Computer Graphics Part 3 (Transformations)

P'=T+P

x'	=	x	+	dx
y'		y		dy

P'=S.P

x'	=	sx  0	.	x
y'		0  sy		y

P'=R.P

x'	=	cos#  -sin#	.	x
y'		sin#   cos#		y

The last coordinate, called homogeneous coordinate. Used to project the scene onto the screen.

sequentially multiplying matrices to combine scaling, rotation and translation in just one step.

• e.g.
• Scale then Translate
• p' = T S p
• T S = 1 0 3 . 2 0 0   = 2 0 3
•         0 1 1   0 2 0       0 2 1
•         0 0 1   0 0 1       0 0 1

remember: AB != BA

• Vg = M    Vi
• Vi  = M^-1 Vg

where V are coordinate systems