Abstract
Ruled surfaces play an important role in disciplines such as applied mathematics, mechanical engineering, and architecture. We present a general methodology for creating handheld-sized 3D printed models of such surfaces, which can be useful for educational, research, and design purposes. The process begins with a mathematical description of the surface, either by means of establishing a series of line segment endpoint coordinates followed by a "connect the dots" approach or continuously sweeping a portion of a line throughout 3D space using a time varying homogeneous transformation, thereby defining an array of line segments on the surface. Next, MATLAB is used to numerically generate the endpoint coordinates which are imported into SolidWorks via Excel and employs a custom macro to permit graphical display of the line segments in a part file. The array of line segments is then stitched together "manually" into a surface, thickened into a part, and printed out in plastic using a 3D printer. The methodology is illustrated for some simple surfaces in addition to several well-known exotic surfaces that have an architectural theme to them. Specifically, we showcase Antoni Gaudi's conoids and elliptic hyperboloids from La Sagrada Familia, in addition to a twisted circular drum arch and a Solomonic column, both of which are seen in southern European architecture, in particular they are present at either the Museum of Cycladic Art in Athens or at The Vatican (includes museum). In summary, the work presented should be of general interest to the 3D printing, ruled surface, and architecture communities.