How can Three.js help you identify whether a point lies on a given line?

Question

How can Three.js help you identify whether a point lies on a given line?

Is there a way to determine if a specific point (x,y,z) lies on the line segment between two other points, pointA and pointB?

I am looking for a boolean function that can efficiently solve this problem:

pointA        // random THREE.Vector3
pointB        // random THREE.Vector3
pointToCheck  // random THREE.Vector3
var isOnLine = THREE.pointOnLine(pointA, pointB, pointToCheck)

if (isOnLine) {
  console.log('point is on the line');
}

Please refer to the image below for better understanding:

https://i.sstatic.net/LmStm.gif

javascript vector 3d three.js

Answer 1

Answer №1

Utilizing the cross product operation of two vectors can provide a solution to this particular problem.

function verifyPointAlignment (point1, point2, pointToVerify) {
    var check = new THREE.Vector3();   
    check.crossVectors(point1.clone().sub(pointToVerify), point2.clone().sub(pointToVerify));
    return !check.length();
}

THREE.verifyPointOnLineAndBetweenPoints = function (point1, point2, pointToVerify) {
    if (!verifyPointAlignment(point1, point2, pointToVerify)) {
        return false;
    }

    var dx = point2.x - point1.x;
    var dy = point2.y - point1.y;

    // determining if the line is more horizontal or vertical:
    if (Math.abs(dx) >= Math.abs(dy)) {
        if (dx > 0) {
            return point1.x <= pointToVerify.x && pointToVerify.x <= point2.x;
        } else {
            return point2.x <= pointToVerify.x && pointToVerify.x <= point1.x;
        }
    } else {
        if (dy > 0 ) {
            return point1.y <= pointToVerify.y && pointToVerify.y <= point2.y;
        } else {
            return point2.y <= pointToVerify.y && pointToVerify.y <= point1.y;
        }
    }
}

A sample call:

THREE.verifyPointOnLineAndBetweenPoints(new THREE.Vector3(1, 0, 0), new THREE.Vector3(2, 0, 0), new THREE.Vector3(2, 0, 0));

If you only need to determine if a point lies on a line, use the following function:

verifyPointAlignment(new THREE.Vector3(1, 0, 0), new THREE.Vector3(2, 0, 0), new THREE.Vector3(2, 0, 0));

Answer 2

Utilizing the cross product operation of two vectors can provide a solution to this particular problem.

function verifyPointAlignment (point1, point2, pointToVerify) {
    var check = new THREE.Vector3();   
    check.crossVectors(point1.clone().sub(pointToVerify), point2.clone().sub(pointToVerify));
    return !check.length();
}

THREE.verifyPointOnLineAndBetweenPoints = function (point1, point2, pointToVerify) {
    if (!verifyPointAlignment(point1, point2, pointToVerify)) {
        return false;
    }

    var dx = point2.x - point1.x;
    var dy = point2.y - point1.y;

    // determining if the line is more horizontal or vertical:
    if (Math.abs(dx) >= Math.abs(dy)) {
        if (dx > 0) {
            return point1.x <= pointToVerify.x && pointToVerify.x <= point2.x;
        } else {
            return point2.x <= pointToVerify.x && pointToVerify.x <= point1.x;
        }
    } else {
        if (dy > 0 ) {
            return point1.y <= pointToVerify.y && pointToVerify.y <= point2.y;
        } else {
            return point2.y <= pointToVerify.y && pointToVerify.y <= point1.y;
        }
    }
}

A sample call:

THREE.verifyPointOnLineAndBetweenPoints(new THREE.Vector3(1, 0, 0), new THREE.Vector3(2, 0, 0), new THREE.Vector3(2, 0, 0));

If you only need to determine if a point lies on a line, use the following function:

verifyPointAlignment(new THREE.Vector3(1, 0, 0), new THREE.Vector3(2, 0, 0), new THREE.Vector3(2, 0, 0));

Answer 3

Answer №2

This is a much simpler approach.

function checkIfPointIsOnLine (pointA, pointB, targetPoint) {
    var vectorC = new THREE.Vector3();   
    vectorC.crossVectors(pointA.clone().sub(targetPoint), pointB.clone().sub(targetPoint));
    return !vectorC.length(); }

THREE.checkIfPointIsOnLineAndBetweenPoints = function (pointA, pointB, targetPoint) {
    if (!checkIfPointIsOnLine(pointA, pointB, targetPoint)) {
        return false;
    }

    let distanceAB = pointA.distanceTo(pointB);

    return pointA.distanceTo(targetPoint) < distanceAB && pointB.distanceTo(targetPoint) < distanceAB;
}

Answer 4

This is a much simpler approach.

function checkIfPointIsOnLine (pointA, pointB, targetPoint) {
    var vectorC = new THREE.Vector3();   
    vectorC.crossVectors(pointA.clone().sub(targetPoint), pointB.clone().sub(targetPoint));
    return !vectorC.length(); }

THREE.checkIfPointIsOnLineAndBetweenPoints = function (pointA, pointB, targetPoint) {
    if (!checkIfPointIsOnLine(pointA, pointB, targetPoint)) {
        return false;
    }

    let distanceAB = pointA.distanceTo(pointB);

    return pointA.distanceTo(targetPoint) < distanceAB && pointB.distanceTo(targetPoint) < distanceAB;
}

Answer 5

Answer №3

To determine if a point lies on a three-dimensional line, you can convert the equation into symmetric form and evaluate using the given points. Here's an example code snippet for reference:

// Select two random points to define the line
var pointA = new THREE.Vector3(-70, -4, -100);
var pointB = new THREE.Vector3(65, 22, 14);

// Function to check if pointToCheck lies on the line defined by pointA and pointB
var isOnLine = function(pointA, pointB, pointToCheck, betweenCheck) {
    // Calculating directional vectors
    xVector = pointB.x - pointA.x;
    yVector = pointB.y - pointA.y;
    zVector = pointB.z - pointA.z;
    vector = [xVector, yVector, zVector];

    // Additional check for points lying between pointA and pointB
    if (!!betweenCheck) {
        // Implement logic to validate between condition
    }

    // Convert to symmetric form for evaluation
    var x = (pointToCheck.x - pointA.x) / xVector;
    var y = (pointToCheck.y - pointA.y) / yVector;
    var z = (pointToCheck.z - pointA.z) / zVector;
    var results = [x, y, z];
    
    // Further processing to handle irrelevant coordinates

    return true; // Return result after evaluating symmetric equations
}

Here are some test scenarios:

// Generate multiple test points for validation
pointsOnLine = [];
pointsOffLine = [];
pointsOnLineBetween = [];
pointsOffLineBetween = [];

// Populate test arrays with generated points for various conditions

// Perform tests using the isOnLine function for each point category
for (var i = 0; i < pointsOnLine.length; i++) {
    // Execute test cases and log results
}

// Repeat above process for other point categories

Explore the Plunkr for live demonstration.

Answer 6

To determine if a point lies on a three-dimensional line, you can convert the equation into symmetric form and evaluate using the given points. Here's an example code snippet for reference:

// Select two random points to define the line
var pointA = new THREE.Vector3(-70, -4, -100);
var pointB = new THREE.Vector3(65, 22, 14);

// Function to check if pointToCheck lies on the line defined by pointA and pointB
var isOnLine = function(pointA, pointB, pointToCheck, betweenCheck) {
    // Calculating directional vectors
    xVector = pointB.x - pointA.x;
    yVector = pointB.y - pointA.y;
    zVector = pointB.z - pointA.z;
    vector = [xVector, yVector, zVector];

    // Additional check for points lying between pointA and pointB
    if (!!betweenCheck) {
        // Implement logic to validate between condition
    }

    // Convert to symmetric form for evaluation
    var x = (pointToCheck.x - pointA.x) / xVector;
    var y = (pointToCheck.y - pointA.y) / yVector;
    var z = (pointToCheck.z - pointA.z) / zVector;
    var results = [x, y, z];
    
    // Further processing to handle irrelevant coordinates

    return true; // Return result after evaluating symmetric equations
}

Here are some test scenarios:

// Generate multiple test points for validation
pointsOnLine = [];
pointsOffLine = [];
pointsOnLineBetween = [];
pointsOffLineBetween = [];

// Populate test arrays with generated points for various conditions

// Perform tests using the isOnLine function for each point category
for (var i = 0; i < pointsOnLine.length; i++) {
    // Execute test cases and log results
}

// Repeat above process for other point categories

Explore the Plunkr for live demonstration.

How can Three.js help you identify whether a point lies on a given line?

Answer №1

Answer №2

Answer №3

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