1. Classical Viewing – Definition

Classical viewing is a method used in 3D computer graphics to project a 3D scene onto a 2D view plane (screen) for visualization.

• The goal is to simulate the process of looking at a 3D object from a particular viewpoint.
• It involves defining a viewing coordinate system, view reference point, viewing plane, and projection method.

Key Idea:

• Transform objects from world coordinates → view coordinates → projection coordinates → screen coordinates.

2. Steps in Classical Viewing

Step 1: Define View Reference Point (VRP)

• The VRP is the position of the observer or camera in 3D space.
• Acts as the origin of the viewing coordinate system.

Step 2: Define View Plane and Viewing Direction

• View plane (or projection plane) is where the 3D scene is projected.
• Viewing direction (VD) is a vector from VRP pointing toward the scene.

Step 3: Define the View Coordinate System

• Local axes relative to the VRP:

  • u-axis → horizontal in view plane
  • v-axis → vertical in view plane
  • n-axis → viewing direction (normal to view plane)

• Transformation converts world coordinates to view coordinates.

Step 4: Clipping

• Clipping removes parts of the scene outside the view volume.

• The view volume can be:

  • Parallel (orthographic projection) → box-shaped
  • Perspective projection → pyramid-shaped

Step 5: Projection

• Converts 3D view coordinates to 2D screen coordinates.

• Two types of projections:

  1. Orthographic (parallel) projection

     • Lines remain parallel
     • No perspective distortion

  2. Perspective projection

     • Objects farther away appear smaller
     • Simulates human vision

3. Classical Viewing Transformation Matrices

1. Translation: Move VRP to the origin
2. Rotation: Align viewing axes $(u, v, n)$ with world axes
3. Scaling (optional): Normalize view volume
4. Projection: Map 3D to 2D

Combined Transformation:

4. Summary Table

Key Points:

• Classical viewing simulates camera-based viewing in 3D.
• Essential for rendering, CAD, and visualization.
• In modern graphics, it forms the basis of the view and projection matrices used in OpenGL and DirectX.