Isometric Freehand Quadrature of Urban Sights: The “Squares-are-the-Key Method”

In this paper, I propose the “squares-are-the-key method” as an update of the outdoor freehand-drawing class for architectural design. Let’s generate simplified 2D grids of site and floor plans, transform them to isometric grids, and insert essential height edges, taken from simplified elevations and sections, into it, on site.

Freehand drawing had been a staple since the inauguration of the education of architects: Visit famous buildings and sketch them in artistic fashion. Twentieth century architecture called for both novelty and appreciation of the crafts-Walter Gropius famously stated in his "Bauhaus Manifesto" (1919) that artists were considered exalted artisans. Students of architecture started to visit architectural heritage only to realize that what they saw no longer applied to current standards of aesthetics or construction. Computer-aided design further added to the mental split between old masterpieces and contemporary mediocrity, an alienation between architectural history and practice. In this paper, I propose an update of the freehanddrawing class outdoors. With pencils and digital pens, we train for desirable 3D virtual reality pencil tools, possibly helping to bridge the cumbersome first 30 + years of computer-aided design.

Research: Applying Descriptive Geometry to High-Performance Landscape-/Architecture in the Field by Square Grids, to be Reconstructed in Isometric Projection = Flatten the World in Order to Pump it up Again
Can we multitask with freehand drawing in the field with attention to digital design in architecture?-Yes. This research rests on three fundamentals: Neuroscience concerning freehand drawing, the immediacy of strollology, and imperatives of information design: • Freehand drawing is widely accepted as a fundamental design-orientated spatialtemporal cognitive training "for hand-eye coordination, fine motor control and procedural memory" (Chamberlain 2013, p. 267). Students can be taught to draw as "somewhat like teaching someone to ride a bicycle" (Edwards 1999, p. 2) despite the "uncertain future of handwriting" (Trubek 2016). Let's be aware of what Dexter (2006) calls "Vitamin D" as in drawing, our wonderful mentalphysical flow path from the brain via the arm, wrist and hand into the fingers, and the extensibility to pens and brushes, applied to surfaces suitable for sketching. • "Strollology" (Burckhardt 2015) with "the mind at three miles per hour" (Solnit 2016, p. 15) allows us-augmented with research on situational awareness-to instantaneously reflect on our environment in the field, beyond sheer visibility and touristy entertainment. • Information design recommends being brief: Transfer information to knowledge, omit redundancy, spare ink (Tufte 2002, p. 93) and pay attention to the "narratives of space and time" (Tufte 1998, p. 97).
Firstly, let's draw a didactic triangle composed of applied philosophy, field trip didactics and drawing skills focused on architectural design. We want to connect to our physical world, both mentally and ethically. Strollology allows us, secondly, to understand our environment actively, while we are in it, including weather capers and insect bites. Thirdly, we want to learn to draw from scratch, as we would in the design studio on white sheets of paper and blank screens, ideally without proverbial fear of the first line. The ulterior, subjacent goal is to preserve drawing routines for emerging technology such as virtual 3D pens. We may soon be able to thoroughly design by freehand drawing without having to use a computer mouse to navigate on a separate screen rather clumsily. How do we integrate applied philosophy and drawing skills on a field trip?

Let's Pick Isometric Projection as the Means of Choice and Departure from Traditional Nature Studies
Estimating perspective-distorted proportions in the field is challenging. Apparently, this skill was not desirable enough during evolution to foster, in comparison to a sophisticated sense for distances in order to judge our chances for food or detect predatory threats. Is there an easy way to circumnavigate our weakness in estimating perspective-distorted proportions when drawing? Perhaps yes. Isometric projection, derived from the Greek term "equal measure", represents length, width and height in the proportions 1:1:1 at the expense of a compressed floor plan (Figs. 1, 2). Isometric projection combines the clearness of everyday perspective view and the accuracy of technical drawings (Fritsche 2018(Fritsche , p. 1563).

Let's Distil Interior Spaces, Buildings and Landscape Architecture to Patterns Composed of Squares: The Squares-are-the-key Method
How do we design the simplest approach to spatial drawing for students of architecture, sometimes intimidated by their biographical gap in drawing, the so-called "crisis period" (Edwards 1999, p. 69)? Answer: Let's flatten the world to squares in orthographic projections, regular quadrilaterals with equal sides and angles, in order to pump it up again in isometric projections. Virtually everyone can draw credible squares on a sheet of paper and, with the help of a digital pen, on a tablet computer. Students grasp length, width and height in front of them. There it is. I drew a line, and another one, and a few more lines that add up to a believable square. I did it! Gradually, students represent proportions of complex structures in short periods of time.
How does the squares-are-the-key method work?
1. By iteration, I distil complex structures in landscape and architecture to square grid sketches with motive proportions reasonably recognizable, yet greatly reduced. On the grid, I mark building edges and intersections of landscape patters. Square grids work for site and floor plans as well as for sections and elevations. Some squares may feature subdivisions, easily determined with the help of diagonal lines, while others remain unused, empty. 2. Next, I suggest drawing the square pattern as isometric grid on a new sheet of paper (or new file on a tablet computer). Then, students transfer intersection points and edges from their orthogonal templates into isometric projection. 3. I suggest modal splits in color: Decide with what pencil-lead or color-you want to draw the 2D square-based proportions. Suggestion: Use a color pencil  (2021) since that saves the lead pencil for the 3D sketch construction efforts with easier correction via eraser. Stick to the square-based-proportions color when you translate your 2D plan sketches into the comprehensive isometric drawing with distorted floor plan squares (Figs. 1, 2). 4. As an optional necessity, I recommend putting tracing paper on top of the sketch development to trace crucial lines only, even more so when someone gets confused with their artificial grid, auxiliary lines and the essential outlines.

Didactics of the Seminars Transcend Perception, Knowledge and Drawing Skills: Let's Meet in a Worthwhile, Ideally High-Performance Landscape and Architectural Environment to Draw it, Including Historical and Architectural Aspects
On site, I demonstrate the reducibility of the overwhelming information in front and around us to knowledge through seminar posters (Fig. 3a). Students are encouraged to synthesize field experience, square pattern templates and background knowledge to simultaneous (all in one) and successive forms (series) of representations with continuous labelling by hand and, if appropriate, with additional principle sketches. For a first seminar series, I selected locations inductively, from worthwhile phenomena in and around the student city of Dresden, to categories: • Complex geometries such as baroque and contemporary landscape architecture (Fig. 3), urban design, architecture and interior design. • Buildings and areas that underwent, undergo, or expect major structural changes (Fig. 5).
In a redevelopment of the seminars with the squares-are-the-key method, I reverted the selection process and deduced locations from categories such as: • Stairs and ramps as ultimate 3D features (= space) (Figs. 1c, d, 4). • Old and new as two states in one (= time) (Fig. 5).
The category "old and new" introduces the transition from the twentieth century construction doctrine of excessive growth to intensive repair (Fig. 5).

Breadth of Research: The Squares-are-the-Key Method Works Well for Interior and Exterior Applications
Since climate change is ticking quietly, responsible design of landscape and architecture has to consider butterfly and domino effects. I utilize a range of scales along the "adjustment staircase of sustainability, resilience and ecological indestructibility" (Fritsche 2022, p. 926): • Interior spaces, by definition, are difficult to portray since the motive surrounds us. With the help of the grid made of squares we, from within, cut through the structure with potential and limitations (Figs. 4c, d, 5). • Traditionally, depicting a single building implies drawing what is visible from the outside with the relinquishment of knowledge about the inside. With the squares-are-the-key method, we X-ray to compose a 2-in-1 show, "the outer shape of a building" with surroundings and "important spaces within", an "Isometric Nolli Map" (Fritsche 2018, p. 1565) (Fig. 5). • The portrayal of urban places and landscape architecture usually features photographic views. With the squares-are-the-key method, we portray the entirety (Fig. 3) to illustrate the metaphor of saving the world in climate shock through landscape architecture.
While I suggest practical viewing directions in the field, students are welcome to experiment different lines of vision. In the digital world, models work seamlessly all around, after all.

Conclusion: Design-Oriented Freehand Quadrature of and for High-Performance Landscape-/Architectural Environments
Are there ways to connect tangible architecture with the training of intangible geometry in the field?-Yes! The squares-are-the-key method allows highlighting essential features of landscape and architecture in the field actively and comprehensively, far beyond outer appearances. Students develop low-threshold freehand-drawing skills, applicable, but not restricted, to architectural design. The method helps to draw using basic geometry from scratch fearlessly (thereby architecting between 2 and 3D), to discuss general education and vocational training, as well as to compare analogue and digital work patterns. Outlook = need for research: Will true 3D digital sketching, consisting of rather exploratory, brisk and searching drawing strokes, allow for an intuitive, uninhibited design motif search? Such work should be easily developable in, and exportable to, extended realities while continuing to look like what it is meant to be, an early attempt to improve our environment … Funding Open Access funding enabled and organized by Projekt DEAL.