In theater design, the stage visibility from the auditorium has a dramatic impact on viewer satisfaction, and thus, theater revenue. Therefore, visibility is among the most important factors in theater planning. By accommodating design requirements for sound, lighting, air conditioning, etc., the shape of auditorium space takes on a complex three-dimensional (3D) geometry. This makes it difficult for the designers to account for stage visibility from each seat.
This study proposes a method using visible area ratio (a geometric parameter that refers to the degree of evaluation target's visible area) to evaluate stage visibility from the auditorium as a tool for theater planning. It is intended for use during the design phase and allows for estimating the visible area ratio using a 3D model created during planning. Visible area ratio is the ratio of the actual visible area (including obstacles in the line of sight) to the area that would be visible without any obstacles.
The apparent area is comparable to the configuration factor of the evaluation target. In this study, the apparent area was calculated using a numerical analytical approach adopting the hemisphere algorithm, wherein the surface elements of the evaluation target are first projected onto a hemisphere of unit radius. Then, the elements are re-projected onto the hemisphere base. The area projected on the hemisphere base is comparable to the apparent area. The projected area is numerically calculated by cell division of the hemisphere base. Although high-resolution imagery improves calculation accuracy, increasing the number of cell divisions requires large computational capability. Nonetheless, the algorithm considerably reduces the computational load compared to other methods, such as the ray tracing or area integral methods. Serially calculating the visible area ratio for all seats allows seat visibilities to be estimated without the need for a large number of perspective drawings.
The method is applied to a typical multipurpose theater design with 1,518 seats. For this study, the evaluation target is the acting area on the stage. The calculation points used for determining the visible area ratio is the viewpoint of each person on every seat. In addition to chairs, handrails, and spandrels, human bodies are considered as obstacles in the line of sight.
The influence of the number of cell divisions on calculation accuracy and time is investigated. The required accuracy for visible area ratio analysis is assumed less than 1 %. The resulting number of cell divisions required to satisfy this accuracy is 1,000 in both the horizontal and vertical directions.
Next, for two different auditorium geometries and seat arrangements, visible area ratios are calculated for all seats. One of these geometries represents the original design, while the other is the revised design, which optimizes the shape of the auditorium to improve the visible area ratio for the seats with poor visibility. When human bodies do not interrupt lines of sight, each seat in both plans has a good view of the stage. When considering human body interruptions, however, the visible area ratio in the original plan decreases for the 1F forward and 2F forward and backward seats. The revised auditorium plan incorporates design revisions based on the visible area ratio analysis of the original plan. These revisions include decreasing the flat area for the 1F forward seats and increasing the slope of the second floor. With these revisions, the visible area ratios of the poor-visibility seats are improved.
In conclusion, the simulation of “visible area ratio” provides very useful and effective indications for auditorium planning. It is shown that the proposed method using visible area ratio enhances stage visibility from all seats.
