Journal for Geometry and Graphics - Volume 12 - No. 1 - Drawing as Insight into Wholeness

Oct 29, 2026

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The technique of perspective drawing evolved over six centuries, often treating space as a mechanical external visualization shaped by rigid Cartesian coordinate influence. In architecture this approach can produce environments that are banal and emotionally and intuitively limiting. Based on masters-level thesis collaboration, the paper proposes reverse engineered perspective (REP), transforming space from immediate feelings into a mathematical model. The method starts with intuitive sketching, reverses conventional perspective order to extract plans, and is tested through a chapel case study to extend inner geometries into outdoor surroundings.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Introduction

The Renaissance: Development of the Conventional Perspective Drawing Method

Journal for Geometry and Graphics Volume 12 (2008), No. 1, 87􀀕98 . Drawing as Insight into Wholeness Michael Sciarrillo, Scott Aker Catholic University School of Architecture and Planning 620 Michigan Ave. , N. E. Washington, DC 20064, USA [emails: msciarri@gmail.com](emails: msciarri@gmail.com), [scottlaker@gmail.com](scottlaker@gmail.com) Abstract. The technique of perspective drawing has evolved over the past 600 years. Yet this has been primarily an external approach to visualizing and has lead to a mechanical interpretation of space. The in􀀝uence of the Cartesian coordinate system has further forced perspective drawing into a rigid response to one’s surroundings. In the domain of creating architecture, this mechanical approach has led our culture into a banal and characterless environment. Furthermore, it has suppressed our emotions and crippled our intuition. Through the collaboration of our thesis for masters of architecture, we developed an approach to transforming space that begins immediately with one’s feelings. With the use of our method called the reverse engineered perspective, we have created a successful mathematical model that can be used to unfold one’s inner vision into physical space. The process takes the form of an intuitive sketch, from which a plan can be extracted by reversing the sequence of conventional perspective. Our case study focused on creating a chapel and extending inner geometries into the surrounding outdoor spaces. With this method of perspective art, drawing one’s inner feelings provides us with new insight into Christopher Alexander’s theory of wholeness and our unfolding surroundings. Key Words: perspective geometry, representation of art in architecture (Claude Monet: ‘The Bridge over the Water Lily Pond’, 1900), Brunelleschi, Alberti, C. Alexander and wholeness, N. Salingaros, B. Mandelbrot, morphology, projective geometry, proportions, transformations, reverse engineering. MSC 2007: 51N05 1. Introduction Drawing can be perceived as an act in forming harmonious relationships between lines and shapes. At any point in time, the arrangement of lines and shapes forms a whole. The phenomenon of wholeness, in a drawing, occurs when individual geometries begin to interact with each other forming harmonious relationships. ISSN 1433-8157/$ 2.50 􀀍c 2008 Heldermann Verlag 88 M. Sciarrillo, S. Aker: Drawing as Insight into Wholeness Through the writings of architect and mathematician Christopher Alexander, he has described wholeness in relation to architecture and the design process. In The Nature of Order, Alexander de􀀜nes wholeness as a collection of centers working together to form an overall con􀀜guration of a place or thing. He describes wholeness as a state of perception, through a ‘broad gestalt’ or ‘sweep of a 􀀜gure’. Wholeness can be experienced emotionally through our perception of space. It can also be studied analytically; because a center or part, which is the focal point(s) of any whole, can be identi􀀜ed diagrammatically1 . With the desire to create a whole while designing, drawing becomes an essential tool for the design process [3] . If wholeness is somehow connected to our visual perception, as designers and architects, we presently have two methods available to us to articulate the feeling of the space we are designing; the conventional perspective and the conceptual sketch (natural perspective) . The conventional perspective is constructed following the development of a plan and section. The natural perspective sketch is a rough idea, usually done in some perspective view. It is free of the constraints of a developed plan, and section. The aim of this paper is to present a case study which explored a synthesis between drawing and wholeness, in which geometry of a place can inspire a context sensitive design. This paper follows a design process which a working tool called the reverse engineered perspective (REP) was used to delineate a plan from a ‘n

FAQs

What problem does the paper identify with conventional perspective drawing in architecture?

It argues that conventional perspective has become an external, mechanical visualization of space, reinforced by Cartesian rigidity. This can suppress emotion and intuition, leading to characterless environments.

What is reverse engineered perspective (REP) in this study?

REP is a process that begins with intuitive sketching grounded in feelings. By reversing the sequence of conventional perspective, it extracts a plan and supports unfolding inner vision into physical space.

How does the paper connect drawing, wholeness, and architectural design?

Drawing is presented as a way to form harmonious relationships between geometries. The study links this to Christopher Alexander’s theory of wholeness, treating wholeness as both perceptual and analytically identifiable through diagrammed centers.

Oct 29, 2026

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