Objects in OnSceneGUI() are only visible when they are selected

I have created an editor for some game objects to be viewed in the scene view, but they only appear when selected in hierarchy view. Below is my editor script. Is the something I am missing?

using UnityEditor;
using UnityEngine;

[CustomEditor(typeof(BezierCurve))]
public class BezierCurveInspector : Editor {

    private BezierCurve curve;
    private Transform handleTransform;
    private Quaternion handleRotation;

    private void OnSceneGUI () {
        curve = target as BezierCurve;
        handleTransform = curve.transform;
        handleRotation = Tools.pivotRotation == PivotRotation.Local ?
            handleTransform.rotation : Quaternion.identity;

        Vector3 p0 = ShowPoint(0);
        Vector3 p1 = ShowPoint(1);
        Vector3 p2 = ShowPoint(2);

        Handles.color = Color.white;
        Handles.DrawLine(p0, p1);
        Handles.DrawLine(p1, p2);
    }

    private Vector3 ShowPoint (int index) {
        Vector3 point = handleTransform.TransformPoint(curve.points[index]);
        EditorGUI.BeginChangeCheck();
        point = Handles.DoPositionHandle(point, handleRotation);
        if (EditorGUI.EndChangeCheck()) {
            Undo.RecordObject(curve, "Move Point");
            EditorUtility.SetDirty(curve);
            curve.points[index] = handleTransform.InverseTransformPoint(point);
        }
        return point;
    }
}

My non editor script is:

using UnityEngine;

public class BezierCurve : MonoBehaviour {

    public Vector3[] points;

    public void Reset () {
        points = new Vector3[] {
            new Vector3(1f, 0f, 0f),
            new Vector3(2f, 0f, 0f),
            new Vector3(3f, 0f, 0f)
        };
    }
}