We give a short survey of the main principles of our software for the visualisation and animation in mathematics and study the visibility and contour problems in the representation of surfaces, which we solve for generalised tubular surfaces, including their special cases, the envelopes of spheres, surfaces of rotation and ruled surfaces. We apply our results to visualise several results from differential geometry. M.S.C. 2000: 53A05; 68N05. Key words: Computer graphics, visualisation, visibility and contour problems.