This study proposes a new mathematical optimization method to evaluate exhibition spaces. Speciﬁcally, we focus on the asymmetry of visual cognition and clarify the diversity of spatial analysis based on multiple criteria.
In architectural spaces used by many people, such as art museums, people usually incorporate the existence of others when they determine the position to pause. In such exhibition space that multiple people exist at the same time, it is important to develop an architectural plan not to recognize each other as much as possible because it directly links to the usability of space.
The visual intersection of people is one of the critical factors to analyze such exhibition spaces. The important thing is the asymmetry of visual cognition between two people. In other words, the amount by which we perceive others and that to which others perceive us is diﬀerent. In this research, we pay attention to such asymmetry of visual cognition and evaluate spatial acceptance based on mathematical optimization.
For the purpose, we propose new mathematical optimization models which focus on the positions and the number of appreciators. We discuss spatial acceptance in terms of the following two factors: 1) The maximum number of appreciators without any mutual recognition; 2) The relationship between the increase of visual cognition and that of the number of appreciators. In the formulation, we compare various objective functions, for example, the diﬀerence between average value and the maximum value, as well as the diﬀerence between the active and passive visual recognition. These comparisons help us to understand the diversity and the diﬃculty in evaluating spatial acceptance with multiple criteria.
The methods are applied to an idealized square region and Hiroshi Senju Museum Karuizawa to describe characteristics as an appreciating space. Through the numerical calculation, we clarify several trade-oﬀ relation-ships which characterize spatial acceptance of the museum. The example shows that it is diﬃcult to minimize “both” values of active visual cognition and passive visual cognition. This result would be a severe insight to evaluate such exhibition spaces.
The following three results are obtained with our study:
1. The maximum number of appreciators without mutual visual intersection.
2. Relationship between an increase in visual cognition and an increase in the number of appreciators.
3. The spatial position of appreciators in the exhibition space.
All of these are key factors to illustrate the characteristics of exhibition space.
We consider that our model can be applied to initial study phase in architectural design. Since the model quickly returns the spatial position of appreciators, we can compare various candidate layouts. In the future, it is excellent if we can construct a mathematical framework which outputs the optimal layout subject to required spatial characteristics. We believe that this study is the ﬁrst step to achieve such an ultimate goal.