**TANGENCIES - GEOMETRY & TECTONIC ARTICULATION EXPERIMENT**

**2010**

Differential geometry offers a mode of understanding surface geometry at the rate of curvature variation within the surface itself. A surface inscribed with lines of constant tangency, finds an inherent tectonic logic to the geometric description of surface. The experiment at hand looked at a series of surfaces that change continuously from an ellipse to a rectangle, from the curved to the flat. These surfaces are inscribed with the lines negotiating constant tangency in two directions. Another way to describe this is through the lofting techniques of shipbuilding and airplane design. Even though the majority of our digital modeling software can calculate a lofted surface between almost any set of guiding curves, the surface constructed is automatically described within the UV coordinates of the digital computation. The Tangencies experiment required a further mapping of lines containing constant tangency across the surface.

The second part of the experiment involves a pattern that interrupts the legibility of these lines. Partial ellipses are brought into the surface articulation to open a continuity of pattern against the grain of the primary tangency lines. The motivation for this second part is to inflict a range of sensory effects. The lines of constant tangency develop a scaffold within which sensations of inherent surface curvature and applied ornamental pattern continuously exchange. The curvature of an architectural surface sponsors affects in excess of its geometric description. Geometric debauchery.

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