Descriptive Geometry for Designers — Introduction

Descriptive geometry for designers is very useful because it provides three-dimensional solutions through plans that are projected on technical drawings.

Descriptive geometry is the science that studies the methods of representation of figures in space on a plane, solving problems in which its three dimensions are considered. It is the basis for architectural, mechanical engineering, construction, and design studies.

Table of Contents

• What is Descriptive Geometry?
• Definition
• Historical Context
• During The Renaissance
• During The Enlightenment Period
• Present Context
• What is Descriptive Geometry used for?
• Applications in the Design Field
• Applications in Other Fields
• Summary
• Some Insights
• Any Thoughts?

What is Descriptive Geometry?

Definition

The Merriam-Webster dictionary defines this term as “the theory of projecting an exactly defined body to deduce both projective and metrical properties from its projections, the projections usually being made on two planes at right angles to each other”.

In other words, Descriptive Geometry is a branch of mathematics that transforms three-dimensional objects into two-dimensional drawings that can be represented on paper, computer screens, or other similar media.

It sounds like a complicated science; however, to learn it, designers just need:

Fortunately, designers have very well-developed visual-spatial intelligence! 😉

Do you have any doubts? Let’s try an example:

Can you see the cube (Figure 1)? I’m sure you can!

Your visual-spatial intelligence makes you see a three-dimensional object, a figure with volume when you see a two-dimensional image that is completely flat.

The set of points, lines, and segments shapes a figure, which only has width and height, which in your brain are described with depth, giving it volume (Figure 2).

Visual-spatial intelligence is important for descriptive geometry, but it is not enough to solve some three-dimensional problems in a plane. Graphic Projections in Descriptive Geometry are fundamental techniques used to represent three-dimensional objects on a two-dimensional plane, such as a sheet of paper.

Descriptive Geometry for Designers — Projections

In simple terms, imagine you have a three-dimensional object, such as a box or a building, and want to represent it accurately on a flat paper drawing. Graphic projections allow you to do this. From this need, descriptive geometry was developed.

Historical Context

Since Prehistory, humans have felt the urge to visually represent their ideas through images and drawings, as seen in caves. Several projection methods have been created throughout history, from Euclid’s time to the present.

During The Renaissance

Leonardo da Vinci and Filippo Brunelleschi are two Renaissance-era figures who made significant contributions to the development and application of descriptive geometry. While they lived in different periods, their work laid the foundation for this important field, which is crucial in fields like engineering, architecture, and art.

Brunelleschi’s most famous contribution to descriptive geometry was his design and construction of the dome of the Florence Cathedral (Santa Maria del Fiore). To achieve this remarkable architectural feat, he developed innovative techniques, including the use of perspective and geometric principles. His meticulous calculations and understanding of geometric projection were instrumental in creating a dome that harmoniously integrated with the existing structure.

Leonardo da Vinci was not only a painter but also a scientist and inventor. His keen observation skills and meticulous studies of the natural world led to advancements in the understanding of perspective and descriptive geometry. His famous works, such as the “Vitruvian Man” and the “Last Supper,” demonstrate his mastery of perspective projection and the accurate representation of three-dimensional objects on a two-dimensional plane.

Both Brunelleschi and Leonardo da Vinci not only influenced the fields of architecture and engineering but also had a profound impact on art and visual representation. However, descriptive geometry achieved its pinnacle with the French mathematician Gaspard Monge (1746–1818).

During The Enlightenment Period

Monge’s motivation for developing descriptive geometry was rooted in the practical needs of fields like engineering and architecture. At that time, advancements in industrialization were leading to more complex and intricate designs in various industries.

Monge’s method involved using orthogonal projections, which are effectively numerous images of an object from different angles, to capture its whole form and dimensions. This invention not only simplified the sharing of design concepts but also facilitated precision production and construction methods.

Architects, engineers, and designers were grappling with the challenge of accurately conveying their ideas and designs on paper while still preserving the three-dimensional aspects of their creations.

Present Context

In the 1960s, designers and architects began to move from mechanical aids and drafting machines to computers and plotters. In addition to hardware, the associated software has also steadily evolved; three-dimensional “computer-aided design” (3D CAD) is now indispensable in today’s construction planning and product development processes.

Despite the widespread use of CAD for three-dimensional designs, learning and practicing descriptive geometry reinforces algorithmic thinking skills when dealing with spatial geometric problems.

What is Descriptive Geometry used for?

Applications in the Design Field

Certainly, the application of descriptive geometry spans various fields and industries. Let’s delve into some key applications:

Applications in Other Fields

Some Insights

Although nowadays, much of the 3D CAD software solves many of the projections and problems that used to be solved with descriptive geometry, this discipline has not lost its relevance. In many educational institutions, it is taught as a compulsory subject because it enhances the development of visual-spatial intelligence, a highly valued ability among designers.

In conclusion, descriptive geometry provides students with the skills to understand and communicate spatial relationships effectively. It remains a cornerstone of education in fields like architecture, engineering, and design. The principles of projection, perspective, and spatial visualization that Monge introduced remain integral to the way designers communicate their ideas visually.

Any Thoughts?

In the comments section, tell me if you already knew what descriptive geometry was. As a designer, do you know about graphic projections?