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Algorithm for the geometric construction of an optimum shading device

source

Automation in Construction 5 (3) (1996) pp. 211-217

summary

Given that there is a need to shade a window from the summer sun and also a need to expose it to the winter sun, this article describes an algorithm to design automatically a geometric construct that satisfies both requirements. The construct obtained represents the minimum solution to the simultaneous requirements. The window may be described by an arbitrary convex polygon and it may be oriented in any direction, and it may be placed at any chosen latitude. The algorithm consists of two sequential steps: first to find a winter solar funnel surface; and the second to clip the surface subject to the summer shading conditions. The article introduces the design problem, illustrates the results through two examples, outlines the logic of the algorithm and includes the derivation of the mathematical relations required to implement the algorithm. This work is part of the MUSES project, which is a long term research effort to integrate Energy Consciousness with Computer Graphics in Architectural Design.