A Horopter for TwoPoint Perspective
Christopher W. Tyler
Smith-Kettlewell Institute
Perspective is an exact construction of the scene viewed from a particular location
One-point perspective
3
3
2
1
1
2
One-point perspective distortion analysis by Jules de la Gournerie (1859)
‘Horned Perspective’ by Viator (Jean Pélérin) (1505)
Roman Fresco with Two-Point Geometry
Fra Angelico ‘The Martydom of St Mark’ (1433)
90º
The vanishing
two-point
are 90° apart
points for
perspective
at the eye
90º
All pairs of lines through the two vanishing points have an angle of 90° in space
Top view of observer and painting
Euclidean Theorem
‘Fisherman’
by Homero Aguilar (2003)
View from left side
View from right side
Conclusions
• In general, any perspective picture gives an accurate
representation only from its precise center of projection
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
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
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
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
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.