What perspective is: horizon line and eye level
Perspective is a way to draw 3D things on a flat page so they look the way our eyes see them. Two simple facts: things far away look smaller, and parallel lines going away from us seem to meet.
The horizon line (HL) is at the height of your eyes (eye level). On a beach, it is where sea meets sky. If you sit, it moves down; if you climb, it moves up. Objects below it show their top; objects above it show their bottom.
Artists of the Renaissance in Europe set out the rules of linear perspective; artists in other places (Chinese scroll painters, Mughal miniaturists) used other ways to show depth, like overlapping and placing far things higher up the page.
One-point perspective
Use one-point (central) perspective when you look straight at the front of something: a road, a corridor, a room.
- Draw the horizon line and mark one vanishing point (VP) on it.
- Draw the front face as a true rectangle (horizontal and vertical lines).
- Join each corner to the VP with light guide lines.
- Choose the depth and draw the back edges parallel to the front edges.
- Erase the guide lines you do not need.
Size and distance
For a simple eye-and-picture model, drawn size is proportional to 1 ÷ distance:
h′ = h × d₀ ÷ d, where h is the real height, d the distance and d₀ a fixed reference distance (the picture plane).
So at twice the distance an object is drawn half as tall. Equal-height objects in a row have their tops on a line that runs to the vanishing point.
Two-point and three-point perspective
Two-point (angular) perspective: when a corner of a box or building faces you, there are two vanishing points, one at each end of the horizon. Vertical edges stay vertical. Each set of horizontal edges runs to its own VP. This is the classic view of a building on a street corner.
Three-point perspective adds a third VP above or below for tall towers seen from the ground or from a plane.
Freehand sketching tip: put the VPs far apart (even off the page) so boxes do not look stretched.
Shadows in perspective
With a lamp (point light): draw a light ray from the lamp through the top of an object, and a ground line from the point under the lamp through the foot of the object. Where they cross is the tip of the shadow.
With sunlight, rays are parallel, so all shadows point in the same direction. A low sun makes long shadows; a high sun makes short ones. Shading (light side, shade side, cast shadow) makes forms look solid.
Try it
In a long corridor or on a straight road, hold a pencil at arm's length along an edge line. Follow two edge lines to where they meet: that is your vanishing point. Then sit down and see it move.
Key formulas and definitions
- Horizon line = eye level
- Receding parallel lines meet at a vanishing point (VP) on the horizon
- One-point: 1 VP; two-point: 2 VPs; three-point: 3 VPs
- Drawn height h′ = h × d₀ ÷ d (size ∝ 1 ÷ distance)
- Shadow tip = light ray through top ∩ ground line through foot
- Shadow length (sun) = height ÷ tan(sun angle)
Worked examples
1. A 2 m pole is drawn 4 cm tall when it is 5 m away. How tall is the same pole drawn at 10 m?
Size ∝ 1 ÷ distance. Distance doubles (5 → 10 m), so drawn size halves: 4 ÷ 2 = 2 cm.
2. A tree drawn 6 cm tall is 3 m away. Where must an identical tree stand to be drawn 2 cm tall?
h′ × d is constant: 6 × 3 = 18. So d = 18 ÷ 2 = 9 m.
3. You draw a box above the horizon line. Do you see its top or bottom?
Above eye level you see the bottom face, like looking up at a shelf.
4. How many vanishing points do you need for a cube viewed with one edge pointing straight at you?
Two: each set of horizontal edges runs to its own VP (two-point perspective). The vertical edges stay vertical.
5. A 1.5 m stick stands in sunlight. The sun is 45° above the horizon. How long is its shadow?
Shadow = height ÷ tan 45° = 1.5 ÷ 1 = 1.5 m.
6. A lamp is 4 m high. A 1 m stick stands 3 m from the foot of the lamp. How long is the shadow?
Similar triangles: 4 ÷ (3 + s) = 1 ÷ s → 4s = 3 + s → 3s = 3 → s = 1 m.
Common mistakes
- Putting the vanishing point above or below the horizon. In one- and two-point perspective, VPs sit on the horizon line.
- Slanting vertical edges in one- or two-point perspective. Verticals stay vertical.
- Making far objects the same size as near ones. Size shrinks with distance.
- Drawing shadows in random directions. Find them with the light ray and the ground line.