Visualizing curve and trajectory data is a common task in many scientific fields including medicine and physics. Tubes are an effective visualization primitive for this sort of data, but they require highly specialized renderers to achieve high image quality at frame rates sufficient for interactive visualization. We present a rendering algorithm for Hermite spline tubes, i.e. tubes that result from Hermite splines interpolating the data, with support for varying-radii circular tube cross sections. Our approach employs raycasting and works directly on this continuous representation without the need for surface tessellation, made possible by an efficient ray-tube intersection routine suitable for execution on modern GPUs.