A Horopter for Two- Point Perspective Christopher W. Tyler Smith-Kettlewell Institute

1. A Horopter for Two- Point Perspective Christopher W. Tyler Smith-Kettlewell Institute

2. Perspective is an exact construction of the scene viewed from a particular location

3. One-point perspective

4. 3 2 1 3 1 2 One-point perspective distortion analysis by Jules de la Gournerie (1859)

5. ‘Horned Perspective’ by Viator (Jean Pélérin) (1505)

6. Roman Fresco with Two-Point Geometry

8. Fra Angelico ‘The Martydom of St Mark’ (1433)

11. 90º The vanishing points for two-point perspective are 90° apartat the eye

12. 90º All pairs of lines through the two vanishing points have an angle of 90° in space

13. Top view of observer and painting

14. Euclidean Theorem

17. ‘Fisherman’ by Homero Aguilar (2003)

18. View from left side

19. View from right side

20. Conclusions • In general, any perspective picture gives an accurate representation only from its precise center of projection

21. Conclusions • In general, any perspective picture gives an accurate representation only from its precise center of projection • One-, two- and three-point projections limit consideration to simplified scene structure

22. Conclusions • In general, any perspective picture gives an accurate representation only from its precise center of projection • One-, two- and three-point projections limit consideration to simplified scene structure • If we restrict the issue of right angles, two-point perspectives have a semicircle of locations along which the projections of right angles is preserved

23. Conclusions • In general, any perspective picture gives an accurate representation only from its precise center of projection • One-, two- and three-point projections limit consideration to simplified scene structure • If we restrict the issue of right angles, two-point perspectives have a semicircle of locations along which the projections of right angles is preserved • This semicircle passes through the two vanishing points

24. Conclusions • In general, any perspective picture gives an accurate representation only from its precise center of projection • One-, two- and three-point projections limit consideration to simplified scene structure • If we restrict the issue of right angles, two-point perspectives have a semicircle of locations along which the projections of right angles is preserved • This semicircle passes through the two vanishing points

25. Conclusions • In general, any perspective picture gives an accurate representation only from its precise center of projection • One-, two- and three-point projections limit consideration to simplified scene structure • If we restrict the issue of right angles, two-point perspectives have a semicircle of locations along which the projections of right angles is preserved • This semicircle passes through the two vanishing points • This semicircular locus may be called a ‘horopter’ for non deviation from right-angles in two-point perspective.