Projection

Definition ,[object Object],P(x,y,z) P’(x’,y’,z’) Projector projection plane

Perspective Projection ,[object Object],[object Object]

Mathematical Description ,[object Object]

View Plane Center of projection View Plane P 1 (x,y,z) P 2 P’ 1 (x’,y’,z’) Z Y X C N View Plane Normal

Perspective Characteristics/Anomalies ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],A B Vanishing point Viewing plane Y

2. Vanishing Points ,[object Object]

3. View Confusion ,[object Object],center of projection P 1 P 3 P 2 P 2 ’ P 1 ’ P 3 ’ X Y Z X O

4. Topological Distortion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],X Y Viewing Plane A’ at infinity A C B INFINITY B’ C’ A’ Centre of projection

Types of Vanishing Points ,[object Object],[object Object],[object Object]

One Principal Vanishing Point Perspective Projection ,[object Object],[object Object],P 3 X 3 =a 1 Y 3 =b 1 Z 3 =c 1 + d 1 n 3 : Therefore, V=V 1 I+V 2 J+V 3 K X=V 1 t+l Y=V 2 t+m Z=V 3 t +n P(l,m,n) K=N.V=n 1 v 1 +n 2 v 2 +n 3 v 3 Where a 1 ,b 1 ,c 1 are coordinates of the centre of projection n 1 ,n 2 ,n 3 are components of view plane normal vector d 1 is proportional to distance D from the view plane to the Centre of Projection

Two Principal Vanishing Point Perspective Projection ,[object Object],Horizon Line VP 1 VP 2

Continue……….. ,[object Object],[object Object],[object Object],[object Object],X 1 =a 1 + d 1 n 1 Y 1 =b 1 Z 1 =c 1 P 1 : X 2 =a 1 Y 2 =b 1 + d 1 n 2 Z 2 =c 1 P 2 :

Three Principal Vanishing Point Perspective Projection ,[object Object],P 1 P 3 P 2 X 1 =a 1 + d 1 n 1 Y 1 =b 1 Z 1 =c 1 P 1 X 2 =a 1 Y 2 =b 1 + d 1 n 2 Z 2 =c 1 P 2 X 3 =a 1 Y 3 =b 1 Z 3 =c 1 + d 1 n 3 P 3

Parallel Projection ,[object Object],[object Object]

Continue………. ,[object Object],P(x,y,z) P 2 P’(x’,y’,z’) P 2 ’ X Z Y Direction of V Projection View Plane N

Types of Parallel Projection ,[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Categories/ Types of Orthographic Projections ,[object Object],[object Object],[object Object]

Continue………… ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Continue……………. ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

SUB-CATEGORIES OF AXONOMETRIC PROJECTIONS ARE : - ,[object Object],[object Object],[object Object],[object Object]

Cabinet Projection y x C’ H’ E’ D’ G’ A’ B’

Projection

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Projection