1. Definition

Specifying a view in 3D means defining how a 3D scene should be observed and projected onto a 2D screen.

• It involves positioning the camera (or viewpoint), orienting it, and defining the viewing volume.
• The goal is to control what part of the scene is visible and how it appears (size, perspective, orientation).

2. Components of a 3D View Specification

A. View Reference Point (VRP)

• The position of the observer or camera in world coordinates.
• Acts as the origin of the view coordinate system.

B. View Plane

• The 2D plane where the 3D scene is projected.
• Analogous to a camera film or screen.
• Defined relative to the VRP and viewing direction.

C. Viewing Direction (VPN – View Plane Normal)

• A vector pointing from the VRP toward the scene.
• Determines where the observer is looking.

D. Up Vector (VUP – View Up Vector)

• Defines which direction is “up” in the view.
• Ensures the view is not tilted or rotated incorrectly.

E. View Window

• Defines how much of the scene fits on the view plane.
• Specifies the size of the rectangle or field of view in world units.

F. View Volume

• The 3D region of space visible from the VRP.

• Determines clipping of objects outside the view.

• Types:

  1. Parallel (orthographic) view volume – rectangular box
  2. Perspective view volume – pyramid frustum

3. Transformations for 3D Viewing

To display a 3D scene on a 2D screen:

1. Translate VRP to origin:

   • Moves the camera position to (0,0,0)

2. Rotate to align axes:

   • Align the view coordinate system $(u, v, n)$ with world axes

3. Apply scaling (optional):

   • Normalize the view volume to fit the canonical view volume

4. Project:

   • Orthographic: parallel lines remain parallel
   • Perspective: lines converge to simulate depth

4. Canonical View Volume

• After translation, rotation, and scaling, the view volume is mapped to a standard cube:

• This simplifies clipping, projection, and rasterization.

5. Summary Table

Key Points:

• Specifying a view defines what the observer sees and how it is projected.
• Essential in CAD, 3D modeling, and rendering pipelines.
• Forms the basis for view and projection matrices in graphics APIs like OpenGL and DirectX.