1. METHODOLOGY
Research using various primary and secondary sources provides evidence to support the assertion that da Vinci developed a system of
surface mapping which mapped out the implementation of Chiaroscuro and Sfumato.
Leonardo’s use of cartoons
According to writer Bulent Atalay, Leonardo da Vinci often created a cartoon of his subjects and took them back to his studio for later
embellishments. These embellishments would be the application of color and shading. Considering the mastery of his shadows and color
tonalities, it would be require an astounding sense of visual memory, or imagination, to recreate the forms within the conditions of an
environment where he was no longer present. Having a system through which environmental conditions relate to an object’s surface
provides consistency, accuracy, and buys time for perfection.
The availability Euclid’s treatises and understanding its benefits
Art historian, Rocco Sinisgalli explains Euclid’s treatises; Optics, Catroptics, and Mirrors, as a construct on the appearance of objects
as they relate to the eye. In his treatise Optics, Euclid’s theories are based on the idea that the eye perceives objects in their environment
with a series of visual rays which come together at the eye in order to create a visual cone. Sinisgalli explains Euclid’s ideas in which visual
rays connect along the exterior of a shape and create an angle of appearance. As the eyes move over the object, it collects the different
angles of appearance and connects them to the eye, through the visual cone, and forms as; C.D. Brownson calls it, a “measure of visual
appearance”. The collaboration of the measurements in the cone communicates the appearance of the object as a whole. Brownson
concludes this explanation by saying; the position and size of the angle of appearance communicates to the eye; an understanding of the
size and distance of the object perceived. Euclid’s treatises on optics would have provided Leonardo with a mathematical measurement in
which he could measure appearance of objects (or sections of their surface area) in his work. Visual rays and their relationships to mirrors,
presented in Euclid’s work an opportunity for Leonardo to observe the pathways of theoretical light rays.
Mirrors
The work of art historian Yvonne Yiu, created a connection between mirrors and visual reproduction. Yiu explains how the
surface of mirrors provided the stability necessary to articulate geometrical relationships within illusionary space and helped to enable the
replication of these forms on a picture plane. For Leonardo, mirrors would have enabled his reproduction of appearances by establishing a
conditionally flexible but referentially stable situation in which he could take his time to analyze the object. It is a considerable possibility
that Leonardo’s famous mirror writing was a matter of convenience, if he was looking in mirror to make observations; the journals were
most likely directly beside him. Inverse writing would have made it easier for the artist to read what he wrote while he was studying.
His Writings:
Through the study of Leonardo da Vinci’s Treatise on Painting, it is certain that Leonardo placed significant focus and care on the
articulation of light and shadow. He describes how they function and interact with objects as an understanding of how they appear in the
condition of their environment. The conditions and demonstration of “relievo” (an articulation of planar forms which creates the
appearance of three-dimensionality) are well documented by him, and support the idea that the definition of surface area leads to the
pronouncement of Chiaroscuro and sfumato.
In his treatise da Vinci :
• specifies which direction light should come from for the best sense of relievo
• where the painter should place himself to best observe objects
• states that the management of shadows are essential if wants to becomes a “universal painter”
• specifies how light should be distributed on objects/figures in different environments
• describes light’s interactions with varying angles on an object’s surface - intensity of the light depends on the projection of parts
• suggested there are shapes within the shapes of shadows and each of these forms represented a variation of light.
In his journals, as examined by Fritof Capra, da Vinci:
•pursues the reconstruction of three-dimensional forms without losing perceived area or volume
•pursued a solution to the sought after Alhazen’s problem
•analyzed the obscuration of forms seen from a distance (From his Treatise on Painting)
•examines planar shapes, and reconstructs them in two-dimensional and three dimensional forms
• predicted the trajectories of reflected light rays on concave spherical mirrors
Leonardo da Vinci’s Animation of Images through the
Development of Shadow
ABSTRACT
Since the 15th century, people have been fascinated with Leonardo da Vinci’s incredible ability to
articulate forms on canvas. His figures seem to move, breathe, and embody an illusion which mimics
the viewer’s understanding of living flesh. While completing his fresco, The Last Supper, da Vinci
determined that linear perspective lacked the flexibility necessary to give two-dimensional forms the
illusion of life. Leonardo understood that in order to mimic the life of a subject, one must first articulate
its transformative nature in relation to the viewer’s eye. Through the analysis of his journals and his
Treatise on Painting, art historians can witness his pursuit to capture the malleability of bodies in two
dimensional spaces. Da Vinci experimented with mirrors to understand the principals outlined in
Euclid’s geometrical analysis of appearances, and applied them in the development of artistic forms
which appear to move based on the position of the eye. The outcome was a reconstruction of shape
which transformed two dimensional surfaces into three, by deconstructing the surface of an object in
order to create the illusion of volume. Mimicking topography, the angles of these multiple surfaces
created a resource to predict the intensity of shadow and light. Once applied and blended, the
articulation of these various tonalities became chiaroscuro and sfumato, which provided surface
contours with the qualities of movement and transformation which articulates the essence of life within
Leonardo’s subjects.
INTRODUCTION
Early in his studies of visual reproduction, Leonardo da Vinci understood that the mathematics of the Renaissance were
insufficient to describe the true nature of appearances. In his research, physicist Fritof Capra described the dilemma Leonardo
faced while gazing up at The Last Supper in the Santa Maria della Grazie in Milan. Although da Vinci had constructed his
composition as a divine articulation of linear perspective, the average viewer would not be able to appreciate the work
because the fresco was too high on the wall. Since the illusion of linear perspective depended on the viewer’s position to the
work, the shapes of the Last Supper would look distorted from the ground. Da Vinci then understood that in order to create
shapes which were truly illusionistic, you had to find a way to make the image flexible enough to work with a moving
observation point.
As Capra examines in Leonardo’s journals, the geometrical branches used by artists at the time, linear perspective and
Euclidian geometry, lacked a method which could replicate the fluid nature of form in real space. Since the appearance of
objects are constantly moving, changing, and mutating with the condition of their environment, the precise nature of
renaissance mathematics could not capture forms as they actually appear to the eye. In the pursuit of a mathematical
description for the conditional nature of objects, Leonardo used his journals to make visual recordings of experiments of the
transformative possibilities of shapes. As Capra describes in his research, Leonardo was able reconstruct planar shapes into
three-dimensional forms. These three-dimensional surfaces mapped out intricate measures of the exterior areas of objects by
applying the geometrical theories of Optics as outlined by Euclid.
Although he was never able to mathematically communicate the appearance of a form moving through space and time,
Capra states that he was able to illustrate the illusion of movement, by the subtle obscuration of a detailed depiction of surface
area through the use of shadow. Without the subject in front of him, it would be nearly impossible to replicate the kind of
shadow and tone necessary to complete his artwork unless he had a system which guided him based on a measured prediction
of the form’s appearance. My proposal is that Leonardo used Euclid’s geometry in Optics, to not only articulate the complex
surface areas of objects but also to predict how light would interact with these complex surface. This created Chiaroscuro and
sfumato which articulate their appearance to the eye by providing flexibility between the various surfaces.
Samantha Mealing, sguile@masonlive.gmu.edu
Department of Art History, George Mason University
RESULTS
Through the practice of these initial experiments, Capra has concluded that Leonardo was able to produce arithmetic progressions
which attempted to predict the progression of forms through space and time. These transitions, facilitated by movement, affect the
environmental and spatial conditions of the forms. Movement alters the appearance of the objects, which could be quantified (or affirmed)
by Euclidean Optics. Altogether it is the articulation of form which seeks to free itself from the planar surface. In the Renaissance, this was
the goal of relievo, to relieve a form from its surface. As Capra describes, Leonardo wanted to take relievo a step further; he wanted to
relieve forms from their surfaces through the appearance of movement. In order to create forms which appeared to move through space,
one needs to create the appearance of a space to occupy. In the case of Leonardo’s drawings, movement of the drawing within the pictorial
plane was instigated with the transformation of the surface of the object itself.
The concept of geometrical transformation of surfaces is thoroughly executed in da Vinci’s journals. In his Treatise on Painting, he
also describes forms which are broken into “several surfaces, or sides producing angles, either regular or irregular”. These forms, “of
different sides and angles will always detach [from the picture plane], because they are always disposed so as to produce shades on some of
their sides, which cannot happen to a plain superficies” (Da Vinci 171). If the transformation of form requires the existence of light and
shadow, then light and shadow must be able to be translated into geometrical forms.
From the science of perspective he understood the figure’s placement in the picture plane as well as the mathematical elements which
created distance between one object and another. He then combined it with Euclid’s explanation of appearances, in which he connected the
measurement of an object with how it appears to the eye (Capra). When these two systems combine it creates a three-dimensional
illustration of the world, in which the figures both recede into the space it occupied and reach out toward the world of the viewer. It is the
pictorial representation of relievo, the illusion of three-dimensionality orchestrated through the multitude of shadows (and light) on
depicted on the surface of da Vinci’s objects.
DISCUSSION
Leonardo’s studies of transitional shapes show that the artist had spent extensive effort observing the nature of changing geometric
forms. According to author and scholar Kim H Veltman, da Vinci was familiar with breaking a form into smaller shapes, and
rearranging them to create new ones. These new shapes would have angles and these angles are subject to the conditions of the light.
When these angles interact with light, they create the shading of an object. The degree to which the light hits an object creates their
appearance, which then, theoretically, could be judged for its accuracy using Euclid. As described in his treatise, these individual angles
all interact with the light source in different ways. Once they fuse together, the shapes are presented as a whole which outweighs the
sum of its parts. Together they create an articulation of the form’s surface demonstrated by light. This is da Vinci’s chiaroscuro and
sfumato.
These scientific and intuitive observations of light, not only create discrete variations of shadow necessary for chiaroscuro, but
also communicate the complex effect light has on the appearance of an object’s surface. His illustrations project not a mathematically
realistic representation of form, but a conceptual one where appearance of form is presented realistically in relation to the human eye.
Capra explored da Vinci’s complicated set of geometrical prediction and execution through diagrams, Leonardo reached the height
of his talent by using these predictions to apply light and shadow for the purpose demonstrating the appearance an object’s transitional
bodies through time and space. Chiaroscuro and sfumato gave a breath of life in his subjects with the implication of movement. Their
development and execution through the barriers of established geometrical systems provided a pathway of mathematical and artistic
discovery which set the tone for the depiction of three-dimensional forms today.
ACKNOWLEDGEMENTS
Assistance and guidance for the development of this project was provided by Dr. Lisa Passaglia
Bauman, of George Mason University’s Department of History and Art History.
REFERENCES
Atalay, Bulent. Math and the Mona Lisa. Smithsonian Books and HarperCollins: New York, 2006. Book.
Brownson, C.D. “Euclid's Optics and its Compatibility with Linear Perspective”.
Archive for History of Exact Sciences, Vol. 24, No. 3 (1981), pp. 165-194. Web. 18, October 2013.
Capra, Fritjof. The Science of Leonardo. Doubleday: New York. 2007. Book.
Da Vinci, Leonardo. A Treatise on Painting. Translated by John Francis Rigaud. Amherst: Prometheus Books, 2002. Book
Sinisgalli, Rocco. Perspective in the Visual Culture of Classical Antiquity. Cambridge: Cambridge University Press, 2012. Book.
Veltman, Kim H. “Perspective, Anamorphosis and Vision”. Marburger Jahrbuch Fur Kunstwissenschaft, 21. 1986. pp 93-117. Web. October
29, 2013.
Yiu, Yvonne. “The Mirror and Painting in early Renaissance Texts”. Early Science and Medicine, Vol. 10, No. 2, Optics, Instruments and
Painting, 1420-1720 Reflections on the Hockney-Flaco Thesis (2005), pp 187-210. Web. 10, October 2013.