CS321 Dr' Mark L' Hornick

1
2-D Transformations
Local/Modelling Coordinates
y

• Object descriptions
• Often defined in model coordinates
• Must be mapped to world coordinates
• Groups of objects are combined complete image is
  formed by combining primitives

x
World Coordinates
2
2-D Transformations
Local/Modelling Coordinates
y

• Problem statement
• Convert points from coordinates in one system to
  a second coordinate system

x
World Coordinates
3
Combining Rotation and Translation

• T(?,p) can be expressed in terms of submatrices
  as
• The inverse of T(?,p) is given by

y2
x1
v1
v2
?
x2
p
y1
4
Scaling
Scaling affects every coordinate in the shape
e.g. doubling each value when the scale factor2
Sx and Sy usually have the same values this Is
called Uniform Scaling
Before scaling
After scaling by 2
5
Combining Rotation, Translation and Scaling to
convert from coordinates in x2y2 to x1y1
6
Inverse transformation converting from
coordinates in x1y1 to x2y2
Typically, you just take the inverse of TS,
rather than inverting each component matrix. Here
were just showing what the inverses of the
component matrices are.