Introduction to Perspective Projection

1. Introduction to Perspective Projection

2. 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

3. Perspective Projection One point Perspective Two point Perspective Auxiliary vanishing points

4. Vanishing point 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.

5. Vanishing Point Vanishing Point Horizon Line Perspective Projection The height of the horizon line always corresponds to the height of the spectator’s eye

6. 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)

7. Cone of Vision blind to right eye distorted 60° angle cone of vision 30° angle distorted blind to left eye

8. 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

9. 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

10. Terminology Sight Lines: The straight lines drawn from various points on the object to the eye of the spectator The points of intersection of the sight lines with the picture plane yield the perspective view of the object

11. 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.

12. 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.

13. Perspective Projection Two point perspective Worksheet 2

14. PerspectiveProjection 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.

15. Perspective Projection • Work sheet 4

16. Height line 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 .

17. 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

18. Perspective Projection Work sheets 9,10

19. Perspective Projection Worksheet 9

20. 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.

21. 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.