Exploring the connection between the mathematics and art of three-dimensional chalk drawings using the idea of perspective
Introduction
The purpose of this paper and a relating practical project will be to explore the individual subjects and also the relationship between the mathematical perspective of a piece of art and the artistic and aesthetic beauty of the piece. Also to be explored is the influence that the mathematics has on the final outcome.
Description
The practice/method of perspective along with its mathematical principles is used in many different genres of art, some of which are architecture, painting, photography and illusions. However, in this paper I will focus specifically on the art of chalk drawings and attempt to explain the connection between the mathematics and art of chalk drawings by way of perspective.
Definition
To understand how perspective is used in creative art it is first necessary to understand the meaning of the term. The most relevant definition for the subject I will be covering is the following; “The theory or art of suggesting 3 dimensions on a 2 dimension surface, in order to recreate the appearance and spatial relationships that objects or a scene in recession to the eye” (Franklin Collins, 2009).
Anamorphism and Trompe l’oeil
The art of three-dimensional chalk drawings uses a projection called anamorphism. Anamorphosis describes a distorted projection or perspective, particularly an image or drawing, which is distorted in such a way so that it becomes recognisable only when viewed from a specific angle, or seen through a fish eye lens in order to enhance the effect. Kurt Wenner who, inspired by the anamorphism used in frescoed ceilings, devised a unique geometry that enabled him to use the same technique on his own street drawings. It has also been described simply as, the logical mathematical continuation of Perspective. This technique, which can also be known as Trompe l’oeil, creates a convincing illusion of reality. Trompe l’oeil is a French term literally translating to ‘deception of the eye’ or ‘trick the eye’. Using the art of morphing, three-dimensional images are produced from a two-dimensional surface and can seem to almost defy the laws of perspective by creating optical illusions that deceive the eye.
Perspective, Scale and Foreshortening
The mathematical principles necessary to create and produce effective and realistic looking chalk drawings are mainly foreshortening, scale and of course also perspective. Perspective is used mathematically in art in order depict spatial depth and reality and all drawings using this technique assume that the viewer is standing a certain distance away from the drawing. By assuming that, the objects are scaled relative to the viewer. The two most characteristic features of perspective, when used in art, are how the objects are drawn on a two-dimensional surface in order to create a three-dimensional effect. These features are:
- The objects begin to get smaller as their distance from the observer increases.
- Foreshortening: altering the scale of an image by shortening lines in order to suggest perspective and create an illusion of depth. This also means that an object is often not scaled evenly and effectively appears distorted when seen from the wrong angle.
In the two figures below the method of foreshortening is depicted effectively in a chalk drawing by 3-D artist Julian Beever. Figure 1 shows the drawing seen from the correct angle, while figure 2 shows the same drawing seen from an incorrect angle. The photos effectively depict the use of foreshortening as a technique.
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| Figure 1. Lady in a swimming pool (seen from the right angle) |
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| Figure 2. Lady in a swimming pool (seen from the wrong angle) |
Beauty of chalk drawings
The mathematical techniques and methods used to create chalk drawings are also the reasons for the artistic nature and aesthetic beauty of the drawings. In order for a drawing to become realistic and also pleasing to the eye the methods of mathematical elements such as perspective, scale and foreshortening are essential to the final outcome of the drawing. Without these techniques the drawing would be unable to effectively become a three-dimensional illusion as is necessary for the practice.
Many successfully completed chalk drawings are generally and widely acknowledged to be beautiful. The ones that are traditionally labelled as beautiful are generally, but not always, the drawings of nature. Any successful chalk drawing is always amazing to see because of the way that the artist has twisted the rules of perspective to make a realistic three-dimensional drawing from a two-dimensional surface.
Realism of three-dimensional chalk drawings
The mathematical techniques of chalk drawing, which have been explained above also play a big role in making sure that the drawing looks realistic. It is also necessary to get the techniques right in order for the images to look accurate and seen in 3-D from one specific viewpoint.
The mathematical techniques of chalk drawing, which have been explained above also play a big role in making sure that the drawing looks realistic. It is also necessary to get the techniques right in order for the images to look accurate and seen in 3-D from one specific viewpoint.
It is artistically necessary for a three-dimensional image to look realistic in order for it to be seen in an appropriate aesthetic manner. When a chalk drawing is successfully made to look realistic it is always astounding to look at. Ones that are especially exceptional are when it is possible for a person to be able to interact with the objects in the image and they, effectively come to life.
Below are some examples of three-dimensional chalk drawings that effectively show people being able to interact with the realistic images. Figure 3 is the text ‘world’ made to look three-dimensional with people being able to interact with it in a number of different ways. A man is holding up the letter ‘w’ which is in turn resting on the other letters. There is also a women in the distance made to look like she is lying on the ‘w’. Figure 4 is incredible in the way that it is possible to see snow falling onto the ground around the snowman. Lastly, figure 5 is extraordinary in the amount of detail that is used and how extremely it realistic it looks.
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| Figure 3. Three dimension text 'world' by Julian Beever |
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| Figure 4. Falling snow and snowman by Julian Beever |
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| Figure 5. Waterfall by Julian Beever |
Conclusion
In conclusion, the mathematics behind three-dimensional chalk drawings, for example perspective, scale and foreshortening, have an important influence on the artistic side of the drawings and are essential to the aesthetic look of the final outcome.
In conclusion, the mathematics behind three-dimensional chalk drawings, for example perspective, scale and foreshortening, have an important influence on the artistic side of the drawings and are essential to the aesthetic look of the final outcome.
References
Kurt Wenner – Master Artist and Architect Street Painting. (n.d.) Retrieved from
The Daily Haggis: The 3D Chalk Art of Julian Beever. (n.d.) Retrieved from
Lilo Magazines: Amazing 3-D Art. (n.d.) Retrieved from
(2009). Perspective. In Franklin Collins English Dictionary (Vol. N/A, p. N/A). N/A: Franklin Collins.
Lady in swimming pool 1 image, retrieved from
Lady in swimming pool 2 image, retrieved from
Three-dimension text image, retrieved from
Snowman image, retrieved from
Waterfall image, retrieved from
