Transparency study of architectural space based on a scalar field function

ABSTRACT This paper studies the sufficient, necessary, and optimal conditions of the phenomenal transparency of architectural space (PTAS) by the eigenvector and eigenvalue of the gradient function of Scalar Field Function (SFF). Then, the SFF’s method is used to analyze the PTAS of significant contemporary or canonical architectural works. The conclusions are: the eigenvalue of the SFF and its integral can be used to describe PTAS; the sufficient and necessary conditions of PTAS are the eigenvalue cannot be zero, and the area integral of the eigenvalue should be greater than a certain value; the optimal condition of PTAS is that the eigenvalue is the largest; the corresponding design methods include spatial stratification, graphic overlay, and grid rotation.