活動等高線 (AC) に関する研究 : その 1. 閉曲線図形における構造概念の確立

抄録

The contour line which can be used to express the multiple activities of urbanism and architecture is called "Activity Contour." The fundamental study on AC is started with the geometrical analysis of the closed curve. In this report, as part I. of the study, three kinds of structural concept "Ridge (R^*)" of closed curve are defined. 1. "Ridge" of a closed curve. 2. "Ridge" of belt-shaped area of double closed curve. 3. "Ridge" of multiple closed curve. The definition of the "Ridge" of a closed curve C is as follows. Let ε be positive, parallel closed curve C′is defined as a set of points from which the distance to the curve C is ε. As to the correspondence between the points on curve C to the points on curve C′; four patterns of correspondence are classified. This correspondence is related to the distance between the two curves. Now let ε be any value andif the diatance from a point P on curve C to curve C′is not equal to ε, this point P is defined as a singular point on curve C. The same holds ture on curve C′. When the distance ε varies, a set of singular points of the parallel closed curves can be got, and we call this as the "Ridge" of a closed curve. The fact of primary importance about the "Ridge" of a closed curve is that every closed curve has a "Ridge" and it can be defined uniquely.