Geometric modelling

In Open Design problems, as in nearly all architectural and urban design problems, not only the quantities of and the preferences for the resources to be allocated play a role, but also the location of the resources in the architectural and urban space. A lot has been studied and written in the domain of architectural design methods about this spatial dimension of architectural and urban resources. In this chapter we will explain mathematical techniques and tools for negotiations on the spatial dimension of resources. We will do this within, and as an extension of, the mathematical framework for Open Design negotiations on quantities and preferences. Since the techniques and tools of this chapter are an extension of the basic Open Design tool, the linear programming model with negotiable constraints, we will start with the general LP model from Chapter 1 and extend this numerical tool step by step with a geometrical component.

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