• Nettie Ni

Work in Process: Explore Non-Orthogonal Spatial Geometry




A courtyard space designed by Ortner und Ortner is enclosed by a clear indication of perimeter, the solid brick wall. As shown in Figure xxx, through a series of analytical study of the space, the courtyard wall is realised via its vastness in scale containing a triple and quadruple height space. The point of entrance is clearly indicative on the perimeter walls, in which enhances a sense of separation and isolation from the internal courtyard space to the exterior. The height of the perimeter walls indicates a vertical growth towards the sky, extending both upwards towards and downwards to the underground space. Two spatial volumes at different levels are contained within one solid perimeter of a courtyard space. The vertical space is enriched by a split-level typology, establishing a spatial dialogue along with an interplay of light and shadow displayed against the depth of the courtyard space.

When the spatial principles of the courtyard designed by Ortner und Ortner is studied in terms of intersecting vertical spaces, Piranesi’s etching series of the Carceri is brought into consideration. Within the Carceri, the notion of verticality is reflected upon the ‘sublimity’ of the Roman Architecture. This almost ‘romantic horror’[1] of the imaginary prison manifests itself in the complex circulatory routes in a vast void space. The intertwining staircases composed visually in the etching depicts a sense of vertical rotation, a space constantly directorial in diagonal planes while ascending upwards. Along with a complex containment of repetitious ‘formal motifs’, such as staircases and colonnades, Piranesi’s treatment of the vertical space seems to suggest an infinite expansion towards the sky without limitations. The perception of depth in space is enhanced via a glow of the chiaroscuro effect. The notion of sublime is enriched by Piranesi’s use of complex circulations and penetration of architectural elements. The spatial experiences become a constant interplay in scale, an orchestral composition that lingers around a constant shift in moments of suppression to openness.

To further explore the potential of this spatial composition, the seven-stories office building located in Shibaura designed by SANAA demonstrates an inhabited application of vertical intersection of spaces. As shown in Figure xx, the square footprint assigned with a regular façade grid is divided by a series of curves, adjoined vertically by an off-centered rectangular core. The core suggests a point of central circulation with an assigned service function. The floor plates which cantilevers off the core indicates a spiral motion in spatial movement. Its continuity, in fact, is disrupted occasionally by a series of localised staircases linking between adjacent floor plates. The vertical spatial interplay of double height and triple height spaces provokes a spatial dynamic, a continuation of discourse between intertwining programs. The building becomes a ‘social centre’ of the town, creating constant overlap of workshop, office areas, cafeteria, art and design functions, social event spaces and the terrace. The public space is celebrated and optimised within the intersection of vertical spaces, amplifying a sense of social awareness and co-existence in space.

Design Methodology

In response to the atlas case studies, in order to pursue a precise set of spatial, structural and functional principles relevant to the project, hand drawing, physical modelling and computer modelling were used as part of the iterative process.

The Bordeaux Courthouse plan triggers a thought process and speculation upon the possibilities of spatial arrangement within a triangular form. A series of sketches were produced to study the triangular geometrical form and ways in which the triangular geometry maybe divided in plan.

Three methods of spatial division are concluded on my initial study of a symmetrical triangle. They are the concentric, the gridded and the dissected. The concentric spatial division is to begin with the perimeter of a triangular form to concentrically divide the space towards the centre. Such spatial arrangement allows for possibilities to generate layers of spaces with similar corner experiences. The gridded division allows for an equal distribution of triangular forms with identical angular spaces. The dissected division is, in fact, conducted by dividing spaces via joining the corners spaces to the perimeter of the triangular form. Such division allows for the opportunity for non-repetitive triangular geometry to appear, creating an irregular sub-group of triangular spaces.

The design was made via a non-linear intuitive formal research process triggered by the selection of atlas images. The initial formal study of the triangular geometry in plan was evolved to become a series of plan iterations experimenting upon the forms of triangular division. Each plan was hand drawn to study the associated spatial principles previously outlined in the Bordeaux Courthouse and the Carlo Rameos Pavilion plan. The series of detailed intuitive plan studies results in a complex outcome, adjoining spatial considerations of several triangular formal divisions, the incorporation of internal courtyards, various structural and the functional principles. Such detailed plan drawings, in fact, appears to distract the architectural principles from its purist form. As shown in figure xxx, the irregularity of the internal courtyard space convolutes the study of the corner spaces. Accompanying the plan study, associated possible elevation and sectional spaces are imagined accordingly. The search for a set of clear architectural principles, at this stage, still remains in progress.

In response to the convolution of principles, one of the simplest plan studies was selected, as shown in figure xxx, to rebegin the process of extracting and formulated a concise set architectural principle essential to my project. This plan was selected due to my subconscious fascination with the dissecting division of a triangular plan. By joining the corners with tangents to the triangular space, more non-orthogonal spaces are created with different corner angles and sizes. This method of spatial division envisions a project with rich experiences of angular spaces and diagonal planes in which defines views to be diagonally directional.

The plan was then developed further through physical and computer modelling to consider the spatial possibilities in vertical dimension. The first test model, as shown in figure xxx, imagined the two crossing planes as extrusions of a continuous core space while floor plates stack consistently in between. Due to the strong gesture of the cross in plan, vertical spatial arrangement became restricted in the imagination if only extruded. Several computer modelling tests were made to reconsider the formal typology. The process was then directed to explore interior intertwining spatial interactions established between openings of the crossing vertical planes and the floor plates. This spatial experiment directs the project towards a non-monotonous spatial dynamic and an interchangeable spatial experience.

Based on the drawing shown in Figure xxx, the spatial principle was urged to further concentrate on a particular aspect. Accompanying a subconscious link to the intersection of vertical spaces introduced in the Ortner und Ortner, the design focus abandons the complication, shifting the concentration towards purely to the split-floor spatial typology. An initial 1:50 study model was made to test the spatial outcome of the split-floor typology when applied to a triangular footprint. The first study model, as shown in Figure xxx, does not follow a rule of how the triangular footprint is divided. The model was treated as a pure spatial compositional experiment. To evolve from the first model iteration, the second 1:50 model as shown in Figure xxx, begins to rationalise the study with the consideration of order and structure. Coincidentally similar to the SANAA’s Office building in Shibaura, a set of façade grid is applied to the perimeter of the triangular footprint. The divergence of floor plates occurs in between the connection of the façade structures. Unlike the SANAA Office building, the model principle of dissecting floor plates based on a façade grid enhances the overlapping of vertical spaces. Moments of low ceiling space accompanied by moments of double height spaces interweave into each other in the interior space, hinting towards moments of privacy and publicness. The 1:100 model enhances this principle by introducing a circulation core to the high-rise interior. The spiral triangular staircase centralises the circulation, reinforces a sense of rotation.

[1] Sergio Roncato, ‘Piranesi and the Infinite Prisons’, Spatial Vision 1-2 v. 21 (2007): 8-9.


In conclusion to the primary and secondary spatial research, the final model settles upon the following architectural principles as the project basis.



1. A plan of a non-orthogonal geometry, in this case, a triangular shape, is to be spatially dissected in according to mid-points and corners of the building perimeter.

2. The core which intends for structural, service and centralised circulation purposes is located in the centre in between lines of intersections.

3. The floors are split in vertical dimension suspending off the core structure, forming an interplay of overlapping spaces varying in heights. The spiral staircase spins upwards in vertical rotation connecting the horizonal planes.

4. Partition walls are placed along the lines of dissection to reinforce moments of privacy and enclosure.

5. A load bearing façade with defined openings encloses the interior space, distinguishing the interior with the exterior.

6. For future design, improvement is to be made by adding a de-centralised circulation system in between the floors and rework on relationship between the façade and the interior space.







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