1/17/2024 0 Comments Fibonacci rectangleKalay ( 2004) talked about two approaches for solving the space allocation problem, namely, an additive approach and a permutation approach. This work is concerned with the space allocation problem associated with the rectangular floor plans. If two connected dual graphs have the same number of vertices, then the dual graph having more edges is considered to be more connected, i.e., if two floor plans are made up of the same number of rooms, then the floor plan whose dual graph has more edges is more connected.Ī rectangular floor plan is a floor plan in which the plan’s boundary and each room are rectangles. Therefore, connectivity of a floor plan is defined in terms of adjacency relations among rooms and the comparison of the connectivity of different floor plans is done by comparing the connectivity of the corresponding dual graphs. Furthermore, the rooms having adjacencies to the exterior can have windows, thus enabling natural lighting and ventilation. Also, the overall patterns of adjacency relations determine circulation routes in a building. It is easy to perceive why adjacency relations are important in architectural designs if two rooms are adjacent then it is possible to make them accessible to each other via a door. Clearly, the dual graph is always planar and connected. If in an adjacency graph, the exterior is ignored then it is called weak dual or dual of the graph, i.e., the dual graph of a floor plan is a simple undirected graph obtained by representing each room as a vertex and then drawing an edge between any two vertices if the corresponding rooms are adjacent. The adjacency graph is the dual of the floor plan which is treated as a graph. The dimensional constraints involve shapes or sizes of each room and the actual floor plan.įor every floor plan there exist an adjacency graph where vertices represent rooms and the exterior, and two vertices are joined by an edge whenever the corresponding rooms are adjacent. 1a, R 1, R 2 and R 3 are adjacent R 1 is sharing a complete wall with R 2 and R 3 but R 3 is not sharing a complete wall with R 1. Therefore, to have an architectural meaning and to guarantee the sufficient space for insertion of a door between adjacent rooms, in this paper, we are generating floor plans where the adjacent rooms share a complete wall of at least one of the rooms. Architecturally, we can say that the portion of shared wall should permit one to insert a door to go through. Mathematically, two rooms of any floor plan are adjacent if they share a wall or a section of wall it is not sufficient for them to touch at a point only. The topological constraints are usually given in terms of adjacencies between rooms and between them and the exterior of the plan. It is concerned with the computational arrangement of rooms in a floor plan while satisfying given topological and dimensional constraints. One of the well-known problems associated with the generation of floor plans is called space allocation problem. For a detailed discussion regarding definitions related to floor plans, refer to Rinsma ( 1987a). The region not enclosed by the boundary is called exterior. The edges forming the perimeter of each room are termed walls. The goal is to provide an optimal solution for the rectangular space allocation problem, while satisfying given topological and dimensional requirements.Ī floor plan is a polygon, the plan boundary, divided by straight lines into component polygons called rooms. Then, this concept is further extended for constructing the best connected dimensioned rectangular floor plans. In this work, an alternative algorithm is presented which generates n − 3 best connected rectangular arrangements, being n the number of rooms. In 2015, Shekhawat showed that they are among the best connected rectangular arrangements (dimensionless rectangular floor plans) and that this may well be another reason for their frequent use in architectural design. It has been seen that architects, knowingly or unknowingly, have often used either the golden rectangle or the Fibonacci rectangle in their works throughout history.īut it was hard to find any specific reason for such use, other than aesthetic. As part of a larger research aimed at developing design aids for architects, this paper presents the “automated” generation of the “best connected” rectangular floor plans, satisfying given topological and dimensional constraints.
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