Visual Plane
every picture states the point it is correct from
Concept

three-point perspective — where it appears

The case where the picture plane is oblique to all three of a box's axes, so all three families of edges have finite vanishing points.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

horizon3 vanishing points at a finite distance2564 px · 8129 px · 531 px

One, two and three point are one construction

The names count how many vanishing points sit at a finite place in the picture, and the count is a fact about how the object is turned and the camera is aimed. Nothing about the method changes between them, and a vanishing point does not appear — it arrives from infinity.

construction · pointcount correct from 20 cm, at 160 mm wideverticals converge 3.59° · horizon 213 px off centre

The plane is a choice

A projection has a centre and a surface, and they move independently. Keep the eye and turn the picture plane and every point of any scene lands where one 3×3 matrix says, to 2.5e-13 px. Move the eye instead and the matrix fitted to four points is exact at those four and out by 32.0 px everywhere else. The first is a homography of the picture; the second is parallax, and nothing about the picture can undo it.

construction · planechoice

Named alongside it

The objects these essays reach for when they reach for this one.

HorizonPicture planeCamera tiltcentre of projectionHomographyone-point perspectiveParallaxpole and polarPrincipal pointProjective maptwo-point perspectiveVanishing point

All concepts