In this research efficiency of using the algorithmic software in building a design project is evaluated by using algorithmic methods. The design problem is calculating the lengths of a series of hanging catenaries to create a free polyline/curve form. To find the optimum design, three approaches are used: Newton-RaphsonEvolutionary Algorithm and Breath-First Algorithm all done within Grasshopper3d. For a fair comparison, all these three algorithms are implemented and tested on an identical hardware and software. The performance of the proposed algorithms are analysed and evaluated in terms of three criterions; correctness and accuracy, running time, and space (memory) efficiency.

Manipulating the reference curve points will result in a different set of hanging catenaries with different lengths

The design scenario is to draw a free curve (Reference Curve) and transform the vertex (minimum) of each catenary on the relative closest point on the drawn curve so that these hanging catenaries with various lengths create a free curved form together. The hypothetical baseline which is used to measure the height of catenary vertex (minimum) is located on the same plane where the Reference Curve is placed. Any alternation in the form of the Reference Curve will affect the lengths of hanging catenaries. Thus for the modelling of this free form, the lengths of catenaries should be determined.