## Parametric design

• Parametric design is a process based on algorithmic thinking that enables the expression of parameters and rules that, together, define, encode and clarify the relationship between design intent and design response.

Parametric design is a paradigm in design where the relationship between elements is used to manipulate and inform the design of complex geometries and structures.

The term parametric originates from mathematics (parametric equation) and refers to the use of certain parameters or variables that can be edited to manipulate or alter the end result of an equation or system. While today the term is used in reference to computational design systems, there are precedents for these modern systems in the works of architects such as Antoni Gaudí, who used analog models to explore design space.

Parametric modeling systems can be divided into two main types:

Form-finding is one of the strategies implemented through propagation-based systems. The idea behind form-finding is to optimize certain design goals against a set of design constraints.

One of the earliest examples of parametric design was the upside down model of churches by Antonio Gaudi. In his design for the Church of Colònia Güell he created a model of strings weighted down with birdshot to create complex vaulted ceilings and arches. By adjusting the position of the weights or the length of the strings he could alter the shape of each arch and also see how this change influenced the arches connected to it. He placed a mirror on the bottom of the model to see how it should look upside-down.

Gaudi's analogue method includes the main features of a computational of a parametric model (input parameters, equation, output):

By modifying individual parameters of these models Gaudi could generate different versions of his model while being certain the resulting structure would stand in pure compression. Instead of having to manually calculate the results of parametric equations he could automatically derive the shape of the catenary curves through the force of gravity acting on the strings.

Where Gaudi used physical laws to speed up his calculation of parametric equations, Ivan Sutherland looked to the processing power of digital computers.

Sutherland created an interactive computer-aided design program called Sketchpad. Using a light pen, users could draw lines and arcs that could be related to each other using constraints. These constraints contained all the essential properties of parametric equations. Users could experiment and explore different designs by altering the parameters of an entity and let Sketchpad do the calculations and redraw the geometry according to the constraints imposed upon it.

• Propagation-based systems where one computes from known to unknowns with a dataflow model.
• Constraint systems which solve sets of continuous and discrete constraints.
• The string length, birdshot weight and anchor point location all form independent input parameters
• The vertex locations of the points on the strings being the outcomes of the model
• The outcomes are derived by explicit functions, in this case gravity or Newtons law of motion.
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