Geometric Objects And Transformation (Part 2)

Transformations
• one example of a transformation is the windows to view port transformation
• to allow us to move objects to more complex locations
• OpenGL pipeline makes transformations easy
• transformation consists of (occur in 2d and 3d)
     • a rotation
     • a scaling
     • a translation
     • a shearing


• transformation allow for:

1. scene composition
2. easily create symmetrical object
3. viewing object at different angles
4. computer animation where several objects need to more relative to one another

• Transformation points ( simply takes a point and maps it to another location)

transformation point

• Affine Transformations : there are 4 types of transformations that can be combined to produce an affine transformation

1. Translation: moving point/object around in the x,y, and z direction

This means that values are being added or subtracted to the existing coordinates

      2. Scaling : This means that x, y and z coordinates are being multiplied by a scalar

Scale point; P = (6,2) to Q = (3,4)

     3. Rotation : This means that x,y,z rotated araound a point

rotation matrix

     4. Shearing : That a point is dragged in a particular direction, coordinated affected but other are not

     5. Combining Transformation : rotate scaling, translation and shearing can be combined into matrix