oa Civil Engineer in South Africa - Grondwerke : die plasing van huisplatforms
The position and height of rectangular platforms for new houses in undulating terrain are to be determined. Cut must be accommodated on the stand. Slopes from the edge of platform or fill must be within given bounds and must meet the natural surface within the boundaries of the stand. The objective is to minimize cut. The problem can be formulated as a separable mathematical programming problem.
A quadratic function of the two horizontal coordinates approximates height adequately in this particular case. Such a function is fitted for each stand and exploited to find certain line integrals, potential fills, etc analytically. The constraints are so severe that there is little opportunity for optimization and the problem reduces to one of satisficing.
Inputs consist of a list of (x, y, z) points generated by stereoplotter, exact (x, y) corner points of stands and for each stand the seven numbers which identify the (x, y, z) points covering the stand. Output specifies positions and heights of platforms as well as meeting points with the natural surface. Cut, fill and excess figures are also produced per stand and in total, while a computer plot of the township shows all information needed for the execution of the groundworks.
This new application of computers in the field of civil engineering proved to be a time and money saver in the best tradition of automation.
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