Perspective drawing
Every perspective drawing is a picture traced on an imaginary sheet of glass between your eye and the world. Walk round a 3D room with an eye point and a glass picture plane, switch between one-point, two-point and three-point views, raise your eye height and watch the horizon and the vanishing points move.
About this course
Every perspective drawing is a picture traced on an imaginary sheet of glass between your eye and the world. In the 3D room you can walk round an eye point and a glass picture plane, switch between one-point, two-point and three-point views, raise your eye height and watch the horizon and the vanishing points move. The picture plane stands upright, and a sight line aimed at anything as high as your eye is level, so it crosses the glass at eye height. That is why the horizon line is your eye level.
The seven units are the picture plane, the horizon line, one-point perspective, two-point perspective, three-point perspective, measuring in depth, and Brunelleschi, Alberti and the history of perspective. Face the back wall square on and every depth edge in the room runs to one point straight ahead of your eye. In practice vanishing points often fall off the paper, so artists tape extra sheets to either side rather than move the points inward and distort the drawing. For equal spaces such as fence posts, a line from the top of post 1 through the middle of post 2 hits the ground line at the foot of post 3.
The last unit tells the history. The first correct method is credited to Filippo Brunelleschi (1377 to 1446), the Florentine architect who later built the great dome of Florence Cathedral, completed in 1436. The date of his discovery is not recorded exactly: the St Andrews history puts it at about 1413, and other accounts say about 1420. He painted two demonstration panels of Florence, one of the octagonal Baptistery of San Giovanni and one of the Palazzo dei Signori, both now lost.
Before you start
Ratios help with the examples that compare an object’s height and distance with its size on the picture plane. Start by noticing the eye point and the glass plane in the room. Their positions explain the drawing before you work with horizon lines or add more vanishing points.
When you finish
You can locate the horizon from eye height and distinguish one-point, two-point and three-point perspective. You can follow depth edges towards vanishing points, explain what changes when the view turns or tilts, and compare projected sizes at different distances. You can also describe the glass-plane idea behind a perspective drawing.
- 1The picture plane: drawing on a windowA 2 m door 6 m from your eye, traced on glass 1.5 m from your eye, comes out exactly 50 cm tall.
- 2The horizon line is your eye levelOn an upright picture the horizon is always drawn at the height of your eye: raise your eye from 1.6 m to 3 m and the horizon climbs the back wall with it.
- 3One-point perspectiveFace the back wall square on and every depth edge in the room, from the floor tiles to the tops of the walls, runs to one point straight ahead of your eye.
- 4Two-point perspectiveTurn the boxes 30° and the drawing gains a second vanishing point: with the glass 1.5 m from the eye, they sit 2.60 m to the right and 0.87 m to the left of the centre.
- 5Three-point perspectiveTilt the glass up by 22° and the upright edges of the tower meet at a third point 3.71 m above the centre, while the horizon drops 0.61 m below it.
- 6Measuring in depthPosts 1.5 m tall standing 4, 6 and 8 m from the eye are drawn 37.5, 25 and 18.75 cm tall on glass 1 m away: equal steps in the room, shrinking steps on the paper.
- 7Brunelleschi, Alberti and the history of perspectiveBrunelleschi's test panel of the Florence Baptistery had a small hole at its vanishing point; you looked through it from behind at a mirror, and the painted building lined up with the real one.
Sources for this course (7)
- MacTutor (University of St Andrews)
- J J O'Connor and E F Robertson, Mathematics and art: perspective (mathshistory.st-andrews.ac.uk/HistTopics/Art/): Giotto's rules, Brunelleschi about 1413, the two panels, hole and mirror, Alberti De pictura 1435 and Della pittura 1436 dedicated to Brunelleschi, the visual pyramid definition, the tiled floor and the distance point, Ghiberti, Piero della Francesca, Leonardo's diminution numbers, Dürer 1525, Guidobaldo del Monte 1600, Desargues 1636 and 1639, Brook Taylor 1715 and 1719
- The Metropolitan Museum of Art, Heilbrunn Timeline of Art History, Florence and Central Italy 1400 to 1600 (metmuseum.org/toah/ht/08/eustc): Masaccio's Trinity applies Brunelleschi's perspective, Alberti On Painting 1435 to 1436, Alberti 1404 to 1472, the cathedral dome completed 1436
- Nelson-Atkins Museum of Art, Gaining Perspective (nelson-atkins.org/gates/gaining-perspective.html): Brunelleschi 1377 to 1446, Masaccio 1401 to 1428 and the Trinity about 1427, Ghiberti's Gates of Paradise 1425 to 1452
- Smarthistory and Khan Academy, Linear Perspective: Brunelleschi's Experiment (khanacademy.org, video transcript): vanishing point on the horizon line, orthogonals, the mirror test
- Alberti, On Painting, trans. Sinisgalli (Cambridge UP 2011)
- Book 1 §19: the rectangle as "an open window".
Checked: 2026-10-17