09-07-2012, 11:12 AM
Computer Graphics 3:2D Transformations
Graphics3-2DTransformations.ppt (Size: 681.5 KB / Downloads: 94)
Why Transformations?
In graphics, once we have an object described, transformations are used to move that object, scale it and rotate it
Why Homogeneous Coordinates?
Mathematicians commonly use homogeneous coordinates as they allow scaling factors to be removed from equations
We will see in a moment that all of the transformations we discussed previously can be represented as 3*3 matrices
Using homogeneous coordinates allows us use matrix multiplication to calculate transformations – extremely efficient!
Combining Transformations
A number of transformations can be combined into one matrix to make things easy
Allowed by the fact that we use homogenous coordinates
Imagine rotating a polygon around a point other than the origin
Transform to centre point to origin
Rotate around origin
Transform back to centre point