Introduction to Perspective Projection

Perspective Projection is a geometric technique used to produce a three-dimensional graphic image on a plane, corresponding to what a person actually sees

Perspective Projection

Perspective Projection

One point Perspective

Two point Perspective

Auxiliary vanishing points

Perspective Projection

• Parallel lines appear to converge as they recede from the spectator.

• Equal distances appear to get shorter.

• Objects of the same size seem to diminish in size as they recede.

Vanishing point

Perspective Projection

The height of the horizon line always corresponds to the height of the spectator’s eye

Vanishing Point

Vanishing Point

Horizon Line

Terminology

Ground Plane: The plane on which the spectator is standing. The plan of the object to be drawn lies on it - the object itself may also rest on it

Picture Plane: The transparent plane perpendicular to the ground plane

Ground Line: The line of intersection between the picture plane and the ground plane

Spectator: The person observing the object (or objects)

30° angle

distorted

distorted

60° angle cone of vision

blind to

left eye

blind to

right eye

Cone of Vision

Cone of Vision

A 60° cone of vision gives a good perspective view of an object

The axis of the cone is called the centre line of vision

The picture plane is drawn perpendicular to the centre line of vision

Terminology

Horizon Line: The height of the horizon line above the ground line is equal to that of the spectator’s eye above the ground plane

Vanishing Point: The vanishing point for any line is found on the Picture Plane and is located by drawing a sight line from the spectator parallel to that line

The vanishing points for all horizontal lines lie on the horizon line

Terminology

The points of intersection of the sight lines with the picture plane

yield the perspective view of the object

Sight Lines: The straight lines drawn from various points on the object

to the eye of the spectator

Perspective Projection

Work sheet 1

One point perspective The centre line of vision is perpendicular to a side of the object.

This side and all lines parallel to this side will be parallel to the picture plane so they do not converge.

Perspective Projection

Work sheet 1

• Parallel lines vanish to the same vanishing point.

• Lines parallel to the picture plane in plan do not converge.

• If lines are parallel to the horizontal plane then the vanishing point is on the horizon line.

• The sides touching the picture plane are true dimensions.

Perspective Projection

Worksheet 2 Two point perspective

Perspective Projection

Work sheets 2,3• Picture plane perpendicular to centre line of

vision.

• Sets of parallel lines appear to converge to the same vanishing point.

• The vanishing points for all horizontal lines lie on the horizon line.

• The edge touching the picture plane is a true height.

Perspective Projection

• Work sheet 4

Perspective Projection

Work sheet 4,5,6

Height line• When the edge of the object is not touching the picture plane a height line

must be established on the picture plane.

Identify a surface that contains necessary heights. Extend the surface to intersect the picture plane i.e. extend the surface parallel to its vanishing parallel. The elevation of the line of intersection gives the necessary heights .

Height line

Auxiliary Vanishing points

Parallel lines vanish to the same vanishing point

The vanishing point for any line is found on the Picture Plane and is located by drawing a sight line from the spectator parallel to that line

The sight line for sloping lines intersects the PP at a height above or below the vanishing points

Perspective Projection

Work sheets 9,10

Perspective Projection

Worksheet 9

Perspective Projection

• The picture plane can be placed in front of, behind, or even through an object.• The perspective view is drawn by projecting the sight lines from the spectator

through the points of the object onto the picture plane. • If the picture plane is located behind the object the perspective view is larger

than the object.

Perspective Projection

Work sheets 11,12,13,14

• True heights can be measured where the object is intersected by the picture plane.

• The closer to the spectator the picture plane is located the smaller the drawing, the further away the larger the drawing.

• If the picture plane is located between the object and the spectator, the resulting perspective view is smaller than the object.

• If the picture plane is positioned behind the object, relative to the spectator the resulting perspective view is larger than the object.