How to make parallel curves in three.js for road marking?

Question

I´m trying to draw some parallel curved lines, one next to other, but if I separate them by modifying/translating their position in one axis, the result is not what I am looking for.

Code is simple, a bezier to make the central path and clones with other material for the sides.

var bezier = new THREE.CubicBezierCurve3(
                new THREE.Vector3(initx, inity, 0),
                new THREE.Vector3(cp1x, cp1y, 0),
                new THREE.Vector3( cp2x, cp2y, 0),
                new THREE.Vector3(finalx, finaly, 0)
                );

var curvePath = new THREE.CurvePath();
curvePath.add(bezier);

var path = curvePath.createPointsGeometry( 5 );
path.computeLineDistances();

var lineMat = new THREE.LineDashedMaterial({ color: 0xFFFFFF,
                                             dashSize: 3,
                                             gapSize: 2, 
                                             linewidth: 10});

var curveLine = new THREE.Line(path, lineMat);

curveLine.rotation.set(-Math.PI/2,0,0);
curveLine.position.y = 0.1;

var leftLine = curveLine.clone();
leftLine.material = matLine;

var rightLine = curveLine.clone();
rightLine.material = matLine;

leftLine.translateX(-3.5);
rightLine.position.set(3.5,0,0);

scene.add(curveLine);
scene.add(leftLine);
curveLine.add(rightLine);

This is the result:

And this are some examples of what I am looking for:

Last two images are from Bezier.js library.

I think that applying an offset to the curved line, or drawing another line using the normals of the first one might be the solution, but I can't find anything useful to do it in the documentation. I think that it could also be done drawing a line from a distance of the tangent axis or something like that, but it may be a easier way, any ideas?

I had a look on this but its for straight lines.

Answer 1

In the end, I did it by myself.

I calculated the tangent and the normal of the main curve on its points using getTangent() and rotating it 90 degrees to obtain the normal. I created more vertices for that normal multiplying its values by a scalar. Then I got the point I wanted from the normals in world coordinates and connect them creating a CatmullRomCurve3 Geometry:

for(var i = 0.0; i <= 1.0; i += 0.2){

    var point = curvePath.getPointAt(i);

    var tangent = curvePath.getTangent(i);
    var extension1 = new THREE.Vector3(tangent.x*2, tangent.y*2, 0);
    var extension2 = new THREE.Vector3(extension1.x*2, extension1.y*2, 0);

    var tangentGeometry = new THREE.Geometry();
    tangentGeometry.vertices.push(tangent, extension1, extension2);

    var tangentLine = new THREE.Line(tangentGeometry,greenMaterial);
    tangentLine.position.set(point.x, point.y, point.z);

    normal.updateMatrixWorld(); // VERY IMPORTANT

    var normal = tangentLine.clone();
    normal.rotateZ(Math.PI/2);

    var normalLastVertex = normal.geometry.vertices[2].clone();
    normalLastVertex.applyMatrix4(normal.matrixWorld); //convert to world coords.

    pointsArray.push(normalLastVertex); //for using them out of the loop

    curveLine.add(tangentLine);
    curveLine.add(normal);
}

Here I have last normals vertices in the points array, so I have to create the spline connecting them out of the loop.

    var splineCurveOffsetLeft = new THREE.CatmullRomCurve3([

       new THREE.Vector3((pointsArray[0].x), pointsArray[0].y, 0),
       new THREE.Vector3((pointsArray[1].x), pointsArray[1].y, 0),
       new THREE.Vector3((pointsArray[2].x), pointsArray[2].y, 0),
       new THREE.Vector3((pointsArray[3].x), pointsArray[3].y, 0),
       new THREE.Vector3((pointsArray[4].x), pointsArray[4].y, 0),
       new THREE.Vector3((pointsArray[5].x), pointsArray[5].y, 0)           
    ]);
splineCurveOffsetLeft.type = 'catmullrom';
splineCurveOffsetLeft.closed = false;

var offsetGeometry = new THREE.Geometry();
offsetGeometry.vertices = splineCurveOffsetLeft.getPoints(6);

var offsetLine = new THREE.Line(offsetGeometry, cyanMaterial);

offsetLine.rotation.set(-Math.PI/2, 0, 0);
offsetLine.position.y=0.1;

scene.add(offsetLine);

I made the same for the other offset line just inverting its rotation and this is the result:

Green = Tangents, Red = Normals, Cyan = Parallel curve