3D Viewing

3D Viewing

•     World coordinate system(where the objects are modeled and defined)

•     Viewing coordinate system(viewing objects with respect to another user defined coordinate system)

•     Projection coordinate system(coordinate positions to be on the projection plane)

•     Device Coordinate System (pixel positions in the plane of the output device)

steps to establish a Viewing coordinate system or view reference coordinate system and the view plane

Transformation from world to viewing coordinates

•     Translate the view reference point to the origin of the world coordinate system

•     Apply rotations to align the axes

– Three rotations of three axes

– Composite transformation matrix (unit vectors u, v, n)

•   n= N/|N|

• u = (V*N) / |V*N|

 • v = n * u

Projections

Our 3-D scenes are all specified in 3-D world coordinates. To display these we need to generate a 2-D image - project objects onto a picture plane

Converting From 3-D To 2-D

•     Projection is just one part of the process of transforming 3D world coordinates to a 2-D projection plane