Software those artist should know

Step by Step Perspective

One Point Perspective - The Perspective of a Rectangle

In our perspective drawing above, you can see the lines of construction used to draw the two rectangles from our illustration.

There are two types of construction lines used in perspective drawing:

1) Orthogonal Lines which we have drawn in red.

2) Transversal Lines which we have drawn in green.

We will continue to use this colour coding in subsequent illustrations.

Orthogonal Lines

Orthogonal lines are parallel to the ground plane and move back from the picture plane.

Orthogonal lines set the varying heights or widths of a rectangular plane as it recedes from view.

Orthogonal lines always appear to meet at a vanishing point on the eye level.

Transversal Lines

Transversal lines are always at right angles to the orthogonals.

Transversal lines are parallel to the picture plane and to one another.

Transversal lines establish a fixed height or width between two orthogonal lines.

Transversal lines form the nearest and furthest edges of a rectangle as it recedes from view.

Vanishing Points

Vanishing points, which we have drawn in blue, are dots on the eye-level where parallel lines seem to converge and disappear.

Our illustration uses a single vanishing point and is the simplest form of perspective drawing.

It is an example of One Point Perspective.

One Point Perspective

One point perspective is so named because it uses a single vanishing point to draw an object. Used here to draw a box, it is the simplest form of perspective drawing.

In one point perspective, the front and back transversal planes of the box always remain parallel to the picture plane. Only their scale changes as they recede into the distance.

Note that it is only the receding orthogonal lines which change their angles. 

If you mouse over the image to view the completed illustration, you will notice that the front and back planes of our box have been left unfilled to make its construction more visible.

Two Point Perspective

Two point perspective is used in this illustration to draw our box which has now been rotated at an angle to the picture plane.

Two point perspective uses two sets of orthogonal lines and two vanishing points to draw each object.

There are no longer any planes parallel to the picture plane. However the vertical transversal lines are still drawn parallel to one another and at right angles to the ground plane.

It is at this stage that perspective drawing starts to become more awkward because the second vanishing point is often situated well outside the frame of the picture. 

Click here to view an illustration that displays the position of the second vanishing point.

If both vanishing points are situated within the picture frame, the angles of objects appear to be extremely foreshortened.

In the completed illustration, which you can see when you mouse over the image, the front and back planes of our box have been left unfilled to make the construction more visible.

Three Point Perspective

Three point perspective uses three sets of orthogonal lines and three vanishing points to draw each object.

Click here to view the illustration with all the vanishing points displayed.

Three Point Perspective is the most complex form of perspective drawing.

This technique is most commonly used when drawing buildings viewed from a low or high eye-level.

A Low Eye Level

The low eye level in our illustration above creates the illusion that the box is towering over us. It now has the scale of a tall building.

As the viewer has to tilt their head back to look up, the picture plane is no longer at right angles to the ground plane. 

In one and two point perspective, the picture plane is fixed at right angles to the ground plane.

In three point perspective, the picture plane is set at an angle.

As a consequence, the transversal lines, which were parallel in one and two point perspective, now appear to recede. They form a third set of orthogonal lines, which rise from the ground plane and eventually meet at vanishing point 3, high above the picture plane.

A High Eye Level

Three point perspective is also used when drawing an object from a high eye level as in our illustration below.

It creates the illusion of looking down from a high viewpoint.

This drawing process is simply a reversal of the method used for drawing a box from a low eye level.

The Perspective of a Circle

A circle in perspective is called an ellipse. The drawing of ellipses is controlled by rectangular perspective.

Our drawing above of an ellipse illustrates this technique. There are two distinct stages in its creation:

fig.1 The circle is first visualised in plan form on a flat square grid . Each section of the grid contains one quarter of the circle. 

fig.2 The square grid is distorted according to the laws of perspective. The circle is then redrawn onto the distorted grid to create an ellipse.

The diagonals of the grid have been drawn on both illustrations to help with the plotting of the circle and ellipse.

Mouse over the image to view the completed illustration without its lines of construction.

The Perspective of a Cylinder

Before you study the perspective of a cylinder, it helps if you understand the perspective of a circle which is explained on the previous page.

A cylinder is simply a circle which is projected into three dimensions.

fig.1 is an illustration of a cylinder which is formed by a circle projected vertically from the ground plane. 

The ellipses that outline the cylinder are all the same width. However, the roundness of their curves gradually increases as they rise above or drop below eye level.

Note how the ellipse at the eye level is seen as a straight line.

fig.2 is an illustration of a cylinder which is formed by a circle projected horizontally from the picture plane.

The circular curves that form the cylinder are all the same shape, but their scale reduces as they recede from the picture plane towards the vanishing point.

Our examples use one point perspective, the simplest form of perspective drawing.

A Central Eye Level

If you can see or if you know the position of the horizon in a picture, the image automatically becomes an extension of your own personal space.

As the horizon is also your eye level, you can understand the scale and space of the image in relation to your own body. Any part of the image which is in line with the eye level, feels as if it is close to your own personal height. This effect works whether objects are small or large, near or far, or whether the viewer is standing, sitting or lying down.

Wherever you choose to place the eye level in a picture will have a crucial effect on its composition.

FAMOUS ARTWORKS
THAT USE A CENTRAL EYE LEVEL

Jan Vermeer (1632-1675)
The Kitchen Maid (1658)
Rijksmuseum, Amsterdam

The eye level in this painting, which is just above the kitchen maid's hand, implies that the viewer is seated. This suggests that the scene is observed from a position of comfort which enhances the quiet and pensive atmosphere of the work.

John Constable (1776-1837)
Flatford Mill (1817)
Tate Gallery, London

Constable uses a centrally positioned eye level to create a balanced composition where all elements of the subject - figures, foreground, background and sky - are of equal importance to its design.

Vincent Van Gogh (1853-90)
'The Night Cafe' (1888)
Kröller-Müller Museum

The diagonals of this painting form the lines of perspective which meet at a vanishing point in the centre of the picture. It is a simple composition which divides the image diagonally into star-lit and lamp-lit sections. This is a bold example of one-point perspective.

Gustave Caillebotte (1848 -1894)
Paris Street, A Rainy Day (1877)
Art Institute of Chicago

In Caillebotte's famous image of a Paris street, the viewer shares a common central eye level with the figures in the paintings. This forms a spatial link between you and the characters in the composition and psychologically you feel that you are part of the scene. The picture frame becomes your field of vision and you almost get the sense that you need to move aside to avoid brushing shoulders with the approaching people.

This painting is an excellent example of how to use a central eye level.

The position of the eye level is the key compositional element in many of Caillebotte's works.

In this scene, the viewer shares the same eye level as the strolling figures. This creates the strong illusion that you are walking or standing on the same street. The common eye level forms a spatial link between you and the other figures and psychologically you feel that you are part of the scene. The picture frame becomes your field of vision and you almost get the sense that you need to step aside to avoid brushing shoulders with the approaching gentleman.

This intimate relationship between the viewer and the image is what makes the work so popular. It is like taking a look through a window in time.

The painting is very carefully arranged. The strong eye level divides the picture horizontally, while the lamp-post and its reflection bisect the image vertically. These lines intersect at the central vanishing point, creating four rectangles, each of which contributes a separate element to the composition of the painting:

1) The lower right rectangle with the boldest shapes and strongest contrasts, establishes the foreground.

2) The lower left rectangle with its triangular arrangement of figures that echo the shape of the building above, stakes out the middle ground.

3) The upper right rectangle links the foreground and background as the buildings recede in sequence from behind the umbrellas.

4) The upper left rectangle provides the main background interest with both sides of an apartment block viewed in dramatic perspective.

It is hard to avoid the idea that the shapes which fill the upper rectangles are subconsciously influenced by Caillebotte's training as a naval architect. The apartment block on the left is like the bow of a massive ship steaming towards the viewer. If you continue the analogy, the umbrellas on the right suggest the wind-filled forms of sails bobbing about on the sea of wet cobblestones. Yachting, after all, was one of the main pastimes to which Caillebotte returned when he gave up painting in later life.

In common with the Impressionists, Caillebotte captured the everyday scenes of urban Paris, usually from a middle class viewpoint. In Paris Street, A Rainy Day, painted in 1887, he portrays the new look of the city at the end of the 19th century.

Baron Georges Haussmann was given the job of modernising the old Paris of narrow streets and alleys. He replaced these with the network of wide boulevards that characterise Paris to this day.

In this painting, the grid-like arrangement of the space and the radial frames of the umbrellas evoke the arterial structure of this new road system.

What makes Caillebotte's paintings different from typical Impressionist works is the precision of his painting technique. For example:

Gustave Caillebotte (1848 -1894)
The Parquet Floor Polishers (1875)
Musée d’Orsay, Paris

The Floor Scrapers ( 1875 ), which captures the momentary play of light on the floor and on the backs of the workmen, is Impressionistic in its subject matter and in its attempt to portray atmospheric lighting conditions. However the painting technique owes more to earlier traditions. 

What makes this picture modern for the time is that Caillebotte uses an unusual eye level which lies above the picture plane. Psychologically, this elevated viewpoint exaggerates the back-breaking fatigue of the subject. The extreme position of the figures is also reminiscent of the images of stretching dancers by Degas.

Gustave Caillebotte (1848 -1894)
Rooftops under Snow (1878)
Musée d’Orsay, Paris

Caillebotte also created some typical Impressionist works. 'Rooftops under Snow' (1878) is a painting which uses a dramatically high viewpoint. This type of composition originated with the development of photography. Its design is influenced by the cropped photographic images which were popular among the Impressionists at the time. The painting technique used here is more characteristically Impressionistic.

A High Eye Level

A high eye level in perspective drawing focuses more attention on the middle and distant areas of a picture. 

You have a restricted view of objects that are close as you are essentially looking down upon them.

This is not such a suitable viewpoint for our illustration of ancient ruins, as the foreground objects move outside the picture plane and large areas of the background are empty.

The eye is naturally pulled towards the horizon as it forms a strong line across the picture. This also distracts the viewer from the objects in the foreground.

If you mouse-over the image to view the coloured version, this imbalance in the composition has been corrected with the use of landscape elements in the background. The hills are used to break up the horizon and link the background with the foreground.

A high eye level is the ideal arrangement for painting panoramic landscapes. The paintings of the American artist, Grant Wood, perfectly demonstrate this compositional device. 

It is also ideally suited to epic figure compositions, offering the artist a wide physical space to portray several narrative scenes within the one picture. Pieter Bruegel was arguably the greatest master of this technique.

FAMOUS ARTWORKS
THAT USE A HIGH EYE LEVEL

Grant Wood (1892-1942)

'Young Corn' (1931)
Ceder Rapids Museum of Art

This work is typical of the landscapes painted by the American artist, Grant Wood. They often use high eye levels to display the gentle patterns, textures and forms of the rolling landscape. His wonderful images have a silent, dream-like clarity and are a product of the artist's imagination and childhood memories. They are idealised and nostalgic views which look back with a sense of loss, to an age before industrialisation. Today, and as time progresses, that sense of loss continues to increase, and consequently amplifies the power of his work.

Pieter Bruegel (1525-69)
'Children's Games' (1560)
Kunsthistorisches Museum Wien, Vienna

This painting by Pieter Bruegel uses a high eye level to view the scene from above. This allows the artist to arrange the numerous figures into smaller groups which may be viewed separately without much overlapping. The viewer can then clearly identify all the activities in the picture. 

A high eye level is the ideal compositional device for portraying complex narrative subjects.

This narrative figure composition by Bruegel is a classic example of how to use a high eye level.

At first glance, this painting looks like a catalogue of children's games. However, the longer you look at it, the more you question what you are seeing.

Why has Bruegel chosen to set this scene in the 'adult arena' of public buildings like the town hall?

Why are there no adults to be seen?

Is this a realistic image of children at play or does it suggest another meaning? If you look at the range of games being played:

some are gentle and caring (a wedding game);

some are rough and bullying (hair pulling);

some are played alone (a girl with her doll);

some are team games (tug o' war on 'horseback');

some are competitive (see-saw on a barrel);

some are skillful (jacks);

some are imaginative (horse racing);

and some are reckless (disturbing a bee-hive).

Children have always imitated adult behaviour in their games. Today we understand how they reflect their experience of adult life in their play.

However, what does this mean to an adult in 1560, in an age when children had few rights and little psychological understanding?

Is this town centre, swarming with restless children, an allegorical scene of chaos and social disorder?

Is Breugel using 'Children's Games' as a metaphor to suggest that there is not much difference between the fantasy and tomfoolery of children's games and the ignorance and irresponsibility of adult society in his day?

Is the painting a warning to adults that they need to take heed of their conduct, if they want their lives to amount to anything more than the frivolous antics of 'Children's Games'?

Bruegel was well known for his moralistic paintings and engravings of 16th century peasant life. These are often set against dramatic backgrounds which portray the changing landscape across the seasons.

However, when you look past his subject matter to examine how Bruegel organises his pictures, you find a rare visual intelligence that continues to inspire today.

Bruegel understands better than any artist in his century, how to compose figures in a landscape.

'Children's Games' is a complex painting with about 250 children involved in over 80 games. Bruegel uses a high eye level to view the scene from above. This allows him to arrange the children into smaller groups which may be viewed separately without any overlap. The viewer can then clearly identify every child in the picture.

He also assembles the groups into lanes formed by the receding lines of perspective. This imposes a sense of rhythm and order over a very complex picture and allows the viewer to experience the apparent chaos in a more comfortable way.

Note how he attaches a symbolic importance to the town hall by placing it in the centre of the picture. Its facade exactly divides the top of the painting into three sections. To the right of the building is a stark view of the town where the 'games' stretch towards the horizon. In contrast a peaceful image of the countryside fills the left third of the painting. Is this a wry comment on mans' awkward attempts to impose his built environment upon the natural beauty of creation?

A Low Eye Level

Using a low eye level in perspective drawing creates the space for a large area of sky.

The sky, therefore, becomes a major influence on the scale, tone, colour and mood of the picture.

It can be used to dramatic effect in different ways. 

Scale: By lowering the viewpoint, you emphasise the height and power of objects in the foreground. This has the effect of making the viewer feel small.

Tone and Colour: As the sky is the main source of light in a landscape, it sets the key for the tone and colour of the picture.

Tone and colour are the two visual elements which combine to create the mood of the picture.

By varying the contrast or harmony of tones, we can create a dramatic or calm atmosphere.

By varying the colours we can control the strength of its emotional impact. For example, bright colours create a fresh and cheerful atmosphere, while dark colours convey a sense of doom and gloom.

Using a low eye level effectively increases the area of sky and amplifies these effects. 

Mood: the illustrations below demonstrate the effects of different skies on the mood of our landscape.

A Sunny Day

A Dramatic Sunset

After The Storm

A Starry Night

FAMOUS ARTWORKS
THAT USE A LOW EYE LEVEL

John Constable (1776-1837)

'Stonehenge, Wiltshire' (1836)
V&A Museum, London

Constable uses a low eye level to make space for the dramatic sky whose energetic brushwork injects life into what otherwise would be a silent and still image.

Joseph M W Turner (1775-1851)

'The Fighting Temeraire' (1838)
National Gallery, London

As well as creating a spectacularly radiant sky with his setting sun, Turner also uses the low eye level to emphasise the height of the ghostly ship, even although it is still some distance away.

Katsushika Hokusai (1760-1849
The Great Wave off Kanagawa (1823-29)
36 Views of Mount Fuji

In this Hokusai woodblock print, from the series '36 Views of Mount Fuji', a low eye level is used to emphasise the colossal height and power of the huge wave which seems ready to engulf Mount Fuji itself.

Vincent Van Gogh (1853-1890)
'Starry Night' (1889)
Museum of Modern Art, New York

Vincent Van Gogh (1853-1890) uses a very low eye level as a compositional device to display one of the most dramatic skies in the history of painting.

In ancient Greece the followers of Pythagoras believed in 'The Music of the Spheres'. They thought that each planet in our solar system emitted a sound as it orbited the sun and that together they harmonised to create a heavenly tone.

In Van Gogh's picture, the 'music of the spheres' is not so harmonic. It reaches a ferocious crescendo that resonates through the hills, trees and village. This is a painting that depicts colossal power of nature as it overwhelms the scale of man.

If you live in the city today, light pollution from commercial and domestic lighting makes it is difficult to appreciate the power and beauty of the night sky. On a good night you can only make out a few of the major stars.

However in the pitch black night of the countryside, you can literally see countless thousands of sparkling constellations. The awesome wonder of this vision leaves you with a profound sense of humility as you cannot help but appreciate your own smallness.

Van Gogh's imagination confronts the frightening power of this infinite domain and he expresses his amazement in the exaggerated rhythms and colours of his brushstrokes.

Although 'Starry Night' is not a 'realistic' image, there is no more powerful nor honest depiction of the sky at night.

The low eye level divides this painting into two symbolic areas:

The Heavenly Sky - the large area above the eye level which creates the space that is needed to display the convulsive power of a starlit heaven.

The Humble Town - the small area below the eye level which compresses the town into a humble section at the bottom of the picture.

Van Gogh sees this as the natural order where man is diminished when confronted by the greater forces of nature and creation.

He continues this comparison by echoing the shape of cypress tree with the church spire. These symbols, one a creation of nature - one a creation of man - stand out as they are the only vertical elements in the picture. Both symbols point to the heavens: the natural tree - strong, confident and in harmony with the elements; the man-made spire - weak, artificial and straining to reach the stars.

On a technical level he uses the difference in size between the tree and spire to create the illusion of spatial depth, a visual element that is otherwise sacrificed to the strength of texture and pattern in the painting.

Leonardo da Vinci (1452-1519)
The Last Supper (1494-98)
Santa Maria delle Grazie, Milan

Geometry in Art

Perspective Drawing is an application of geometry that artists use to arrange the layout of space in a picture. For many centuries, artists have been inspired by the visual beauty and order that exists in geometry and they have used it in many ways to help the composition of their art. There is no greater nor more obvious example of this than Leonardo's 'Last Supper'. Mouse over the painting above to view how Leonardo uses the geometry of perspective to make Christ the unmistakable focal point of the painting.

Here are some more examples of how artists across the centuries have used geometry in their artworks:

Eadfrith, Bishop of Lindisfarne (died 721)

Illuminated Ornamental Cross
from the Lindisfarne Gospels (715-721)
British Library

The Lindisfarne Gospels were written and illuminated by the monk, Eadfrith, who became the bishop of Lindisfarne in 698. They were created in honour of God and St. Cuthbert, a celtic monk, who was bishop of Lindisfarne (685-86) on Holy Island and died in 687. This cross-carpet page is found at the beginning of St. Matthew's gospel. The complex interlacing of geometrical forms in this beautiful illuminated manuscript pays homage to God who was seen as the Great Geometrician of the Universe.

Paulo Uccello (1396-1475)

Perspective Drawing of a Chalice (c.1450)
Uffizi, Florence

Perspective, first developed by Brunelleschi around 1420, was a new drawing technique when Uccello produced this image. Today, this chalice is a strangely prophetic drawing because it seems to predict the use of wire frame images to visualise forms in 3D software, five and a half centuries later. Were the original designers of these programs influenced by this image?

Mouse-over this image to reveal its hidden geometry

Michelangelo Buonarroti (1475-1564)

The Doni Tondo (The Holy Family) c.1506
Uffizi, Florence

The Doni Tondo was probably painted to commemorate the birth of the first child of Agnolo Doni, the Florentine banker. It depicts the Holy Family with the infant Saint John the Baptist. The nude figures in the background represent pagan mankind before the coming of Christ, and the infant Saint John creates a link, as a symbol of baptism, between this old pagan world and the new Christian world. The frame gives us a clue to the picture's composition. Five carved heads, with Christ at the top and possibly the four evangelists, form a pentagram. These five heads represent the five wounds of Christ while the round frame, whose circular shape is a symbol of continuity and endlessness, represents God. Mary's head, the focal point of the picture, is perfectly placed within the apex triangle of the star. The two walls, one on which the nude figures are seated, and the other which separates the old and new worlds, are carefully aligned on key horizontals within the pentagram.

The pentagram is a mystic symbol that has been around since 3500BC. It has been adopted by many different cultures over the centuries. To the Ancient Greeks, it was a sign of perfection because of the satisfying 'golden section' proportions contained within its structure. It has been used in an inverted form as a satanic emblem, but here Michelangelo definitely claims it as a Christian symbol.

Piet Mondrian (1872-1944)

Composition No.10 - Pier and Ocean (1915)
Rijksmuseum Kröller-Müller

The development of Mondrian's art is a methodical journey from realisic landscape and still life painting, through Expressionism and Cubism, to the total abstraction of the Dutch De Styjl movement. 

'Pier and Ocean' is painted at a stage in the development of Mondrian's art where his work is approaching pure abstraction, but with a few realistic associations still present. He even gives the painting a double title: 'Pier and Ocean' offering a realistic interpretation of the image and 'Composition No.10' suggesting one of an abstract series of images. 

He aimed to, and eventually did, create an international language of pure colour and abstract form which became known as Neo-Plasticism. This style, which formed the foundation of the Dutch De Styjl movement was based on the delicate balancing of rectangular forms within a horizontal and vertical grid, and painted from a restricted palette of primary colours with black and white.

'Pier and Ocean' was created on the road to this purist style. It is a painting of an abstract grid within an oval field. This is a compositional format that Mondrian borrowed from Cubist still lifes. Like the Cubist images, it balances both realistic and abstract elements. 

Mondrian believed that vertical lines expressed male elements in his work, while horizontal lines characterised the female side. In this painting, he combines both into an abstract rhythm that suggests the shimmering light of the sea. The ‘Pier’, which is constructed with longer (male) verticals, projects into the 'Ocean' whose rhythm expands in a network of (female) horizontals. Both elements contrast more in the lower half of the work but gradually come together and unify at the top of the picture. 

A sense of space and distance is achieved by the gradual change in the scale and frequency of the lines. This creates the illusion that they are receding towards a horizon.

Juan Gris (1887-1927)

Le Canigou (1921)
Albright-Knox Gallery, NY

This image by Juan Gris is an example of ‘synthetic’ Cubism, a later and more decorative development of the Cubist style. Cubism was an attempt by artists at the beginning of the 20th century, to revitalise the tired traditions of Western art which they believed had run their course. They challenged conventional forms of representation, such as perspective, which had been the rule since the Renaissance. Their aim was to develop a new way of seeing which reflected the modern age. 

 

Perspective only works from one fixed viewpoint. The Cubists believed that this was a limited visualization technique that did not reflect the way we see the world. In Cubist painting the artist depicts real objects, but not from a fixed viewpoint. They portray and combine many viewpoints of the subject at one time. The whole idea of space is rearranged – the front, back and sides of an image become interchangeable elements. Cubist images combine the artist’s observation with their memory of the subject which are fused together to create a poetic evocation of the theme. The title of this work is the name of the snow clad mountain that can be viewed through the window.

Still life was the most popular of the Cubist themes. It allowed the use of everyday objects whose forms were still recognisable after their simplification and stylisation.

John MacTaggart
Rainbox (2005)

Geometric Abstraction

Artists who use geometric structures as the compositional framework for their pictures often produce an abstract series of images based on the same arrangement. These variations on a theme explore the effects of different visual elements upon the image.

In the 'Rainbox' print above, by John mac Taggart, the underlying perspective drawing is a framework for the exploration of the transparent and reflective qualities of colour. 

(mouse over the image above to see perspective drawing)

Some further developments of the series are illustrated below:

Development 1

This development uses a series of graduated colours across the spectrum which contrast and harmonise as they weave across the design.

Development 2

This development uses graduating tones of opposite colours whose contrast creates a pulse of energy in the heart of the design.

Development 3

This development uses narrow black and white stripes which follow the forms of the cuboids to create a dazzling op art pattern across the design.

Development 4

This development uses broad stripes which negate the forms of the cuboids. The red base is used as a contrasting element which defines the outline of the background.

Development 5

This development uses the refractive distortion of shape and colour to create a liquid surface and suggest a depth beneath that surface.

Whether perspective is used to create abstract or representational images, and although its limitations have been brought into question by several artistic movements in the 20th century, it is still the most powerful visualising device in the artist's toolbox.