Il ruolo del punto nel disegno parametrico delle coniche tra geometria e topologia computazionale

Abstract

In ordinary interaction with CAD systems, the input of coordinates in model space is generally reduced to a deterministic act, sterile and self-contained. The digital sign often emerges mute, devoid of that “tension between intention and meaning” that characterises analogue drawing as a cognitive investigation. Yet, when read through the lens of Projective Geometry, the points entered on screen cease to be isolated entities and reveal a horizon dense with possibilities: they contain, in nuce, the infinite admissible conic sections that may pass through them.
This paper proposes an analysis aimed at resemanticising the vector sign through the presentation of an algorithmic framework, written in AutoLISP for AutoCAD, dedicated to the parametric representation of conic sections. The code analysed is not conceived to passively trace a finite curve, but to act as a maieutic tool. Faced with the horizon of possibilities displayed on screen, the draughtsman does not merely undergo the simplification imposed by the digital medium, but is called upon to undertake a conscious exploration.
The tracing of the final conic section thus becomes a truly intentional gesture: the act of collapsing an exploratory field of infinitely variable possibilities into a single, specific and meaningful geometric reality.