early perspective painting and the beginnings of projective geometry

Early Perspective Painting and the Beginnings of Projective

Geometry

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

by a plane.

Devices

But isn’t the perspective construction something to do with

vanishing points??

That seems like a different idea!

The Tribute Money

Perspective in The Tribute Money

The Arnolfini Marriage

Perspective in The Arnolfini Marriage

Draw a square in perspective:

Construction lines

Horizontals

Last construction line

Why is this construction correct?

DE:BC = AE:AC = HE:GC

But BC = GC, so DE = HE

A Pavimento

…degraded square

Diagonal construction

Orthogonals

Transverals

A ‘degraded’ octagon

A hexagonal well

Heads

The Baptism of Chris

The flagellation of Christ

Perspective in the Flagellation of Christ

Paolo Uccello

A misuse of perspective?

Two pencils of lines

These are EQUIVALENT in projective geometry: one can be transformed into the other.

The Ambassadors

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