.071 (which equals 5 times the square root of 2)

Answer 6

The use of line.closestPointToPoint mentioned earlier is now considered outdated. For the updated method, refer to Line3.closestPointToPoint. The revised code snippet should be:

const pointA = new Vector3(0, 0, 0);

const pointB = new Vector3(5, 2, 5); // defining line base point 1
const pointC = new Vector3(5, -2, 5); // establishing line base point 2

const line = new Line3(pointB, pointC);
const targetPoint = new Vector3();

line.closestPointToPoint(pointA, false, targetPoint);
const distance = targetPoint.distanceTo(pointA);

console.log(distance.toFixed(3)); // Output: 7.071 (which equals 5 times the square root of 2)

Calculating the distance between a point and a line segment in Three.js

Answer №1

Approach 1 Using THREE.js

Approach 2 Employing Algebra

Answer №2

Answer №3

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