Exercises

1. Make a series of line drawings of polyhedral models to show how all of the possible junction labellings given in Fig. 44 may arise in practice.
2. Making the assumptions given in the Section on line labelling, how many different junction types are potentially possible? What fraction of these do the permissible labellings correspond to?
3. Draw a rectangular arch to show how T-junctions can arise when part of an object obscures another part of itself.
4. Amend the line labelling descriptions to take into account shadow information. How many different junction types are potentially possible? What fraction of these do the permissible labellings correspond to? Compare your answer to that of Exercise 2.
5. Design a relaxation labelling algorithm to implement the line labelling method discussed.
6. Design a constraint satisfaction algorithm to implement the line labelling method discussed.
   1. Show how your algorithm works by tracing through a labelling example.
7. Give an example of an ambiguous figure for which the line labelling algorithm would not find a unique label.
8. Label the following figures (fig 46) according the the line labelling scheme:

    

   Fig. 46 Labelling exercise