Geometric-Mechanism Based Impact of Visual Blind Zones on Western Formal Gardens

Objective Based on the visual cone model, the field of view is a conical range formed by the convergence of countless lines of sight. Therefore, there is always a portion of the proximal spatial depth near the viewpoint that lies outside the field of view and cannot be visually captured, resulting in “proximal engulfment”. Proximal engulfment, an unavoidable visual phenomenon, relates to how landscape elements near the observer appear. Its impact on spatial arrangement design in Western formal gardens remains underexplored. Methods Building on the well-established understanding of perspective through the visual cone among Western craftsmen by the end of the 15th century, this research employs the visual cone to establish the core geometric mechanism of proximal engulfment phenomenon under horizontal viewing conditions, proposing LPE (the horizontal ground depth length in front of the viewpoint that is proximally engulfed) as a measurement parameter. Through combined spatial structure analysis and scene presentation simulation within case studies, design responses to proximal engulfment in spatial construction can be extracted. The geometric relationship between proximal engulfment and the visual cone reveals LPE’s dependence on h (viewpoint height above ground) and θ (sight-line depression angle), with LPE=h·cot(θ). Considering that the vertical natural field of vision of the human eye is around 35 degrees, the value of θ can be 17.5 degrees, which means the value of LPE is approximately 3.17h. Thus, with the known viewpoint height above the ground (h), it is possible to calculate the horizontal proximal engulfment depth LPE corresponding to the viewpoint. By comparing dN (the distance from the viewpoint to the near endpoint of the spatial unit) and dF (distance from the viewpoint to the far endpoint of the spatial unit) with this parameter, the visibility of the corresponding spatial unit in the horizontal view from the viewpoint can be determined: If dN>LPE, the spatial unit is fully visible; if dN