Dimensions: 6' x 8'
Medium: Scratched black stained white pine
Location: Promenade Building in Atlanta, GA

Taking inspiration from theoretical mathematics, which states that lines do not exist; only points exist. In applied mathematics, a line is used as an approximation of an infinite number of points between two ends. With the long historical lineage of single line drawings, how do you draw a line that doesn't exist but can still be seen? Using trigonometric functions, a shape was generated with tens of thousands of lines which creased. As the curves inflect across the datum, a horizontal line appears.

The drawing was constructed out of white pine wood panels. The wood was first stained black, and then scratched at an average depth of 0.005". Numerically, the cutting depth along each line undulated up and down. Natural variations in the white pine caused bright highlights to emerge in the foreground, revealing the vibrant wood grain beneath the black stain. This experiment challenges what it means to draw and perceive a horizontal line.

Dimensions: 16' x 20'
Medium: Scratched glossy black painted medium density fiberboard
Location: Barbara Archer Gallery in Atlanta, GA

Typically a drawing is at a scale which can be held in the hands of an observer, but this drawing is significantly larger. At 16' x 20' the drawing climbs a vertical wall while extending across the floor. It is no longer an objectified element on the wall with defined boundaries, but rather is the wall and floor.

Thousands of lines are scratched at a depth of 0.02" into glossy black painted medium density fiberboard panels. Fibers are lifted like carpet with an air compressor. As you walk inside, you feel perceptually attached. Touching its texture, arching your back as you tilt your head to observe the visual seduction. Like a dance performance, the individual and drawing become one, an atmosphere is born.

Dimensions: 26' x 13'
Medium: Ink on 450 paper tiles
Location: SP_ARC Gallery in Marietta, GA

In linguistics, a boundary is anything that defines a limit. Numerically, it may be straightforward to determine a boundary, however, perceptually it is often more ambiguous and subjective. This experiment challenges fixed preconceptions of what it means to draw and experience a drawing. The drawing itself is computationally generated using trigonometric functions. As the sphere thickens over a series of iterations its geometry begins to mediate between multiple envelopes. The shape no longer has one boundary but rather has multiple boundaries.

At 26' x 13' the drawing fills a vertical wall while extending onto the floor. The 450 tiles which compose this installation define a cubic space, while the drawing on its surface portrays the sphere thickening from an object state, to that of an atmosphere. The drawing creases at the center radius of the sphere. A three dimensional illusion emerges as individuals inhabit the drawing. It is no longer enough to have one's eye move across the drawing, the observers themselves must walk, bend and alter their posture.

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.

In this experiment, the role of a vault changes from a global geometric logic to a module for a volume packing structure. The orientation of a vault is normally critical to the structural performance of the catenary curves which define it. In this study, the vault's specific geometry no longer performs structurally, and instead functions perceptually in an unprecedented manner. As the vaults rotate around a common point, the outer boundary becomes defined by quills or spikes, while the inner by pillow-like curvatures.

Boundaries, conventionally a constraint, is a design opportunity in this case. Both the inner and outer boundaries defined by vaults could extend to frame more than one shape. The outer boundary no longer has to be an offset of the inner. The surface begins to have the illusion of material thickness as it mediates between two spatial boundaries. Definitions of boundary, texture and thickness become blurred in this study.

Dimensions: Various
Medium: Thermoformed acrylic
Location: MIT Museum in Cambridge, MA

The experience and consequences associated with digital instrumentation will yield different results than those emerging out of physical material manipulations. A digitally driven design may be seamlessly precise and consistent but may also feel sterile and distant from the human body. A materially driven design may be intimate and tactile but may lack the accuracy needed to connect elements. This experimentation combines digital fabrication techniques with hand craft material manipulations in search of a unique hybrid tectonic that merges connection accuracies with subtle but sensual divergences between repeating modules. The challenges associated with translating a consistent material process over each scale have become explicit within this research.

This research does not claim to have developed a "better" fabrication process, but rather asks the question, how do we qualify fabrication processes in our current discourse? A hybrid fabrication process which combines digital fabrication with hand craft techniques suggests an alternative approach to current fabrication trends; automation and optimization. Perhaps, a slightly slower process which yields a sensibility to intimacy is something to be considered.

A shape could be defined symbolically, like a specific platonic solid, or a shape could be examined through the lens of plasticity, in which all shapes are considered interconnected and related. Assuming that shapes are plastic, it is possible to transform one shape into another. While manipulating a tool which allows a shape to be altered, it is often possible to predict and visualize the result of a particular transformation. However, it is not as easy to imagine the result of a three dimensional geometry mapped into a two dimensional world. Mapping transformations are often more difficult to visualize.

This investigation focuses its concentration on transformations of polyhedra to their respective flattened edge unfolding. When a shape transforms, how does its unfolding pattern transform? In 1975, Geoffrey C. Shephard posed the question, "Does every 3-polytope possess a net?" This problem still remains open to solve. This research does not attempt to make an ultimate proof, but rather attempts to develop an intuitive correlation between these two worlds. The first study in this line of inquiry initiates a mapping dialogue between a geodesic dome to a "textured" dome.

A tool is a device that augments an individual’s ability to perform a particular task. The more specificity a tool has, the narrower its instrumentality. Tools inherently constrain the way individuals design; however, designers are often unaware of their influence and bias. Digital tools are becoming increasingly complex and filled with hierarchical symbolic heuristics, creating a black box in which designers do not understand what is "under the hood" of the tools they drive. And yet designers are becoming fascinated with engineering mentalities: optimization and automation. Simply, it gives a solution. But, this is not design! Designers need to work outside of a fixed atmosphere!

The future of digital instruments is not more complex heuristics, but rather the contrary. It is imperative to go back to the most basic building blocks of these "engines:" mathematics. Within mathematics, functions can be embedded inside other functions at anytime, giving designers endless freedom to alter the computational hierarchy. In this experiment, the boundary of one shape is completely altered to the confines of another shape by simply placing its mathematical definition within the others. The complete hierarchy is transformed while maintaining a consistent framework and parametric equation.

A Guide to Mathematical Transformations for Architects and Designers
Hardcover: 232 pages, 886 illustrations, 220mm x 220mm
Laurence King Publishing
ISBN 978-1-78067-4-131

Cylinders, spheres and cubes are a small handful of shapes that can be defined by a single word. However, most shapes cannot be found in a dictionary. They belong to an alternative plastic world defined by trigonometry: a mathematical world where all shapes can be described under one systematic language and where any shape can transform into another.

This visually striking guidebook clearly and systematically lays out the basic foundation for using these mathematical transformations as design tools. It is intended for architects, designers, and anyone with the curiosity to understand the link between shapes and the equations behind them.

A sphere is a specific type of shape. It defines the boundary of any object whose outer surface perimeter is equidistant to its center point. It is arguably an elegant shape, because of the simple ruled logic which governs its creation. It is not associated with the families of the gestural or sculpted. There is no residue of man or the hand, for it has been created by something greater. A pure shape, defined by trigonometric functions.

How do we get inside? Any puncture or penetration would ruin the purity of such a shape. Don't even mention the thought of a door! A sphere is a closed shape and perhaps it should remain closed. There is no way to get in and there shouldn't be!

Although it is impossible to get inside a sphere, maybe it is possible to get inside one of its relatives. By manipulating the smallest morphemes of the sphere (sine and cosine), it is possible to transform a closed shape into an open one. By incrementally increasing the radius of the outer surface, the sphere begins to peel and spiral. Then, the shape begins to twist and turn, creating two means to enter. Lastly, increasing the period of the shape allows it to grow and loop around itself -never self-intersecting.