Discuss the Taxonomy of Projection in computer graphics, with suitable diagram. Compare and contrast Parallel & Perspective projection, in detail (i.e. with suitable examples, equations, expressions etc.). What is isometric projection? What do you understand by the term vanishing point in context of projections, in computer graphics. Obtain a Projection matrix for perspective projection of a point P(x,y,z) onto z= 5 plane, provided the center of projection is at (0,0,-10), can we find the vanishing point(s) for this projection? Justify

Taxonomy of Projection in Computer Graphics

In computer graphics, projection is the process of transforming a 3D scene into a 2D representation. This is essential for displaying three-dimensional objects on a two-dimensional screen. There are two main types of projections: Parallel Projection and Perspective Projection.

1. Parallel Projection:

In parallel projection, parallel lines in the 3D scene remain parallel in the 2D projection. This type of projection is often used in engineering and architectural drawings, where accurate scaling of objects is crucial. Parallel projection can be further classified into Orthographic and Oblique projections.

   - Orthographic Projection: In orthographic projection, the projection rays are parallel to each other and perpendicular to the projection plane. This results in an image where all lines appear parallel in the projection, and there is no foreshortening.

   - Oblique Projection: Oblique projection is a variation of parallel projection where the projection rays are not necessarily perpendicular to the projection plane, introducing some foreshortening. Common oblique projections include Cavalier and Cabinet projections.

2. Perspective Projection:

In perspective projection, objects appear smaller as they move farther away from the viewer, creating a more realistic representation of depth. Perspective projection is commonly used in computer graphics to simulate how the human eye perceives the world.

   - Mathematical Representation of Perspective Projection:

     Perspective projection involves the use of a projection matrix to transform 3D coordinates into 2D coordinates. The general perspective projection matrix is given by:

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