1. Early Perspective Painting and the Beginnings of Projective Geometry

2. The cone of visual rays has its vertex at the eye. A perspective painting is a section of this cone by a plane.

3. Devices

4. But isnt the perspective construction something to do with vanishing points?? That seems like a different idea!

5. The Tribute Money

6. Perspective in The Tribute Money

7. The Arnolfini Marriage

8. Perspective in The Arnolfini Marriage

9. Draw a square in perspective:

10. Construction lines

11. Horizontals

12. Last construction line

13. Why is this construction correct? DE:BC = AE:AC = HE:GC But BC = GC, so DE = HE

14. A Pavimento

15. …degraded square

16. Diagonal construction

17. Orthogonals

18. Transverals

19. A degraded octagon

20. A hexagonal well

21. Heads

22. The Baptism of Chris

23. The flagellation of Christ

24. Perspective in the Flagellation of Christ

25. Paolo Uccello

26. A misuse of perspective?

27. Two pencils of lines These are EQUIVALENT in projective geometry: one can be transformed into the other.

28. The Ambassadors

29. Art and optics A recent symposium considered the possibility that Renaissance perspective effects did not require geometrical construction after all! The suggestion is that artists used lenses and mirrors to project images, and trace them. http://www.artandoptics.com