Spatial Frequency Analysis of Perforated Board Designs

For example, with a 90% cut-off, the above thresholded ranma image becomes:ResultsA correlation scatterplot of the power within 95% versus 68% spatial frequencies indicates some features to investigate:Most notably, some perforated board designs have lower spatial frequencies while some have more high frequency content..To better see this, the normalized characteristic feature dimensions are summarized for each category in a box plot:The roll-off of 1D Power Spectral Density were fit to a power law, as described earlier..A lower value indicates more high frequency content, which can be seen in the box plot of power law exponents:The anisotropy metric [1] A varies between 0 (isotropic) and 1 (maximum anisotropy)..Values for the design motif categories are:Finally, note that the “ranma” designs have a higher aspect ratio in general:Aspect ratio was calculated with panel dimensions (not design window dimensions as in earlier work) for convenience.ConclusionUsonian perforated board designs generally have the highest spectral anisotropy and largest characteristic feature size for the data set in this analysis..Across individual designs, there is overlap with the ‘southwest’ designs in the data set on these parameters..The power law exponents between these categories are also close.The higher anisotropy of the Usonian designs is due to lower symmetry of their oblique lines compared with “southwest” designs..For example, the Usonian rhomboidal shapes create spectral power in the vertical and one oblique direction..The triangular shapes of “southwest” designs will have energy in two oblique directions as well as a horizontal or vertical direction..This is shown below for a rhomboid and triangle of equal area and similar angles:Japanese ranma designs contain more detail which is quantified by smaller characteristic feature sizes and lower power law exponents..These designs offer closer depictions of natural scenes..The higher aspect ratios of these designs (notice the correlation for “ranma”) is responsible for slightly higher anisotropy:The “leaves” and “organic” categories can be viewed as having a level of abstraction mid-way between natural scenes and Usonian designs..The parameters in this study are aligned with this interpretation.References[1] J.. More details

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