Overview

Perspective is the illusion of depth. It’s the math trick that makes a flat canvas look like a window into a 3D world.

Core Idea

The core idea is Convergence. Parallel lines appear to meet in the distance.

Formal Definition

  • Linear Perspective: Using vanishing points and horizon lines to create depth.
  • Atmospheric Perspective: Things further away look bluer and hazier.

Intuition

  • Railroad Tracks: You know the tracks are parallel, but they look like they touch at the horizon. That point is the Vanishing Point.
  • The Box:
    • 1-Point Perspective: Looking straight at the front of the box.
    • 2-Point Perspective: Looking at the corner of the box.
    • 3-Point Perspective: Looking down from a skyscraper (vertical lines converge too).

Examples

  • Brunelleschi: The architect who “discovered” linear perspective in the Renaissance.
  • Escher: Played with perspective to create impossible objects (stairs that go up forever).

Common Misconceptions

  • Misconception: It’s how we really see.
    • Correction: We have two eyes (binocular vision) and curved retinas. Linear perspective is a mathematical approximation of vision (like a camera).
  • Misconception: Ancient art was “bad” at perspective.
    • Correction: They often used Hierarchical Perspective (Kings are big, servants are small) because they cared about status, not realism.
  • Geometry: The math behind it.
  • Optics: How light travels in straight lines.

Applications

  • 3D Modeling: Video games use perspective projection matrices.
  • Architecture: Rendering buildings.

Criticism and Limitations

  • Distortion: Wide-angle perspective distorts shapes at the edges.

Further Reading

  • Perspective Made Easy by Ernest Norling