Analyzing topological changes for structural shape simplification

• We developed a shape-explicit representation of topological relations.
• The methods were developed to derive the topological changes for shape simplification.
• The methods were presented to analyze topological changes for hierarchical shape simplification.
• A case analysis was conducted to illustrate the usefulness of the presented approaches.

The shapes of regions tend to be simplified with the decrease of spatial scale or resolution, which further leads to topological changes. Analyzing topological changes is an important aspect of formalizing semantic relations. An important fact is observed that shape simplification can be considered as a combination of generalizing basic primitives. Based on this fact, a shape is decomposed first into a set of simple primitives including convexities and concavities. And then the topological changes between lines and regions can be derived from the relations between lines and primitives. The approaches presented in this study can help to analyze the exact types and locations of topological changes for generalizing convexities and concavities, respectively. The approaches need not to conduct the real simplification of shapes, and they instead incorporate the idea of simplification for deriving the changes. Thus, they are independent on the algorithms of geometrical simplification. A prototype is developed and tested using the real world examples. The results show that the approaches in this study are helpful to analyze topological changes for shape simplification.