A 25-Intersection Model for Representing Topological Relations between Simple Spatial Objects in 3-D Space

Abstract

With the rapid development of the economy, urgent needs for 3-D Geographical Information System (GIS) have sprung up in many application fields. The precise expression of three-dimensional topological relations is the foundation of spatial analysis, topological query, and spatial reasoning in three-dimensional space. In this paper, we subdivide the topological part “boundary„ into face, edge, and vertex and propose a 25-intersection model (25IM) to represent topological relations between two simple spatial objects (point, line, region, and body) in 3-D space. An object in the 25IM has five topological parts: vertex, edge, face, interior, and exterior. The classification of topological relations is simplified by merging contain/inside and cover/coveredby. The 25IM describes ten groups of topological relations: body/body, body/region, body/line, body/point, region/region, region/line, region/point, line/line, line/point, and point/point. The 25IM is demonstrated to be more expressive than the 9IM and the DE-9IM, especially in distinguishing the detail situations when one object meets/covers another object (e.g., two bodies meet/cover at vertex, edge, or face).

Keywords

• Topological Relation
• 25-intersection model
• 3-D topology
• geometric primitive