Spatial Layout of Procedural Dungeons Using Linear Constraints and SMT Solvers

Abstract

Dungeon generation is among the oldest problems in procedural content generation. Creating the spatial aspects of a dungeon requires three steps: random generation of rooms and sizes, placement of these rooms inside a fixed area, and connecting rooms with passageways. This paper uses a series of integer linear constraints, solved by a satisfiability modulo theories (SMT) solver, to perform the placement step. Separation constraints ensure dungeon rooms do not intersect and maintain a minimum fixed separation. Designers can specify control lines, and dungeon rooms will be placed within a fixed distance of these control lines. Generation times vary with number of rooms and constraints, but are often very fast. Spatial distribution of solutions tend to have hot spots, but is surprisingly uniform given the underlying complexity of the solver. The approach demonstrates the effectiveness of a declarative approach to dungeon layout generation, where designers can express desired intent, and the SMT solver satisfies this if possible.