Curves and Projections

SCI_Arc Visual Studies / Fall 13'

Instructor : Jonah Rowen

Although historically, curves in architecture were most often derived from circular geometry, there are some notable exceptions. While many of these exceptions tended to be imprecise curves, evading both mathematical and graphical description, some examples of precise curves derived from non-circular geometry may be identified. In order to understand the range of curvature as applied in architecture, from the intersections of arched pediments and domes in Baroque architecture to the contemporary use of ruled and developable surfaces, we studied many aspects of curved surfaces, including: degrees of curvature, or the number of terms required in the equation that expresses the curve; differences between developable, ruled, and doubly-curved surfaces; and modes of projection that allow an approximation of curved surfaces for the purpose of fabrication.

Following an initial exercise studying different types of projections and curvature, I took my previously-developed form and traced a continuous, closed, three-dimensional path along its faces. The three-dimensional path begins as a line parallel to one of the faces, then continues around the three-dimensional shape, travelling perpendicularly to each edge it hits. Maintaining a perpendicular relationship with the edges reduces the possibility of being confused about the silhouette and limits the randomness of the drawing. In order to adequately describe the form, the path travelled through the doubly-curved hole at least once, included one circular arc, and passed over one of the faces more than once. This guaranteed a minimum representation of the object without omitting or obscuring the angles of its folds or the curvature of its faces. Tracing several of these paths generates just enough information to fully represent the object. I then represented only these three-dimensional lines, producing a coordinated set of orthographic and axonometric drawings that describe the original form without explicitly drawing any of its exterior edges.

Drawings:

Axonometric view

Massing Unrolling Process

Diagrammatic Massing Unroll

Parallel Projection

Model :