Intermittent shimmer of translucent hues appearing as solid

I have a collection of curved see-through lines stacked inside a rotating container. The opacity settings on the lines are inconsistent, working at times but not always.

It's puzzling, as I can't determine what causes it to function in certain scenarios and fail in others.

For reference, below is a simplified version:

http://jsfiddle.net/sccottt/ok7k41c5/

The core part of the code snippet entails:

for (var i = 0; i < LINE_COUNT; i++) {

        var curve       = new THREE.QuadraticBezierCurve3();
            curve.v0    = randomV3();
            curve.v1    = randomV3();
            curve.v2    = randomV3();

        var geom        = new THREE.Geometry();

        for (var j = 0; j <= CURVE_STEPS; j++) {
            var perc            = j / CURVE_STEPS;
            geom.vertices[j]    = curve.getPoint(perc);
        }

        var material    = new THREE.LineBasicMaterial({
            color: Math.random() * 0xffffff,
            linewidth: 10,
            transparent: true,
            opacity: 0.25
        });

        var line        = new THREE.Line(geom, material);

        _wrap.add(line);
    }
    

Is there an error in my approach that prevents consistent transparency overlapping of the lines?

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