Modelling the Initial Parametric Proposal

As a starting point for this research project, a generic dome-like geometry was built in Rhino 3D CAD software. This ‘roof structure’ has a dimension of 5m x 5m, represented by a single Non-Uniform Rational Basis Spline (NURBS) surface. Using only a single surface makes the exact mathematical

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representation of a free form surface possible and allows for precise control by manipulating the control points of the NURBS surface. In a NURBS surface the ‘control points’ determine the shape and curvature of the surface and a single control point only influences those intervals where it is active. Using this method some parts of the surface can be changed while others are kept equal. The manipulation of the control points allows for a kind of parameterisation of the surface. Control points in this case are used in the everyday meaning of the word ‘point’, a location in 3D space defined by its three coordinates in the X, Y and Z planes.

Fig. 20 – “Roof structure” with the NURBS geometry defined by 20 control points.

In the present study a set of 20 control points were defined allowing for virtually unlimited adaption and deformation of the surface geometry based on the coordinates of the 20 control points. Any similar NURBS surface can be specified by either less or more control points what allows for a rougher or a more subtile manipulation of the final outcome. The quantity of control points is directly related to the amount of variables which have to be manipulated by the optimisation algorithm and has thus a direct influence on the

computational time necessary to calculate every instance in the optimisation process. As a compromise between geometric variation and available

computational power a grid of 20 control points was decided upon, which resulted in 60 variables.

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In the generic ‘roof structure’ two holes were rather randomly designed without any dimension or fixed place (Fig. 20). In this way, visual feedback could be obtained as to provide an indication of the correct functioning of the simulation software: numeric average values alone do not give an adequate understanding of eventual localised discrepancies, hence the use of this simple feedback construction. Furthermore, the holes also contribute to the aesthetic perception of the object. Strangely twisted holes are probably not experienced as aesthetically pleasing.

Before the first optimisation run, extended manual modifications of the control points were tested and the results allowed for the clarification and the setting of limits to the variation of the coordinates of the control points, information which was necessary to limit the solution space to reasonable and feasible results for the free form surfaces (Fig. 21).

Fig. 21 – Testing of the variation of the control points – similar results.

However, this process has to be executed with extreme care. If the range of variation is allowed to be large many results will be produced which for sure will contribute to a huge variation in aesthetical possibilities, some completely unexpected, but maybe not suitable as a “roof like” structure (Fig. 22).

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Fig. 22 – Testing of the variation of the control points – unexpected results.

If on the other hand the range of variation is too restricted, large areas of the (possible) solution space will be unexplored and desired interesting solutions can be missed (Fig. 23).

Fig. 23 – Testing of the variation of the control points – too little variation.

Therefore careful selection of constraints and limits are of crucial importance in this optimisation process (Fig. 24).

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In the present construct, the manipulation of the control points will change the shape of the surface, after which the CAD software will calculate the area - as an indication of the weight of the structure - and export the surface to a building analysis software for subsequent numerical analysis, in this case the average Daylight Factor under the structure, as an indication of the light functionality of the structure. The results (Area and Daylight Factor) are saved for subsequent use by the optimisation routine.

The examples presented here make it clear that optimisation without proper preparation of the parametric geometry does not allow for optimisation. This is the first iterative sequence of exploration as explained in detail in paragraph 3.2.3. Iteration in this phase of the design process will help the designer to resolve two important questions at the start of a digital design process: does the geometry allows for significant modifications and can one expect solutions within acceptable aesthetical boundaries? The perception of technical feasibility might or could also be considered as a part of the evaluation process of the designer, but technical or constructive viability is usually an important yes-no parameter in any process of optimisation. An object which is not viable for construction or fabrication cannot (or should not) be considered apt for optimisation in the first place. However, in the conceptual phase of the design process, unrestricted exploration might contribute to better understanding of the design problem.

Opting, in this case study, for a simple NURBS surface with a limited number of control points, allows for detailed exploration of the exchange of

information between the different components of the software construct, demonstrating the technical feasibility of this optimisation method. The use of a GUI, as proposed and described in paragraph 3.3.10, was not considered because of the necessity to monitor the behaviour of the different software components in close detail.