Drawing and Projection | Descriptive Geometry

12:28 PM

 Architectural design involves various forms of drawing and visual communication, such as sketches, technical drawings, and renderings. Although drawing is now an integral part of the design and construction process, it wasn't always the case. In fact, prior to the Italian Renaissance, architects relied on physical models to convey information to builders and craftsmen.

However, during the Renaissance period, the Florentine polymath Leon Battista Alberti introduced the idea of drawing as the primary mode of creating architecture. Alberti claimed that architecture is an idea that is conveyed through drawings and built by manual workers. This led to advancements in descriptive geometry and projection techniques, which further enhanced the role of drawing in architecture.

Drawing played two critical functions during the Renaissance: as a tool for visualizing and exploring building ideas, and as a notational tool for builders during construction. Artists and architects during this period also emphasized the importance of conveying perfect geometric forms that relate to the human body, as described by Vitruvius.

This human-centric approach to design and beauty is evident in Leonardo da Vinci's famous drawing, "The Proportions of the Human Body According to Vitruvius." Overall, drawing has played a vital role in the evolution of architectural design and continues to be an essential tool for architects today.


Leonardo Da Vinci, The Proportions of the Human Body According to Vitruvius, c.1490.


Descriptive Geometry is a crucial method in architectural design that enables the visualization and representation of three-dimensional objects on a two-dimensional plane. It involves two types of projections: parallel projections and perspective projections. In parallel projections, points from a three-dimensional object in space are projected onto a two-dimensional plane resulting in projection lines that remain parallel to each other. Points are zero-dimensional figures that are projected onto a plane and can be connected to form a two-dimensional image of a three-dimensional object. The complexity of the form determines the number of points required for an accurate depiction. 

The Italian painter of the early Renaissance, Piero della Francesca, was known for his works that accurately depicted the human figure through descriptive geometry and perspectival techniques. His interest in mathematics and perspectival theories led to the development of texts, including the treatise De Prospectiva Pingendi (On Perspective in Painting), where he described methods for designing, positioning, and coloring figures in space. The text focuses on perspective and explains the projection of complex surfaces and volumes that form the human body. In one of his drawings, various orthographic projections of a human head are formed by a series of points .

Orthographic projections, a type of parallel projection, use projection lines that remain perpendicular to the projection plane. They provide accurate scale and metric information about forms and spaces and are widely used in conventional architectural drawings such as plans, sections, elevations, and axonometric drawings. Through descriptive geometry, architects can visualize and represent complex forms, enabling effective communication and collaboration with others involved in the construction process.


Piero della Francesca, Projection of a Human Head, from De Prospective Pingendi , c. 1474–1482.





Perspective projections are a powerful tool for architects and artists to convey forms and spaces as we see them in the world around us. By using projection lines that converge at a vanishing point, three-dimensional objects can be accurately represented on a two-dimensional plane. This technique was first discovered by the Italian architect Filippo Brunelleschi, who created accurate perspective drawings by projecting objects onto a plane using a single vanishing point. His methods were further refined and codified by Leon Battista Alberti in his influential text De Pictura (On Painting) in 1435. Alberti's treatise provided artists and architects with techniques for accurately depicting shapes, forms, and spaces as we experience them through the sense of sight.

One of the most significant proponents of perspective projection techniques was Albrecht Dürer, a painter and theorist of the German Renaissance. Dürer illustrated his methods for projecting points of an object onto a plane in his engraving Man Drawing a Lute. In the engraving, a string representing a visual ray is connected from a point on an object to a hook on the wall, which represents the eye. The string traverses a plane with a swinging panel, and points are recorded where the string intersects the plane to form an identical image as perceived by the eye. This process of projecting points onto a plane is known as construction, and it is the basis of all perspective projection techniques used in architectural drawing today.

Albrecht Dürer, Man Drawing a Lute, 1525.


In conclusion, the use of parallel and perspective projections revolutionized the way architects design and communicate their ideas through drawing. The development of descriptive geometry and perspectival techniques allowed for the accurate representation of complex forms and spaces in two-dimensional drawings, providing a means for architects to explore and develop their ideas, and for builders to construct these designs. While these techniques have been traditionally applied through manual drawing methods, digital 3D modeling software now allows for the creation and manipulation of 3D models, with the location of points in space and their projection onto a two-dimensional plane forming the basis for viewing and creating architectural drawings. By using these techniques, architects can effectively communicate their designs to clients, builders, and other stakeholders, ensuring that their vision for a building is accurately realized in its construction.

Étienne-Louis Boullée, Restauration de la Bibliothéque Nationale 







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