A COMPLEX THREE-DIMENSIONAL CONDITION is best worked out by employing both three and two-dimensional views. (Studies for the AUHSD Magnolia High School Center for Excellence Cyber Security Classroom Building, Johnson Favaro)
The office dispersed a year ago and we have been designing at a distance ever since. Online we employ awkward drawing tools offered through primitive digital formats, like Blu Ray PDF, Adobe Power Point, Microsoft Teams, Cisco WebEx, Go To Meeting and Zoom. However much our language has evolved in descriptive efficacy and detail over the last year, we are daily reminded of the limitations of words and the imperative of drawings in advancing design. All words, even specialized ones, are selective, general in meaning and ambiguous in practice and as inadequate as they are for our purposes, were this not true, we would sadly enjoy neither wit nor poetry.
WE SEE AROUND CORNERS AND THROUGH WALLS in plan, section and elevation which in their combination describe a three-dimensional environment that we apprehend by moving through it. (Studies for the AUHSD Magnolia High School Center for Excellence Cyber Security Classroom Building, Johnson Favaro)
WE APPREHEND AT A DISTANCE by using two-dimensional drawings with which we evaluate three-dimensional conditions in the context of the larger experience of the building. (Studies for the AUHSD Magnolia High School Center for Excellence Cyber Security Classroom Building, Johnson Favaro)
As animate beings, we evolved to perceive the world by moving through it, employing not only our eyes and brains but also our feet and head. As we do so, we mostly keep track of what does not change -- the height, width, depth, shapes and substances of surfaces and objects. We gauge their sizes relative to and separation from each other and from us as they and we move around by calibrating invariant relationships among their invariant aspects. This is how we avoid trees and cliffs and why sometimes we “take a step back” to “size things up”. We perceive by comparing, we crunch the math. We know these invariant relationships most simply as ratios and ratios of ratios (proportions) but the math is complex, the scientists and mathematicians have yet to fully (and may never) describe it.
PERPENDICULAR PARALLEL LINE PROJECTION describes invariant aspects of an object, surface or environment by recording in one-to-one relationship two of its three dimensions-- height, width and depth. Oblique projections record all three but at the expense of the one-to-one relationship. (Perpendicular above; Oblique, below)
THE SCULPTOR MICHELANGELO disdained three-dimensional perspective and designed complex architectural compositions with mostly two-dimensional drawings. (Clockwise from upper left: studies for the Medici Chapel, the San Lorenzo papal tombs and the Laurentian Library vestibule in Florence)
MAPS OF THE WORLD are the two-dimensional projections with which we may be most familiar and of which there are many variations because of the impossibility of projecting a sphere’s surface onto a two-dimensional surface in one-to-one relationship.
Compared to the natural environment, a building is a simplified environment. Compared to a building, a drawing is simpler still. The information available in a drawing that describes an environment (natural or built) is always more limited than what is available in the environment itself. Drawings like all images (and words) are selective, general in meaning and ambiguous in practice and were this not true, we would enjoy neither a history nor a future of art.
JAMES J GIBSON was the first to successfully describe human vision as a full-body system (eyes, brain, head, neck, arms, torso and legs) and visual perception as the systemic navigation of our environment through the accumulation of visual information in the form of invariant dimensions, relationships of dimensions and rates of change.
AUTOMATED DRIVING NAVIGATION SYSTEMS are less sophisticated than the human perceptual system in that they make use of radio waves (radar, lidar) -- more like bats (echolocation) and insects (compound eyes) than humans—and for this reason, even with the help of GPS and AI, they may never fully replicate the complexity of human vision.
Drawings we use to design and describe a building are mostly “line” drawings (no color, textures or shading). In descending order of information contained (or in ascending order of “abstraction”), there are three-dimensional views: perspective, isometric and axonometric (3-d parallel line projection); and two-dimensional views: section, elevation (horizontal parallel line projection) and plan (vertical parallel line projection). To design and describe a building, perspectives and plans are the most widely used drawings and they are at opposite poles of abstraction. A perspective is a picture and a plan is a map, the former suggests how a building design might look, the latter conveys how it is laid out. But we would no sooner rely only on how a design looks from one or even a few perspective views than we would on its lay out alone. Every drawing is differently selective and complimentary in the information it offers.
PERHAPS MORE AWKWARD to contemporary eyes, the oblique projection of the late medieval scene (above) nevertheless more successfully describes an overall setting than the accurate perspective of the early renaissance scene (below) which more successfully places us within its setting.
BRUNELLESCHI’S REDISCOVERY OF PERSPECTIVE is the result of an architect’s ability to conceive of the geometry of drawing as a two-dimensional tool with which to objectively describe a three-dimensional environment (what you can and cannot see from where) --that he most elegantly demonstrated with experiments at the main cathedral and baptistry of Florence five hundred years ago.
THE ADOPTION OF PARALLELINE PROJECTION came after the rediscovery of perspective as ever grander and more sophisticated engineering endeavors required more accurate (measured), less impressionistic (apparent) depictions of objects and environments. (Diderot and his Encyclopedia of 1751-1772)
MACHINES SUCH AS PLANES, TRAINS AND AUTOMOBILES would not have been possible without accurate parallel line projection drawings, oblique versions of which were adopted by 20th century architect James Stirling who designed buildings he wanted to look like machines.
Sections and elevations (horizontal parallel line projections) are neither and both a picture and a map. Think of them as perspective views from a distance (hence the parallel lines). Like a perspective, they map aspects of the building that we see but like a plan, only in one-to-one relationship and only those that are invariant. Even though we never really see these aspects directly as mapped (or at all), they are with training and imagination effective tools with which to predict how a building is laid out and what it will look like. The key is the training and the imagination. Just as words are necessarily selective and useful only if we can write and read them, so we must learn to make and make use of parallel line projections. It is a skill.
OBLIQUE PARALLELLINE PROJECTION was informally employed by Michelangelo in his studies of the steps at the Laurentian Library vestibule (left) and five hundred years later more self-consciously by James Stirling in the configuring a complex set of multi-story stairs (right).
HOCKNEY’S LANDSCAPES blend perspective and parallel line projection to capture the experience of both complex and simple environments in a single image that neither a picture nor a map could on its own (Hollywood Hills, left; Yosemite Valley, right).
But is it a necessary one? Has electronic, parametric three-dimensional modeling rendered the two-dimensional drawing, the parallel line projection, obsolete? Could a building be designed without them? Our digital tools these days are Rhino and Revit through which within an imaginary isotropic environment we “model” a design in three dimensions. We can apparently move around and through it as we make it. The illusion on our two-dimensional screens is so powerful we convince ourselves we have worked everything out, even built the building before it is built, and why not then just hand over the model to the builder? And yet not once in the decade or more over which we have employed these tools have we ever worked out or described a building with three dimensional views alone. A three-dimensional model (viewed on a two-dimensional display) provides too much and not enough information.
WE ALL EXPERIENCE an approximation of parallel line projection when we view from a distance, such views as mountain ranges and city skylines.
STAGE SETS with just a little suspension of disbelief easily capture a sense of distance and expanse on a single surface--the backdrop-- by virtue of the simple phenomenon of parallel line projection.
PROFILES in their simplicity offer both accuracy and ambiguity (18th century silhouettes, left; 20th century Gestalt diagrams, right).
RABBIT OR DUCK? The game only works when the drawing yields just enough information to suggest both, and does not work at all when shading, color and texture are put into play (Andrew Wyeth lower left; Albrecht Durer lower right).
When instead we show aspects of a design in two-dimensional parallel line projection—not just plans but also sections and elevations-- we momentarily set aside extraneous three-dimensional information to then assess in manageable tranches large order of magnitude relationships which in their accumulation will result in the experience of the building. It is otherwise too hard to assess things dispassionately, from a distance, to see around corners and through walls—all of which are obligatory when designing, not just perceiving an environment. But because these drawings omit information, they are also ambiguous and insufficient on their own. We therefore toggle in our heads between three dimensional and two-dimensional views both of which it turns out are indispensable.
THE BENEFITS OF AN ELEVATION’S ACCURACY (a measurable record of two dimensions) are offset by its ambiguities.
THREE-DIMENSIONAL MODELING TOOLS, such as Revit, offer quick access to a variety of 2-D and 3-D assessments of a building design but in no way have they rendered 2-D assessments obsolete.