Because of the finite number of digits available for both integral and fractional part, floating point errors are also dependent on the operands’ magnitudes, which is why the exact same operation might succeed at the model origin [0,0,0] but fail at [1015,1015,1015]. Increasing the tolerance can help working with imprecise input geometry, but will also lower the resulting quality. Nevertheless, today’s architectural discourse rarely dives below this level, even though designers are gradually becoming programmers who design their own, highly sophisticated tools. While this impreciseness is inherent to geometric operations, it is notably not so to their formal description; formally defined models are precise until they are rendered into geometry. What defines the quality of an algorithm and how does it reflect in its output? Which are the defining parameters of a model? We think it is about time to discuss the quality of the processes instead of merely reviewing the end results that can be generated in endless variations. What are the quantifiable – and therefore optimisable – measures for the quality of a design and how are they weighed against each other? Clearly, meaningful evaluation cannot stop at the skin-deep layer of the output’s visible appearance. Especially when using parametric models, the hierarchic dependencies within complex structures have to be thoroughly untangled and precisely described in formal algorithmic and mathematic notations; only then can the output be rebuilt automatically upon changing the input parameters. How are algorithms conceived and rules defined? If we do not want to get lost in parameter space, we need to assess and understand the quality of the algorithmic machines we design, not the designs they produce. Where and how does abstraction strike and why are certain things included and others left out? It is a still common misconception that digital models are infinitely precise. But when a specific design is just one out of a myriad of possible instances a parametric machine can produce, what is the appropriate level to discuss the quality of design? So the transition from formal relations to geometric operations is an important one that should be commenced carefully. Text © 2011 John Wiley & Sons Ltd. Quality
As we have seen, complex shapes can only be handled if digital or even parametric models are an integral part of the architectural design and communication process. This is also the reason for CAD modellers to provide a tolerance setting. Only this prevents algorithmic design, which is largely based on formal descriptions, from itself becoming formalistic. Because in the end ‘designing’ means drawing decisions and taking the responsibility, not delegating them to a machine. Of course, error-bound geometric operations are impossible to avoid in CAD modelling, but knowing
when and why these errors occur can help to improve the construction sequence instead ofjust readjusting the tolerance settings when Boolean intersection fails again.

Updated: 30.10.2014 — 12:23