1. Computer Graphic Creator: Mohsen Asghari Session 4 Fall 2014

2. Agenda  Continue of 2D Transformation (Translation)  Homogenous Coordination  Steps of Create A world  Find 3D position in Image Plane

3. Translation

5. Find 3D position in Image Plane

6. Homogeneous Coordinates  Problem: Two parallel lines can intersect.  What if this point goes far away to infinity? The point at infinity would be (∞,∞), and it becomes meaningless in Euclidean (اقلیدسی) space.  Solution: Homogeneous Coordinates  To make 2D Homogeneous coordinates, we simply add an additional variable, w, into existing coordinates. Therefore, a point in Cartesian coordinates, (X, Y) becomes (x, y, w)

7. Why is it called "homogeneous"?  As mentioned before, in order to convert from Homogeneous coordinates (x, y, w) to Cartesian (دکارتی) coordinates, we simply divide x and y by w;

8. Steps of Create A world Vertex Data Model View Matrix Object Coordinates Projection Matrix Eye Coordinates Divided by W Clip Coordinates View Port Transform GL_MODELVIEW GL_PROJECTION Normalize Device Coordinates Window Coordination GL.ViewPort()

9. END OF SESSION 4 ANY QUESTION?