1. Introduction to constructive graphics Basic ideas - Coordinate systems - Graphics viewing pipeline

2. “The art of 3D graphics is the art of fooling the brain into thinking that it sees a 3D object painted on a flat screen.”

3. Coordinate systems in 3D computer graphics Left and Right handed Local 3D World 3D Viewport Camera

4. 3-Dimensional coordinate systems left handedright handed Z axis goes "into" the pageZ axis goes "out" of the page

5. In this course we use left-handed coordinate system

6. Left-handed coordinate system

7. Local preferred system for construction of object parts 3D Cartesian system Object vertices centred about the local origin Y X Z

8. 3D World 3D Cartesian coordinate system arbitrary centre, handedness and orientation used in the construction stage Y X Z Y X Z Y X Z

9. 3D Viewport similar to a 3D word coordinates uses normalised 3D coordinates used if device independence is important

10. Camera coordinate system used to define the view onto the 3D world that the user will see on the screen centre (0,0,0) is located at the Imaginary User’s eye axes oriented such that –one indicates the direction in which the User looks; –the second indicates roughly the “up” direction –the third indicates the handedness

11. Y X Z U V N U V N

12. 2D Window 2D system related to screen coordinates Y X Z U V N

13. 2D Viewport similar to 2D Window system uses normalised 2D coordinates If 3D Viewport is used, the Camera will first generate 2D Viewport, which will be then converted to 2D window.

14. Graphics viewing pipeline Graphics viewing pipeline describes a sequence of graphics operations needed to display a 3D object on a graphics device.

15. 3D construction

16. Viewpoint specification Viewpoint specification 3D world coordinates Y X Z

17. Viewing volume specification Viewing volume specification 3D (normalised) Coordinates) Y X Z 01 1 1

18. Viewing projection Projection onto a viewing surface 2D (normalised) Coordinates) Y X01 1

19. Display 2D coordinates Y X 0

20. Realistic features Realism 3D / 2D coordinates