Graph Colouring Algorithm for Validating Labelled 2D Line Drawing Objects

Line labelling has been used to determine whether a two-dimensional (2D) line drawing object is a possible or impossible representation of a three-dimensional (3D) solid object. However, the results are not sufficiently robust because the existing line labelling methods do not have any validation method to verify their own result. In this research paper, the concept of graph colouring is applied to a validation technique for a labelled 2D line drawing. As a result, a graph colouring algorithm for validating labelled 2D line drawings is presented. A high-level programming language, MATLAB R2009a, and two primitive 2D line drawing classes, prism and pyramid are used to show how the algorithms can be implemented. The proposed algorithm also shows that the minimum number of colours needed to colour the labelled 2D line drawing object is equal to 3 for prisms and 1 n − for pyramids, where n is the number of vertices (junctions) in the pyramid objects.