Perspective Projection

Perspective Projection

Perspective projections are used to produce images which look natural.When we view scenes in everyday life far away items appear small relative to nearer items.

Basic Principles: -The techniques of projection  are generalizations of the principles used by  artists in preparing perspective drawing of 3D  objects and scenes. The eye of the artist is  placed at the center of projection, and the  canvas (view plane).

• A Perspective projection is determined by prescribing a center of projection and a view plane. The view plane is determined by its  view reference point R0 and view plane normal N.
• The object point P is located in world co-ordinates  at (x,y,z). The problem is to determine the image point co-ordinates P’(x’,y’,z’).

• Perspective Foreshortening:- “ The farther an object is from the center  of projection, the smaller it appears.”

• Example: -Square A is larger in size than square B but at vanishing point in viewing plane they appears to be of same size.

• These points are formed by the intersection of lines parallel to one of the three principal axis.
• The number of principal vanishing points is determined by the number of principal axis intersected by the view plane.
• View Confusion

• Objects behind the center of projection are projected upside down and backward on to the view plane.
• A line segment joining a point which lies in front of the viewer to a point in back of the viewer is projected to a broken line of infinite extent.
• The points of the plane that is parallel to the view plane & also passes through the Centre of projection are projected to infinity by the perspective projection.
• When we join the point which is back of the viewer to the point which is front of the viewer then the line will be projected as a broken line of infinite extent.