Perspective systems and geometric construction
Perspective questions check whether space is constructed or guessed. Even in a free observational drawing, examiners look for a consistent horizon, converging edges and correctly oriented ellipses; in explicit construction questions they look for measuring method, not just a plausible-looking box.
Frame of reference
- The horizon line equals eye level. All vanishing points lie on it.
- Station point, picture plane and a cone of vision of roughly 60°: keep the drawing inside it or the edges distort alarmingly.
- One-point: front face parallel to the picture plane. Two-point: verticals stay vertical, horizontals converge to two points. Three-point adds a vertical vanishing point for looking up or down.
Construction tools
- Measuring lines on the ground line set true widths; a 45° diagonal vanishing point transfers depths; the diagonals of a rectangle in perspective give its centre, which is how doors, windows and ellipse centres are placed.
- A circle in perspective is an ellipse whose major axis is perpendicular to the axis of rotation, with the minor axis along it. An ellipse has no corners.
- Shadows: for sunlight, a direction vanishing point on the horizon; for a lamp, a source point plus its foot on the ground.
Axonometric alternatives
- Isometric (30°/30°), cavalier/caballera (front face true shape, receding axis at 45° at half scale) and planometric. No vanishing points: parallels stay parallel and measurements remain readable.
Worked example
A cube of 5 cm edge seen from 4 m. Horizon at 1.6 m - standing eye height. Place the nearest vertical just off centre, with both vanishing points near the sheet edges, not inside the drawing. Set the true 5 cm front edge on the ground line, project to the vanishing points, then use a 45° diagonal to fix the side depth so the solid reads as a cube rather than a slab. For a cylinder on top, find the square's centre with diagonals, then draw the ellipse about it.
Traps that cost marks
- A horizon that implies a viewer who is neither standing nor seated consistently.
- Vanishing points too close together, giving a fish-eye look.
- Verticals converging in a two-point drawing.
- Ellipses drawn as pointed ovals, or with a major axis parallel to the cylinder axis.
- Shadow directions that disagree with the stated light source.