View Transformation

A 3D scene can be viewed from any posistion in 3D space. A "synthetic" camera positioned and oriented in 3D space can be used to describe the viewing, and the part of the image or scene to be viewed . It has the following three principal ingredients.

1. View plane: The window is defined in this plane.
   • The origin of this plane which defines the position of the eye or camera is called the view reference point .
   • A unit vector to this plane is the view plane normal .
   • Another vector called the viewup vector is a unit vector perpendicular to .
2. View coordinate system: Usually a left handed system called the UVN system is used.
   • , the y-axis of the view coordinate system is the perpendicular projection of on the view plane.
   • , the x-axis of the view coordinates, is orthogonal to and i.e.

     

   • Positive and are to the right and up-direction from eye's point of view.
   • is the z-axis of the view coordinate. It increases in positive direction with depth of a point from the eye.
3. An eye defined within this system. and e determines a plane orthogonal to containing e.

Let be the look-at-point. For perspective views, the view plane normal as a unit vector from eye to a ``look-at point'' is given by

The view up vector is the tilt (rotation) of the head or camera.

For parallel views it is convenient to think of the view plane normal as determining the direction of projection.