THICKENING . 2012
Two seemingly identical lines-each defined by a unique parametric equation-are different, because the location of an object in space is part of a shape's mathematical DNA: the x and y values define the location of points in a two-dimensional Cartesian coordinate system.
If we imagine that this is a section cut through two surfaces in space, this shape acquires thickness. If this example were to be a three-dimensional shape, each surface would be defined by the parameters: u and v. Within digital software, the distance or thickness between two surfaces is considered to be a separate parameter: w. However, w does not always operate separately. For example, a sphere with an offset thickness would require two parametric equations, defining two different spheres in space. Although the parameter w is oriented perpendicular to the surface normal, it is not used to define the inherent geometry or DNA of either shape.
Within typical digital software environments, we do not have a means to manipulate the w parameter-that which is not part of the shape's DNA. However, if we begin to reconsider w as part of the inherent DNA of the shape, the possibility of creating a "thick shape" with one parametric equation arises.