Morphological Study on Three-dimensional Gap between Buildings in Urban Space

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The purpose of this study is to propose a method of quantification of the gap between buildings, which is one of features in Japanese urban space, and to clarify the characteristics of volume, area and distribution pattern of these gaps.The three-dimensional gap was defined as volume where a sphere of radius r cannot sweep through on a three-dimensional building location map. The diameter of the sphere stands for the width of a gap. To extract the gap-volume operations in image-processing method called erosion and dilation were applied and developed. That is, after digital imaging of a three-dimensional building location map, building volume were dilated in terms of a digital figure corresponding to a sphere of rand then eroded. This procedure is equivalent to a dosing operation in morphology and enabled the extracting gaps. We call this method "Sphere Sweeping Method".The following results were obtained by applying this method to the building location of Kyoto city.1) The ratio of gap projected to horizontal area (gross area ratios) at three different widths of gap is 0.4% at 1.5m width, 1.2% at 2.5m, and 2.2% at 3.5m.2) The gap ratios and index of density (building density, perimeter-ratio, building coverage) are con-elated.3) The ratio of three-dimensional gap to the whole volume of buildings at three different widths of gap is 1.5% at 1.5m width, 4.1% at 2.5m, and 7.0% at 3.5m. Therefore the quantity of gap cannot be neglected in urban area.